forked from adnanaziz/EPIJudge
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathenumerate_balanced_parentheses.tsv
We can't make this file beautiful and searchable because it's too large.
12 lines (12 loc) · 537 KB
/
enumerate_balanced_parentheses.tsv
1
2
3
4
5
6
7
8
9
10
11
12
int array(string)
0 [""] TODO
1 ["()"] TODO
2 ["(())", "()()"] TODO
3 ["((()))", "(()())", "(())()", "()(())", "()()()"] TODO
4 ["(((())))", "((()()))", "((())())", "((()))()", "(()(()))", "(()()())", "(()())()", "(())(())", "(())()()", "()((()))", "()(()())", "()(())()", "()()(())", "()()()()"] TODO
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
6 ["(((((())))))", "((((()()))))", "((((())())))", "((((()))()))", "((((())))())", "((((()))))()", "(((()(()))))", "(((()()())))", "(((()())()))", "(((()()))())", "(((()())))()", "(((())(())))", "(((())()()))", "(((())())())", "(((())()))()", "(((()))(()))", "(((()))()())", "(((()))())()", "(((())))(())", "(((())))()()", "((()((()))))", "((()(()())))", "((()(())()))", "((()(()))())", "((()(())))()", "((()()(())))", "((()()()()))", "((()()())())", "((()()()))()", "((()())(()))", "((()())()())", "((()())())()", "((()()))(())", "((()()))()()", "((())((())))", "((())(()()))", "((())(())())", "((())(()))()", "((())()(()))", "((())()()())", "((())()())()", "((())())(())", "((())())()()", "((()))((()))", "((()))(()())", "((()))(())()", "((()))()(())", "((()))()()()", "(()(((()))))", "(()((()())))", "(()((())()))", "(()((()))())", "(()((())))()", "(()(()(())))", "(()(()()()))", "(()(()())())", "(()(()()))()", "(()(())(()))", "(()(())()())", "(()(())())()", "(()(()))(())", "(()(()))()()", "(()()((())))", "(()()(()()))", "(()()(())())", "(()()(()))()", "(()()()(()))", "(()()()()())", "(()()()())()", "(()()())(())", "(()()())()()", "(()())((()))", "(()())(()())", "(()())(())()", "(()())()(())", "(()())()()()", "(())(((())))", "(())((()()))", "(())((())())", "(())((()))()", "(())(()(()))", "(())(()()())", "(())(()())()", "(())(())(())", "(())(())()()", "(())()((()))", "(())()(()())", "(())()(())()", "(())()()(())", "(())()()()()", "()((((()))))", "()(((()())))", "()(((())()))", "()(((()))())", "()(((())))()", "()((()(())))", "()((()()()))", "()((()())())", "()((()()))()", "()((())(()))", "()((())()())", "()((())())()", "()((()))(())", "()((()))()()", "()(()((())))", "()(()(()()))", "()(()(())())", "()(()(()))()", "()(()()(()))", "()(()()()())", "()(()()())()", "()(()())(())", "()(()())()()", "()(())((()))", "()(())(()())", "()(())(())()", "()(())()(())", "()(())()()()", "()()(((())))", "()()((()()))", "()()((())())", "()()((()))()", "()()(()(()))", "()()(()()())", "()()(()())()", "()()(())(())", "()()(())()()", "()()()((()))", "()()()(()())", "()()()(())()", "()()()()(())", "()()()()()()"] TODO
7 ["((((((()))))))", "(((((()())))))", "(((((())()))))", "(((((()))())))", "(((((())))()))", "(((((()))))())", "(((((())))))()", "((((()(())))))", "((((()()()))))", "((((()())())))", "((((()()))()))", "((((()())))())", "((((()()))))()", "((((())(()))))", "((((())()())))", "((((())())()))", "((((())()))())", "((((())())))()", "((((()))(())))", "((((()))()()))", "((((()))())())", "((((()))()))()", "((((())))(()))", "((((())))()())", "((((())))())()", "((((()))))(())", "((((()))))()()", "(((()((())))))", "(((()(()()))))", "(((()(())())))", "(((()(()))()))", "(((()(())))())", "(((()(()))))()", "(((()()(()))))", "(((()()()())))", "(((()()())()))", "(((()()()))())", "(((()()())))()", "(((()())(())))", "(((()())()()))", "(((()())())())", "(((()())()))()", "(((()()))(()))", "(((()()))()())", "(((()()))())()", "(((()())))(())", "(((()())))()()", "(((())((()))))", "(((())(()())))", "(((())(())()))", "(((())(()))())", "(((())(())))()", "(((())()(())))", "(((())()()()))", "(((())()())())", "(((())()()))()", "(((())())(()))", "(((())())()())", "(((())())())()", "(((())()))(())", "(((())()))()()", "(((()))((())))", "(((()))(()()))", "(((()))(())())", "(((()))(()))()", "(((()))()(()))", "(((()))()()())", "(((()))()())()", "(((()))())(())", "(((()))())()()", "(((())))((()))", "(((())))(()())", "(((())))(())()", "(((())))()(())", "(((())))()()()", "((()(((())))))", "((()((()()))))", "((()((())())))", "((()((()))()))", "((()((())))())", "((()((()))))()", "((()(()(()))))", "((()(()()())))", "((()(()())()))", "((()(()()))())", "((()(()())))()", "((()(())(())))", "((()(())()()))", "((()(())())())", "((()(())()))()", "((()(()))(()))", "((()(()))()())", "((()(()))())()", "((()(())))(())", "((()(())))()()", "((()()((()))))", "((()()(()())))", "((()()(())()))", "((()()(()))())", "((()()(())))()", "((()()()(())))", "((()()()()()))", "((()()()())())", "((()()()()))()", "((()()())(()))", "((()()())()())", "((()()())())()", "((()()()))(())", "((()()()))()()", "((()())((())))", "((()())(()()))", "((()())(())())", "((()())(()))()", "((()())()(()))", "((()())()()())", "((()())()())()", "((()())())(())", "((()())())()()", "((()()))((()))", "((()()))(()())", "((()()))(())()", "((()()))()(())", "((()()))()()()", "((())(((()))))", "((())((()())))", "((())((())()))", "((())((()))())", "((())((())))()", "((())(()(())))", "((())(()()()))", "((())(()())())", "((())(()()))()", "((())(())(()))", "((())(())()())", "((())(())())()", "((())(()))(())", "((())(()))()()", "((())()((())))", "((())()(()()))", "((())()(())())", "((())()(()))()", "((())()()(()))", "((())()()()())", "((())()()())()", "((())()())(())", "((())()())()()", "((())())((()))", "((())())(()())", "((())())(())()", "((())())()(())", "((())())()()()", "((()))(((())))", "((()))((()()))", "((()))((())())", "((()))((()))()", "((()))(()(()))", "((()))(()()())", "((()))(()())()", "((()))(())(())", "((()))(())()()", "((()))()((()))", "((()))()(()())", "((()))()(())()", "((()))()()(())", "((()))()()()()", "(()((((())))))", "(()(((()()))))", "(()(((())())))", "(()(((()))()))", "(()(((())))())", "(()(((()))))()", "(()((()(()))))", "(()((()()())))", "(()((()())()))", "(()((()()))())", "(()((()())))()", "(()((())(())))", "(()((())()()))", "(()((())())())", "(()((())()))()", "(()((()))(()))", "(()((()))()())", "(()((()))())()", "(()((())))(())", "(()((())))()()", "(()(()((()))))", "(()(()(()())))", "(()(()(())()))", "(()(()(()))())", "(()(()(())))()", "(()(()()(())))", "(()(()()()()))", "(()(()()())())", "(()(()()()))()", "(()(()())(()))", "(()(()())()())", "(()(()())())()", "(()(()()))(())", "(()(()()))()()", "(()(())((())))", "(()(())(()()))", "(()(())(())())", "(()(())(()))()", "(()(())()(()))", "(()(())()()())", "(()(())()())()", "(()(())())(())", "(()(())())()()", "(()(()))((()))", "(()(()))(()())", "(()(()))(())()", "(()(()))()(())", "(()(()))()()()", "(()()(((()))))", "(()()((()())))", "(()()((())()))", "(()()((()))())", "(()()((())))()", "(()()(()(())))", "(()()(()()()))", "(()()(()())())", "(()()(()()))()", "(()()(())(()))", "(()()(())()())", "(()()(())())()", "(()()(()))(())", "(()()(()))()()", "(()()()((())))", "(()()()(()()))", "(()()()(())())", "(()()()(()))()", "(()()()()(()))", "(()()()()()())", "(()()()()())()", "(()()()())(())", "(()()()())()()", "(()()())((()))", "(()()())(()())", "(()()())(())()", "(()()())()(())", "(()()())()()()", "(()())(((())))", "(()())((()()))", "(()())((())())", "(()())((()))()", "(()())(()(()))", "(()())(()()())", "(()())(()())()", "(()())(())(())", "(()())(())()()", "(()())()((()))", "(()())()(()())", "(()())()(())()", "(()())()()(())", "(()())()()()()", "(())((((()))))", "(())(((()())))", "(())(((())()))", "(())(((()))())", "(())(((())))()", "(())((()(())))", "(())((()()()))", "(())((()())())", "(())((()()))()", "(())((())(()))", "(())((())()())", "(())((())())()", "(())((()))(())", "(())((()))()()", "(())(()((())))", "(())(()(()()))", "(())(()(())())", "(())(()(()))()", "(())(()()(()))", "(())(()()()())", "(())(()()())()", "(())(()())(())", "(())(()())()()", "(())(())((()))", "(())(())(()())", "(())(())(())()", "(())(())()(())", "(())(())()()()", "(())()(((())))", "(())()((()()))", "(())()((())())", "(())()((()))()", "(())()(()(()))", "(())()(()()())", "(())()(()())()", "(())()(())(())", "(())()(())()()", "(())()()((()))", "(())()()(()())", "(())()()(())()", "(())()()()(())", "(())()()()()()", "()(((((())))))", "()((((()()))))", "()((((())())))", "()((((()))()))", "()((((())))())", "()((((()))))()", "()(((()(()))))", "()(((()()())))", "()(((()())()))", "()(((()()))())", "()(((()())))()", "()(((())(())))", "()(((())()()))", "()(((())())())", "()(((())()))()", "()(((()))(()))", "()(((()))()())", "()(((()))())()", "()(((())))(())", "()(((())))()()", "()((()((()))))", "()((()(()())))", "()((()(())()))", "()((()(()))())", "()((()(())))()", "()((()()(())))", "()((()()()()))", "()((()()())())", "()((()()()))()", "()((()())(()))", "()((()())()())", "()((()())())()", "()((()()))(())", "()((()()))()()", "()((())((())))", "()((())(()()))", "()((())(())())", "()((())(()))()", "()((())()(()))", "()((())()()())", "()((())()())()", "()((())())(())", "()((())())()()", "()((()))((()))", "()((()))(()())", "()((()))(())()", "()((()))()(())", "()((()))()()()", "()(()(((()))))", "()(()((()())))", "()(()((())()))", "()(()((()))())", "()(()((())))()", "()(()(()(())))", "()(()(()()()))", "()(()(()())())", "()(()(()()))()", "()(()(())(()))", "()(()(())()())", "()(()(())())()", "()(()(()))(())", "()(()(()))()()", "()(()()((())))", "()(()()(()()))", "()(()()(())())", "()(()()(()))()", "()(()()()(()))", "()(()()()()())", "()(()()()())()", "()(()()())(())", "()(()()())()()", "()(()())((()))", "()(()())(()())", "()(()())(())()", "()(()())()(())", "()(()())()()()", "()(())(((())))", "()(())((()()))", "()(())((())())", "()(())((()))()", "()(())(()(()))", "()(())(()()())", "()(())(()())()", "()(())(())(())", "()(())(())()()", "()(())()((()))", "()(())()(()())", "()(())()(())()", "()(())()()(())", "()(())()()()()", "()()((((()))))", "()()(((()())))", "()()(((())()))", "()()(((()))())", "()()(((())))()", "()()((()(())))", "()()((()()()))", "()()((()())())", "()()((()()))()", "()()((())(()))", "()()((())()())", "()()((())())()", "()()((()))(())", "()()((()))()()", "()()(()((())))", "()()(()(()()))", "()()(()(())())", "()()(()(()))()", "()()(()()(()))", "()()(()()()())", "()()(()()())()", "()()(()())(())", "()()(()())()()", "()()(())((()))", "()()(())(()())", "()()(())(())()", "()()(())()(())", "()()(())()()()", "()()()(((())))", "()()()((()()))", "()()()((())())", "()()()((()))()", "()()()(()(()))", "()()()(()()())", "()()()(()())()", "()()()(())(())", "()()()(())()()", "()()()()((()))", "()()()()(()())", "()()()()(())()", "()()()()()(())", "()()()()()()()"] TODO
8 ["(((((((())))))))", "((((((()()))))))", "((((((())())))))", "((((((()))()))))", "((((((())))())))", "((((((()))))()))", "((((((())))))())", "((((((()))))))()", "(((((()(()))))))", "(((((()()())))))", "(((((()())()))))", "(((((()()))())))", "(((((()())))()))", "(((((()()))))())", "(((((()())))))()", "(((((())(())))))", "(((((())()()))))", "(((((())())())))", "(((((())()))()))", "(((((())())))())", "(((((())()))))()", "(((((()))(()))))", "(((((()))()())))", "(((((()))())()))", "(((((()))()))())", "(((((()))())))()", "(((((())))(())))", "(((((())))()()))", "(((((())))())())", "(((((())))()))()", "(((((()))))(()))", "(((((()))))()())", "(((((()))))())()", "(((((())))))(())", "(((((())))))()()", "((((()((()))))))", "((((()(()())))))", "((((()(())()))))", "((((()(()))())))", "((((()(())))()))", "((((()(()))))())", "((((()(())))))()", "((((()()(())))))", "((((()()()()))))", "((((()()())())))", "((((()()()))()))", "((((()()())))())", "((((()()()))))()", "((((()())(()))))", "((((()())()())))", "((((()())())()))", "((((()())()))())", "((((()())())))()", "((((()()))(())))", "((((()()))()()))", "((((()()))())())", "((((()()))()))()", "((((()())))(()))", "((((()())))()())", "((((()())))())()", "((((()()))))(())", "((((()()))))()()", "((((())((())))))", "((((())(()()))))", "((((())(())())))", "((((())(()))()))", "((((())(())))())", "((((())(()))))()", "((((())()(()))))", "((((())()()())))", "((((())()())()))", "((((())()()))())", "((((())()())))()", "((((())())(())))", "((((())())()()))", "((((())())())())", "((((())())()))()", "((((())()))(()))", "((((())()))()())", "((((())()))())()", "((((())())))(())", "((((())())))()()", "((((()))((()))))", "((((()))(()())))", "((((()))(())()))", "((((()))(()))())", "((((()))(())))()", "((((()))()(())))", "((((()))()()()))", "((((()))()())())", "((((()))()()))()", "((((()))())(()))", "((((()))())()())", "((((()))())())()", "((((()))()))(())", "((((()))()))()()", "((((())))((())))", "((((())))(()()))", "((((())))(())())", "((((())))(()))()", "((((())))()(()))", "((((())))()()())", "((((())))()())()", "((((())))())(())", "((((())))())()()", "((((()))))((()))", "((((()))))(()())", "((((()))))(())()", "((((()))))()(())", "((((()))))()()()", "(((()(((()))))))", "(((()((()())))))", "(((()((())()))))", "(((()((()))())))", "(((()((())))()))", "(((()((()))))())", "(((()((())))))()", "(((()(()(())))))", "(((()(()()()))))", "(((()(()())())))", "(((()(()()))()))", "(((()(()())))())", "(((()(()()))))()", "(((()(())(()))))", "(((()(())()())))", "(((()(())())()))", "(((()(())()))())", "(((()(())())))()", "(((()(()))(())))", "(((()(()))()()))", "(((()(()))())())", "(((()(()))()))()", "(((()(())))(()))", "(((()(())))()())", "(((()(())))())()", "(((()(()))))(())", "(((()(()))))()()", "(((()()((())))))", "(((()()(()()))))", "(((()()(())())))", "(((()()(()))()))", "(((()()(())))())", "(((()()(()))))()", "(((()()()(()))))", "(((()()()()())))", "(((()()()())()))", "(((()()()()))())", "(((()()()())))()", "(((()()())(())))", "(((()()())()()))", "(((()()())())())", "(((()()())()))()", "(((()()()))(()))", "(((()()()))()())", "(((()()()))())()", "(((()()())))(())", "(((()()())))()()", "(((()())((()))))", "(((()())(()())))", "(((()())(())()))", "(((()())(()))())", "(((()())(())))()", "(((()())()(())))", "(((()())()()()))", "(((()())()())())", "(((()())()()))()", "(((()())())(()))", "(((()())())()())", "(((()())())())()", "(((()())()))(())", "(((()())()))()()", "(((()()))((())))", "(((()()))(()()))", "(((()()))(())())", "(((()()))(()))()", "(((()()))()(()))", "(((()()))()()())", "(((()()))()())()", "(((()()))())(())", "(((()()))())()()", "(((()())))((()))", "(((()())))(()())", "(((()())))(())()", "(((()())))()(())", "(((()())))()()()", "(((())(((())))))", "(((())((()()))))", "(((())((())())))", "(((())((()))()))", "(((())((())))())", "(((())((()))))()", "(((())(()(()))))", "(((())(()()())))", "(((())(()())()))", "(((())(()()))())", "(((())(()())))()", "(((())(())(())))", "(((())(())()()))", "(((())(())())())", "(((())(())()))()", "(((())(()))(()))", "(((())(()))()())", "(((())(()))())()", "(((())(())))(())", "(((())(())))()()", "(((())()((()))))", "(((())()(()())))", "(((())()(())()))", "(((())()(()))())", "(((())()(())))()", "(((())()()(())))", "(((())()()()()))", "(((())()()())())", "(((())()()()))()", "(((())()())(()))", "(((())()())()())", "(((())()())())()", "(((())()()))(())", "(((())()()))()()", "(((())())((())))", "(((())())(()()))", "(((())())(())())", "(((())())(()))()", "(((())())()(()))", "(((())())()()())", "(((())())()())()", "(((())())())(())", "(((())())())()()", "(((())()))((()))", "(((())()))(()())", "(((())()))(())()", "(((())()))()(())", "(((())()))()()()", "(((()))(((()))))", "(((()))((()())))", "(((()))((())()))", "(((()))((()))())", "(((()))((())))()", "(((()))(()(())))", "(((()))(()()()))", "(((()))(()())())", "(((()))(()()))()", "(((()))(())(()))", "(((()))(())()())", "(((()))(())())()", "(((()))(()))(())", "(((()))(()))()()", "(((()))()((())))", "(((()))()(()()))", "(((()))()(())())", "(((()))()(()))()", "(((()))()()(()))", "(((()))()()()())", "(((()))()()())()", "(((()))()())(())", "(((()))()())()()", "(((()))())((()))", "(((()))())(()())", "(((()))())(())()", "(((()))())()(())", "(((()))())()()()", "(((())))(((())))", "(((())))((()()))", "(((())))((())())", "(((())))((()))()", "(((())))(()(()))", "(((())))(()()())", "(((())))(()())()", "(((())))(())(())", "(((())))(())()()", "(((())))()((()))", "(((())))()(()())", "(((())))()(())()", "(((())))()()(())", "(((())))()()()()", "((()((((()))))))", "((()(((()())))))", "((()(((())()))))", "((()(((()))())))", "((()(((())))()))", "((()(((()))))())", "((()(((())))))()", "((()((()(())))))", "((()((()()()))))", "((()((()())())))", "((()((()()))()))", "((()((()())))())", "((()((()()))))()", "((()((())(()))))", "((()((())()())))", "((()((())())()))", "((()((())()))())", "((()((())())))()", "((()((()))(())))", "((()((()))()()))", "((()((()))())())", "((()((()))()))()", "((()((())))(()))", "((()((())))()())", "((()((())))())()", "((()((()))))(())", "((()((()))))()()", "((()(()((())))))", "((()(()(()()))))", "((()(()(())())))", "((()(()(()))()))", "((()(()(())))())", "((()(()(()))))()", "((()(()()(()))))", "((()(()()()())))", "((()(()()())()))", "((()(()()()))())", "((()(()()())))()", "((()(()())(())))", "((()(()())()()))", "((()(()())())())", "((()(()())()))()", "((()(()()))(()))", "((()(()()))()())", "((()(()()))())()", "((()(()())))(())", "((()(()())))()()", "((()(())((()))))", "((()(())(()())))", "((()(())(())()))", "((()(())(()))())", "((()(())(())))()", "((()(())()(())))", "((()(())()()()))", "((()(())()())())", "((()(())()()))()", "((()(())())(()))", "((()(())())()())", "((()(())())())()", "((()(())()))(())", "((()(())()))()()", "((()(()))((())))", "((()(()))(()()))", "((()(()))(())())", "((()(()))(()))()", "((()(()))()(()))", "((()(()))()()())", "((()(()))()())()", "((()(()))())(())", "((()(()))())()()", "((()(())))((()))", "((()(())))(()())", "((()(())))(())()", "((()(())))()(())", "((()(())))()()()", "((()()(((())))))", "((()()((()()))))", "((()()((())())))", "((()()((()))()))", "((()()((())))())", "((()()((()))))()", "((()()(()(()))))", "((()()(()()())))", "((()()(()())()))", "((()()(()()))())", "((()()(()())))()", "((()()(())(())))", "((()()(())()()))", "((()()(())())())", "((()()(())()))()", "((()()(()))(()))", "((()()(()))()())", "((()()(()))())()", "((()()(())))(())", "((()()(())))()()", "((()()()((()))))", "((()()()(()())))", "((()()()(())()))", "((()()()(()))())", "((()()()(())))()", "((()()()()(())))", "((()()()()()()))", "((()()()()())())", "((()()()()()))()", "((()()()())(()))", "((()()()())()())", "((()()()())())()", "((()()()()))(())", "((()()()()))()()", "((()()())((())))", "((()()())(()()))", "((()()())(())())", "((()()())(()))()", "((()()())()(()))", "((()()())()()())", "((()()())()())()", "((()()())())(())", "((()()())())()()", "((()()()))((()))", "((()()()))(()())", "((()()()))(())()", "((()()()))()(())", "((()()()))()()()", "((()())(((()))))", "((()())((()())))", "((()())((())()))", "((()())((()))())", "((()())((())))()", "((()())(()(())))", "((()())(()()()))", "((()())(()())())", "((()())(()()))()", "((()())(())(()))", "((()())(())()())", "((()())(())())()", "((()())(()))(())", "((()())(()))()()", "((()())()((())))", "((()())()(()()))", "((()())()(())())", "((()())()(()))()", "((()())()()(()))", "((()())()()()())", "((()())()()())()", "((()())()())(())", "((()())()())()()", "((()())())((()))", "((()())())(()())", "((()())())(())()", "((()())())()(())", "((()())())()()()", "((()()))(((())))", "((()()))((()()))", "((()()))((())())", "((()()))((()))()", "((()()))(()(()))", "((()()))(()()())", "((()()))(()())()", "((()()))(())(())", "((()()))(())()()", "((()()))()((()))", "((()()))()(()())", "((()()))()(())()", "((()()))()()(())", "((()()))()()()()", "((())((((())))))", "((())(((()()))))", "((())(((())())))", "((())(((()))()))", "((())(((())))())", "((())(((()))))()", "((())((()(()))))", "((())((()()())))", "((())((()())()))", "((())((()()))())", "((())((()())))()", "((())((())(())))", "((())((())()()))", "((())((())())())", "((())((())()))()", "((())((()))(()))", "((())((()))()())", "((())((()))())()", "((())((())))(())", "((())((())))()()", "((())(()((()))))", "((())(()(()())))", "((())(()(())()))", "((())(()(()))())", "((())(()(())))()", "((())(()()(())))", "((())(()()()()))", "((())(()()())())", "((())(()()()))()", "((())(()())(()))", "((())(()())()())", "((())(()())())()", "((())(()()))(())", "((())(()()))()()", "((())(())((())))", "((())(())(()()))", "((())(())(())())", "((())(())(()))()", "((())(())()(()))", "((())(())()()())", "((())(())()())()", "((())(())())(())", "((())(())())()()", "((())(()))((()))", "((())(()))(()())", "((())(()))(())()", "((())(()))()(())", "((())(()))()()()", "((())()(((()))))", "((())()((()())))", "((())()((())()))", "((())()((()))())", "((())()((())))()", "((())()(()(())))", "((())()(()()()))", "((())()(()())())", "((())()(()()))()", "((())()(())(()))", "((())()(())()())", "((())()(())())()", "((())()(()))(())", "((())()(()))()()", "((())()()((())))", "((())()()(()()))", "((())()()(())())", "((())()()(()))()", "((())()()()(()))", "((())()()()()())", "((())()()()())()", "((())()()())(())", "((())()()())()()", "((())()())((()))", "((())()())(()())", "((())()())(())()", "((())()())()(())", "((())()())()()()", "((())())(((())))", "((())())((()()))", "((())())((())())", "((())())((()))()", "((())())(()(()))", "((())())(()()())", "((())())(()())()", "((())())(())(())", "((())())(())()()", "((())())()((()))", "((())())()(()())", "((())())()(())()", "((())())()()(())", "((())())()()()()", "((()))((((()))))", "((()))(((()())))", "((()))(((())()))", "((()))(((()))())", "((()))(((())))()", "((()))((()(())))", "((()))((()()()))", "((()))((()())())", "((()))((()()))()", "((()))((())(()))", "((()))((())()())", "((()))((())())()", "((()))((()))(())", "((()))((()))()()", "((()))(()((())))", "((()))(()(()()))", "((()))(()(())())", "((()))(()(()))()", "((()))(()()(()))", "((()))(()()()())", "((()))(()()())()", "((()))(()())(())", "((()))(()())()()", "((()))(())((()))", "((()))(())(()())", "((()))(())(())()", "((()))(())()(())", "((()))(())()()()", "((()))()(((())))", "((()))()((()()))", "((()))()((())())", "((()))()((()))()", "((()))()(()(()))", "((()))()(()()())", "((()))()(()())()", "((()))()(())(())", "((()))()(())()()", "((()))()()((()))", "((()))()()(()())", "((()))()()(())()", "((()))()()()(())", "((()))()()()()()", "(()(((((()))))))", "(()((((()())))))", "(()((((())()))))", "(()((((()))())))", "(()((((())))()))", "(()((((()))))())", "(()((((())))))()", "(()(((()(())))))", "(()(((()()()))))", "(()(((()())())))", "(()(((()()))()))", "(()(((()())))())", "(()(((()()))))()", "(()(((())(()))))", "(()(((())()())))", "(()(((())())()))", "(()(((())()))())", "(()(((())())))()", "(()(((()))(())))", "(()(((()))()()))", "(()(((()))())())", "(()(((()))()))()", "(()(((())))(()))", "(()(((())))()())", "(()(((())))())()", "(()(((()))))(())", "(()(((()))))()()", "(()((()((())))))", "(()((()(()()))))", "(()((()(())())))", "(()((()(()))()))", "(()((()(())))())", "(()((()(()))))()", "(()((()()(()))))", "(()((()()()())))", "(()((()()())()))", "(()((()()()))())", "(()((()()())))()", "(()((()())(())))", "(()((()())()()))", "(()((()())())())", "(()((()())()))()", "(()((()()))(()))", "(()((()()))()())", "(()((()()))())()", "(()((()())))(())", "(()((()())))()()", "(()((())((()))))", "(()((())(()())))", "(()((())(())()))", "(()((())(()))())", "(()((())(())))()", "(()((())()(())))", "(()((())()()()))", "(()((())()())())", "(()((())()()))()", "(()((())())(()))", "(()((())())()())", "(()((())())())()", "(()((())()))(())", "(()((())()))()()", "(()((()))((())))", "(()((()))(()()))", "(()((()))(())())", "(()((()))(()))()", "(()((()))()(()))", "(()((()))()()())", "(()((()))()())()", "(()((()))())(())", "(()((()))())()()", "(()((())))((()))", "(()((())))(()())", "(()((())))(())()", "(()((())))()(())", "(()((())))()()()", "(()(()(((())))))", "(()(()((()()))))", "(()(()((())())))", "(()(()((()))()))", "(()(()((())))())", "(()(()((()))))()", "(()(()(()(()))))", "(()(()(()()())))", "(()(()(()())()))", "(()(()(()()))())", "(()(()(()())))()", "(()(()(())(())))", "(()(()(())()()))", "(()(()(())())())", "(()(()(())()))()", "(()(()(()))(()))", "(()(()(()))()())", "(()(()(()))())()", "(()(()(())))(())", "(()(()(())))()()", "(()(()()((()))))", "(()(()()(()())))", "(()(()()(())()))", "(()(()()(()))())", "(()(()()(())))()", "(()(()()()(())))", "(()(()()()()()))", "(()(()()()())())", "(()(()()()()))()", "(()(()()())(()))", "(()(()()())()())", "(()(()()())())()", "(()(()()()))(())", "(()(()()()))()()", "(()(()())((())))", "(()(()())(()()))", "(()(()())(())())", "(()(()())(()))()", "(()(()())()(()))", "(()(()())()()())", "(()(()())()())()", "(()(()())())(())", "(()(()())())()()", "(()(()()))((()))", "(()(()()))(()())", "(()(()()))(())()", "(()(()()))()(())", "(()(()()))()()()", "(()(())(((()))))", "(()(())((()())))", "(()(())((())()))", "(()(())((()))())", "(()(())((())))()", "(()(())(()(())))", "(()(())(()()()))", "(()(())(()())())", "(()(())(()()))()", "(()(())(())(()))", "(()(())(())()())", "(()(())(())())()", "(()(())(()))(())", "(()(())(()))()()", "(()(())()((())))", "(()(())()(()()))", "(()(())()(())())", "(()(())()(()))()", "(()(())()()(()))", "(()(())()()()())", "(()(())()()())()", "(()(())()())(())", "(()(())()())()()", "(()(())())((()))", "(()(())())(()())", "(()(())())(())()", "(()(())())()(())", "(()(())())()()()", "(()(()))(((())))", "(()(()))((()()))", "(()(()))((())())", "(()(()))((()))()", "(()(()))(()(()))", "(()(()))(()()())", "(()(()))(()())()", "(()(()))(())(())", "(()(()))(())()()", "(()(()))()((()))", "(()(()))()(()())", "(()(()))()(())()", "(()(()))()()(())", "(()(()))()()()()", "(()()((((())))))", "(()()(((()()))))", "(()()(((())())))", "(()()(((()))()))", "(()()(((())))())", "(()()(((()))))()", "(()()((()(()))))", "(()()((()()())))", "(()()((()())()))", "(()()((()()))())", "(()()((()())))()", "(()()((())(())))", "(()()((())()()))", "(()()((())())())", "(()()((())()))()", "(()()((()))(()))", "(()()((()))()())", "(()()((()))())()", "(()()((())))(())", "(()()((())))()()", "(()()(()((()))))", "(()()(()(()())))", "(()()(()(())()))", "(()()(()(()))())", "(()()(()(())))()", "(()()(()()(())))", "(()()(()()()()))", "(()()(()()())())", "(()()(()()()))()", "(()()(()())(()))", "(()()(()())()())", "(()()(()())())()", "(()()(()()))(())", "(()()(()()))()()", "(()()(())((())))", "(()()(())(()()))", "(()()(())(())())", "(()()(())(()))()", "(()()(())()(()))", "(()()(())()()())", "(()()(())()())()", "(()()(())())(())", "(()()(())())()()", "(()()(()))((()))", "(()()(()))(()())", "(()()(()))(())()", "(()()(()))()(())", "(()()(()))()()()", "(()()()(((()))))", "(()()()((()())))", "(()()()((())()))", "(()()()((()))())", "(()()()((())))()", "(()()()(()(())))", "(()()()(()()()))", "(()()()(()())())", "(()()()(()()))()", "(()()()(())(()))", "(()()()(())()())", "(()()()(())())()", "(()()()(()))(())", "(()()()(()))()()", "(()()()()((())))", "(()()()()(()()))", "(()()()()(())())", "(()()()()(()))()", "(()()()()()(()))", "(()()()()()()())", "(()()()()()())()", "(()()()()())(())", "(()()()()())()()", "(()()()())((()))", "(()()()())(()())", "(()()()())(())()", "(()()()())()(())", "(()()()())()()()", "(()()())(((())))", "(()()())((()()))", "(()()())((())())", "(()()())((()))()", "(()()())(()(()))", "(()()())(()()())", "(()()())(()())()", "(()()())(())(())", "(()()())(())()()", "(()()())()((()))", "(()()())()(()())", "(()()())()(())()", "(()()())()()(())", "(()()())()()()()", "(()())((((()))))", "(()())(((()())))", "(()())(((())()))", "(()())(((()))())", "(()())(((())))()", "(()())((()(())))", "(()())((()()()))", "(()())((()())())", "(()())((()()))()", "(()())((())(()))", "(()())((())()())", "(()())((())())()", "(()())((()))(())", "(()())((()))()()", "(()())(()((())))", "(()())(()(()()))", "(()())(()(())())", "(()())(()(()))()", "(()())(()()(()))", "(()())(()()()())", "(()())(()()())()", "(()())(()())(())", "(()())(()())()()", "(()())(())((()))", "(()())(())(()())", "(()())(())(())()", "(()())(())()(())", "(()())(())()()()", "(()())()(((())))", "(()())()((()()))", "(()())()((())())", "(()())()((()))()", "(()())()(()(()))", "(()())()(()()())", "(()())()(()())()", "(()())()(())(())", "(()())()(())()()", "(()())()()((()))", "(()())()()(()())", "(()())()()(())()", "(()())()()()(())", "(()())()()()()()", "(())(((((())))))", "(())((((()()))))", "(())((((())())))", "(())((((()))()))", "(())((((())))())", "(())((((()))))()", "(())(((()(()))))", "(())(((()()())))", "(())(((()())()))", "(())(((()()))())", "(())(((()())))()", "(())(((())(())))", "(())(((())()()))", "(())(((())())())", "(())(((())()))()", "(())(((()))(()))", "(())(((()))()())", "(())(((()))())()", "(())(((())))(())", "(())(((())))()()", "(())((()((()))))", "(())((()(()())))", "(())((()(())()))", "(())((()(()))())", "(())((()(())))()", "(())((()()(())))", "(())((()()()()))", "(())((()()())())", "(())((()()()))()", "(())((()())(()))", "(())((()())()())", "(())((()())())()", "(())((()()))(())", "(())((()()))()()", "(())((())((())))", "(())((())(()()))", "(())((())(())())", "(())((())(()))()", "(())((())()(()))", "(())((())()()())", "(())((())()())()", "(())((())())(())", "(())((())())()()", "(())((()))((()))", "(())((()))(()())", "(())((()))(())()", "(())((()))()(())", "(())((()))()()()", "(())(()(((()))))", "(())(()((()())))", "(())(()((())()))", "(())(()((()))())", "(())(()((())))()", "(())(()(()(())))", "(())(()(()()()))", "(())(()(()())())", "(())(()(()()))()", "(())(()(())(()))", "(())(()(())()())", "(())(()(())())()", "(())(()(()))(())", "(())(()(()))()()", "(())(()()((())))", "(())(()()(()()))", "(())(()()(())())", "(())(()()(()))()", "(())(()()()(()))", "(())(()()()()())", "(())(()()()())()", "(())(()()())(())", "(())(()()())()()", "(())(()())((()))", "(())(()())(()())", "(())(()())(())()", "(())(()())()(())", "(())(()())()()()", "(())(())(((())))", "(())(())((()()))", "(())(())((())())", "(())(())((()))()", "(())(())(()(()))", "(())(())(()()())", "(())(())(()())()", "(())(())(())(())", "(())(())(())()()", "(())(())()((()))", "(())(())()(()())", "(())(())()(())()", "(())(())()()(())", "(())(())()()()()", "(())()((((()))))", "(())()(((()())))", "(())()(((())()))", "(())()(((()))())", "(())()(((())))()", "(())()((()(())))", "(())()((()()()))", "(())()((()())())", "(())()((()()))()", "(())()((())(()))", "(())()((())()())", "(())()((())())()", "(())()((()))(())", "(())()((()))()()", "(())()(()((())))", "(())()(()(()()))", "(())()(()(())())", "(())()(()(()))()", "(())()(()()(()))", "(())()(()()()())", "(())()(()()())()", "(())()(()())(())", "(())()(()())()()", "(())()(())((()))", "(())()(())(()())", "(())()(())(())()", "(())()(())()(())", "(())()(())()()()", "(())()()(((())))", "(())()()((()()))", "(())()()((())())", "(())()()((()))()", "(())()()(()(()))", "(())()()(()()())", "(())()()(()())()", "(())()()(())(())", "(())()()(())()()", "(())()()()((()))", "(())()()()(()())", "(())()()()(())()", "(())()()()()(())", "(())()()()()()()", "()((((((()))))))", "()(((((()())))))", "()(((((())()))))", "()(((((()))())))", "()(((((())))()))", "()(((((()))))())", "()(((((())))))()", "()((((()(())))))", "()((((()()()))))", "()((((()())())))", "()((((()()))()))", "()((((()())))())", "()((((()()))))()", "()((((())(()))))", "()((((())()())))", "()((((())())()))", "()((((())()))())", "()((((())())))()", "()((((()))(())))", "()((((()))()()))", "()((((()))())())", "()((((()))()))()", "()((((())))(()))", "()((((())))()())", "()((((())))())()", "()((((()))))(())", "()((((()))))()()", "()(((()((())))))", "()(((()(()()))))", "()(((()(())())))", "()(((()(()))()))", "()(((()(())))())", "()(((()(()))))()", "()(((()()(()))))", "()(((()()()())))", "()(((()()())()))", "()(((()()()))())", "()(((()()())))()", "()(((()())(())))", "()(((()())()()))", "()(((()())())())", "()(((()())()))()", "()(((()()))(()))", "()(((()()))()())", "()(((()()))())()", "()(((()())))(())", "()(((()())))()()", "()(((())((()))))", "()(((())(()())))", "()(((())(())()))", "()(((())(()))())", "()(((())(())))()", "()(((())()(())))", "()(((())()()()))", "()(((())()())())", "()(((())()()))()", "()(((())())(()))", "()(((())())()())", "()(((())())())()", "()(((())()))(())", "()(((())()))()()", "()(((()))((())))", "()(((()))(()()))", "()(((()))(())())", "()(((()))(()))()", "()(((()))()(()))", "()(((()))()()())", "()(((()))()())()", "()(((()))())(())", "()(((()))())()()", "()(((())))((()))", "()(((())))(()())", "()(((())))(())()", "()(((())))()(())", "()(((())))()()()", "()((()(((())))))", "()((()((()()))))", "()((()((())())))", "()((()((()))()))", "()((()((())))())", "()((()((()))))()", "()((()(()(()))))", "()((()(()()())))", "()((()(()())()))", "()((()(()()))())", "()((()(()())))()", "()((()(())(())))", "()((()(())()()))", "()((()(())())())", "()((()(())()))()", "()((()(()))(()))", "()((()(()))()())", "()((()(()))())()", "()((()(())))(())", "()((()(())))()()", "()((()()((()))))", "()((()()(()())))", "()((()()(())()))", "()((()()(()))())", "()((()()(())))()", "()((()()()(())))", "()((()()()()()))", "()((()()()())())", "()((()()()()))()", "()((()()())(()))", "()((()()())()())", "()((()()())())()", "()((()()()))(())", "()((()()()))()()", "()((()())((())))", "()((()())(()()))", "()((()())(())())", "()((()())(()))()", "()((()())()(()))", "()((()())()()())", "()((()())()())()", "()((()())())(())", "()((()())())()()", "()((()()))((()))", "()((()()))(()())", "()((()()))(())()", "()((()()))()(())", "()((()()))()()()", "()((())(((()))))", "()((())((()())))", "()((())((())()))", "()((())((()))())", "()((())((())))()", "()((())(()(())))", "()((())(()()()))", "()((())(()())())", "()((())(()()))()", "()((())(())(()))", "()((())(())()())", "()((())(())())()", "()((())(()))(())", "()((())(()))()()", "()((())()((())))", "()((())()(()()))", "()((())()(())())", "()((())()(()))()", "()((())()()(()))", "()((())()()()())", "()((())()()())()", "()((())()())(())", "()((())()())()()", "()((())())((()))", "()((())())(()())", "()((())())(())()", "()((())())()(())", "()((())())()()()", "()((()))(((())))", "()((()))((()()))", "()((()))((())())", "()((()))((()))()", "()((()))(()(()))", "()((()))(()()())", "()((()))(()())()", "()((()))(())(())", "()((()))(())()()", "()((()))()((()))", "()((()))()(()())", "()((()))()(())()", "()((()))()()(())", "()((()))()()()()", "()(()((((())))))", "()(()(((()()))))", "()(()(((())())))", "()(()(((()))()))", "()(()(((())))())", "()(()(((()))))()", "()(()((()(()))))", "()(()((()()())))", "()(()((()())()))", "()(()((()()))())", "()(()((()())))()", "()(()((())(())))", "()(()((())()()))", "()(()((())())())", "()(()((())()))()", "()(()((()))(()))", "()(()((()))()())", "()(()((()))())()", "()(()((())))(())", "()(()((())))()()", "()(()(()((()))))", "()(()(()(()())))", "()(()(()(())()))", "()(()(()(()))())", "()(()(()(())))()", "()(()(()()(())))", "()(()(()()()()))", "()(()(()()())())", "()(()(()()()))()", "()(()(()())(()))", "()(()(()())()())", "()(()(()())())()", "()(()(()()))(())", "()(()(()()))()()", "()(()(())((())))", "()(()(())(()()))", "()(()(())(())())", "()(()(())(()))()", "()(()(())()(()))", "()(()(())()()())", "()(()(())()())()", "()(()(())())(())", "()(()(())())()()", "()(()(()))((()))", "()(()(()))(()())", "()(()(()))(())()", "()(()(()))()(())", "()(()(()))()()()", "()(()()(((()))))", "()(()()((()())))", "()(()()((())()))", "()(()()((()))())", "()(()()((())))()", "()(()()(()(())))", "()(()()(()()()))", "()(()()(()())())", "()(()()(()()))()", "()(()()(())(()))", "()(()()(())()())", "()(()()(())())()", "()(()()(()))(())", "()(()()(()))()()", "()(()()()((())))", "()(()()()(()()))", "()(()()()(())())", "()(()()()(()))()", "()(()()()()(()))", "()(()()()()()())", "()(()()()()())()", "()(()()()())(())", "()(()()()())()()", "()(()()())((()))", "()(()()())(()())", "()(()()())(())()", "()(()()())()(())", "()(()()())()()()", "()(()())(((())))", "()(()())((()()))", "()(()())((())())", "()(()())((()))()", "()(()())(()(()))", "()(()())(()()())", "()(()())(()())()", "()(()())(())(())", "()(()())(())()()", "()(()())()((()))", "()(()())()(()())", "()(()())()(())()", "()(()())()()(())", "()(()())()()()()", "()(())((((()))))", "()(())(((()())))", "()(())(((())()))", "()(())(((()))())", "()(())(((())))()", "()(())((()(())))", "()(())((()()()))", "()(())((()())())", "()(())((()()))()", "()(())((())(()))", "()(())((())()())", "()(())((())())()", "()(())((()))(())", "()(())((()))()()", "()(())(()((())))", "()(())(()(()()))", "()(())(()(())())", "()(())(()(()))()", "()(())(()()(()))", "()(())(()()()())", "()(())(()()())()", "()(())(()())(())", "()(())(()())()()", "()(())(())((()))", "()(())(())(()())", "()(())(())(())()", "()(())(())()(())", "()(())(())()()()", "()(())()(((())))", "()(())()((()()))", "()(())()((())())", "()(())()((()))()", "()(())()(()(()))", "()(())()(()()())", "()(())()(()())()", "()(())()(())(())", "()(())()(())()()", "()(())()()((()))", "()(())()()(()())", "()(())()()(())()", "()(())()()()(())", "()(())()()()()()", "()()(((((())))))", "()()((((()()))))", "()()((((())())))", "()()((((()))()))", "()()((((())))())", "()()((((()))))()", "()()(((()(()))))", "()()(((()()())))", "()()(((()())()))", "()()(((()()))())", "()()(((()())))()", "()()(((())(())))", "()()(((())()()))", "()()(((())())())", "()()(((())()))()", "()()(((()))(()))", "()()(((()))()())", "()()(((()))())()", "()()(((())))(())", "()()(((())))()()", "()()((()((()))))", "()()((()(()())))", "()()((()(())()))", "()()((()(()))())", "()()((()(())))()", "()()((()()(())))", "()()((()()()()))", "()()((()()())())", "()()((()()()))()", "()()((()())(()))", "()()((()())()())", "()()((()())())()", "()()((()()))(())", "()()((()()))()()", "()()((())((())))", "()()((())(()()))", "()()((())(())())", "()()((())(()))()", "()()((())()(()))", "()()((())()()())", "()()((())()())()", "()()((())())(())", "()()((())())()()", "()()((()))((()))", "()()((()))(()())", "()()((()))(())()", "()()((()))()(())", "()()((()))()()()", "()()(()(((()))))", "()()(()((()())))", "()()(()((())()))", "()()(()((()))())", "()()(()((())))()", "()()(()(()(())))", "()()(()(()()()))", "()()(()(()())())", "()()(()(()()))()", "()()(()(())(()))", "()()(()(())()())", "()()(()(())())()", "()()(()(()))(())", "()()(()(()))()()", "()()(()()((())))", "()()(()()(()()))", "()()(()()(())())", "()()(()()(()))()", "()()(()()()(()))", "()()(()()()()())", "()()(()()()())()", "()()(()()())(())", "()()(()()())()()", "()()(()())((()))", "()()(()())(()())", "()()(()())(())()", "()()(()())()(())", "()()(()())()()()", "()()(())(((())))", "()()(())((()()))", "()()(())((())())", "()()(())((()))()", "()()(())(()(()))", "()()(())(()()())", "()()(())(()())()", "()()(())(())(())", "()()(())(())()()", "()()(())()((()))", "()()(())()(()())", "()()(())()(())()", "()()(())()()(())", "()()(())()()()()", "()()()((((()))))", "()()()(((()())))", "()()()(((())()))", "()()()(((()))())", "()()()(((())))()", "()()()((()(())))", "()()()((()()()))", "()()()((()())())", "()()()((()()))()", "()()()((())(()))", "()()()((())()())", "()()()((())())()", "()()()((()))(())", "()()()((()))()()", "()()()(()((())))", "()()()(()(()()))", "()()()(()(())())", "()()()(()(()))()", "()()()(()()(()))", "()()()(()()()())", "()()()(()()())()", "()()()(()())(())", "()()()(()())()()", "()()()(())((()))", "()()()(())(()())", "()()()(())(())()", "()()()(())()(())", "()()()(())()()()", "()()()()(((())))", "()()()()((()()))", "()()()()((())())", "()()()()((()))()", "()()()()(()(()))", "()()()()(()()())", "()()()()(()())()", "()()()()(())(())", "()()()()(())()()", "()()()()()((()))", "()()()()()(()())", "()()()()()(())()", "()()()()()()(())", "()()()()()()()()"] TODO
9 ["((((((((()))))))))", "(((((((()())))))))", "(((((((())()))))))", "(((((((()))())))))", "(((((((())))()))))", "(((((((()))))())))", "(((((((())))))()))", "(((((((()))))))())", "(((((((())))))))()", "((((((()(())))))))", "((((((()()()))))))", "((((((()())())))))", "((((((()()))()))))", "((((((()())))())))", "((((((()()))))()))", "((((((()())))))())", "((((((()()))))))()", "((((((())(()))))))", "((((((())()())))))", "((((((())())()))))", "((((((())()))())))", "((((((())())))()))", "((((((())()))))())", "((((((())())))))()", "((((((()))(())))))", "((((((()))()()))))", "((((((()))())())))", "((((((()))()))()))", "((((((()))())))())", "((((((()))()))))()", "((((((())))(()))))", "((((((())))()())))", "((((((())))())()))", "((((((())))()))())", "((((((())))())))()", "((((((()))))(())))", "((((((()))))()()))", "((((((()))))())())", "((((((()))))()))()", "((((((())))))(()))", "((((((())))))()())", "((((((())))))())()", "((((((()))))))(())", "((((((()))))))()()", "(((((()((())))))))", "(((((()(()()))))))", "(((((()(())())))))", "(((((()(()))()))))", "(((((()(())))())))", "(((((()(()))))()))", "(((((()(())))))())", "(((((()(()))))))()", "(((((()()(()))))))", "(((((()()()())))))", "(((((()()())()))))", "(((((()()()))())))", "(((((()()())))()))", "(((((()()()))))())", "(((((()()())))))()", "(((((()())(())))))", "(((((()())()()))))", "(((((()())())())))", "(((((()())()))()))", "(((((()())())))())", "(((((()())()))))()", "(((((()()))(()))))", "(((((()()))()())))", "(((((()()))())()))", "(((((()()))()))())", "(((((()()))())))()", "(((((()())))(())))", "(((((()())))()()))", "(((((()())))())())", "(((((()())))()))()", "(((((()()))))(()))", "(((((()()))))()())", "(((((()()))))())()", "(((((()())))))(())", "(((((()())))))()()", "(((((())((()))))))", "(((((())(()())))))", "(((((())(())()))))", "(((((())(()))())))", "(((((())(())))()))", "(((((())(()))))())", "(((((())(())))))()", "(((((())()(())))))", "(((((())()()()))))", "(((((())()())())))", "(((((())()()))()))", "(((((())()())))())", "(((((())()()))))()", "(((((())())(()))))", "(((((())())()())))", "(((((())())())()))", "(((((())())()))())", "(((((())())())))()", "(((((())()))(())))", "(((((())()))()()))", "(((((())()))())())", "(((((())()))()))()", "(((((())())))(()))", "(((((())())))()())", "(((((())())))())()", "(((((())()))))(())", "(((((())()))))()()", "(((((()))((())))))", "(((((()))(()()))))", "(((((()))(())())))", "(((((()))(()))()))", "(((((()))(())))())", "(((((()))(()))))()", "(((((()))()(()))))", "(((((()))()()())))", "(((((()))()())()))", "(((((()))()()))())", "(((((()))()())))()", "(((((()))())(())))", "(((((()))())()()))", "(((((()))())())())", "(((((()))())()))()", "(((((()))()))(()))", "(((((()))()))()())", "(((((()))()))())()", "(((((()))())))(())", "(((((()))())))()()", "(((((())))((()))))", "(((((())))(()())))", "(((((())))(())()))", "(((((())))(()))())", "(((((())))(())))()", "(((((())))()(())))", "(((((())))()()()))", "(((((())))()())())", "(((((())))()()))()", "(((((())))())(()))", "(((((())))())()())", "(((((())))())())()", "(((((())))()))(())", "(((((())))()))()()", "(((((()))))((())))", "(((((()))))(()()))", "(((((()))))(())())", "(((((()))))(()))()", "(((((()))))()(()))", "(((((()))))()()())", "(((((()))))()())()", "(((((()))))())(())", "(((((()))))())()()", "(((((())))))((()))", "(((((())))))(()())", "(((((())))))(())()", "(((((())))))()(())", "(((((())))))()()()", "((((()(((())))))))", "((((()((()()))))))", "((((()((())())))))", "((((()((()))()))))", "((((()((())))())))", "((((()((()))))()))", "((((()((())))))())", "((((()((()))))))()", "((((()(()(()))))))", "((((()(()()())))))", "((((()(()())()))))", "((((()(()()))())))", "((((()(()())))()))", "((((()(()()))))())", "((((()(()())))))()", "((((()(())(())))))", "((((()(())()()))))", "((((()(())())())))", "((((()(())()))()))", "((((()(())())))())", "((((()(())()))))()", "((((()(()))(()))))", "((((()(()))()())))", "((((()(()))())()))", "((((()(()))()))())", "((((()(()))())))()", "((((()(())))(())))", "((((()(())))()()))", "((((()(())))())())", "((((()(())))()))()", "((((()(()))))(()))", "((((()(()))))()())", "((((()(()))))())()", "((((()(())))))(())", "((((()(())))))()()", "((((()()((()))))))", "((((()()(()())))))", "((((()()(())()))))", "((((()()(()))())))", "((((()()(())))()))", "((((()()(()))))())", "((((()()(())))))()", "((((()()()(())))))", "((((()()()()()))))", "((((()()()())())))", "((((()()()()))()))", "((((()()()())))())", "((((()()()()))))()", "((((()()())(()))))", "((((()()())()())))", "((((()()())())()))", "((((()()())()))())", "((((()()())())))()", "((((()()()))(())))", "((((()()()))()()))", "((((()()()))())())", "((((()()()))()))()", "((((()()())))(()))", "((((()()())))()())", "((((()()())))())()", "((((()()()))))(())", "((((()()()))))()()", "((((()())((())))))", "((((()())(()()))))", "((((()())(())())))", "((((()())(()))()))", "((((()())(())))())", "((((()())(()))))()", "((((()())()(()))))", "((((()())()()())))", "((((()())()())()))", "((((()())()()))())", "((((()())()())))()", "((((()())())(())))", "((((()())())()()))", "((((()())())())())", "((((()())())()))()", "((((()())()))(()))", "((((()())()))()())", "((((()())()))())()", "((((()())())))(())", "((((()())())))()()", "((((()()))((()))))", "((((()()))(()())))", "((((()()))(())()))", "((((()()))(()))())", "((((()()))(())))()", "((((()()))()(())))", "((((()()))()()()))", "((((()()))()())())", "((((()()))()()))()", "((((()()))())(()))", "((((()()))())()())", "((((()()))())())()", "((((()()))()))(())", "((((()()))()))()()", "((((()())))((())))", "((((()())))(()()))", "((((()())))(())())", "((((()())))(()))()", "((((()())))()(()))", "((((()())))()()())", "((((()())))()())()", "((((()())))())(())", "((((()())))())()()", "((((()()))))((()))", "((((()()))))(()())", "((((()()))))(())()", "((((()()))))()(())", "((((()()))))()()()", "((((())(((()))))))", "((((())((()())))))", "((((())((())()))))", "((((())((()))())))", "((((())((())))()))", "((((())((()))))())", "((((())((())))))()", "((((())(()(())))))", "((((())(()()()))))", "((((())(()())())))", "((((())(()()))()))", "((((())(()())))())", "((((())(()()))))()", "((((())(())(()))))", "((((())(())()())))", "((((())(())())()))", "((((())(())()))())", "((((())(())())))()", "((((())(()))(())))", "((((())(()))()()))", "((((())(()))())())", "((((())(()))()))()", "((((())(())))(()))", "((((())(())))()())", "((((())(())))())()", "((((())(()))))(())", "((((())(()))))()()", "((((())()((())))))", "((((())()(()()))))", "((((())()(())())))", "((((())()(()))()))", "((((())()(())))())", "((((())()(()))))()", "((((())()()(()))))", "((((())()()()())))", "((((())()()())()))", "((((())()()()))())", "((((())()()())))()", "((((())()())(())))", "((((())()())()()))", "((((())()())())())", "((((())()())()))()", "((((())()()))(()))", "((((())()()))()())", "((((())()()))())()", "((((())()())))(())", "((((())()())))()()", "((((())())((()))))", "((((())())(()())))", "((((())())(())()))", "((((())())(()))())", "((((())())(())))()", "((((())())()(())))", "((((())())()()()))", "((((())())()())())", "((((())())()()))()", "((((())())())(()))", "((((())())())()())", "((((())())())())()", "((((())())()))(())", "((((())())()))()()", "((((())()))((())))", "((((())()))(()()))", "((((())()))(())())", "((((())()))(()))()", "((((())()))()(()))", "((((())()))()()())", "((((())()))()())()", "((((())()))())(())", "((((())()))())()()", "((((())())))((()))", "((((())())))(()())", "((((())())))(())()", "((((())())))()(())", "((((())())))()()()", "((((()))(((())))))", "((((()))((()()))))", "((((()))((())())))", "((((()))((()))()))", "((((()))((())))())", "((((()))((()))))()", "((((()))(()(()))))", "((((()))(()()())))", "((((()))(()())()))", "((((()))(()()))())", "((((()))(()())))()", "((((()))(())(())))", "((((()))(())()()))", "((((()))(())())())", "((((()))(())()))()", "((((()))(()))(()))", "((((()))(()))()())", "((((()))(()))())()", "((((()))(())))(())", "((((()))(())))()()", "((((()))()((()))))", "((((()))()(()())))", "((((()))()(())()))", "((((()))()(()))())", "((((()))()(())))()", "((((()))()()(())))", "((((()))()()()()))", "((((()))()()())())", "((((()))()()()))()", "((((()))()())(()))", "((((()))()())()())", "((((()))()())())()", "((((()))()()))(())", "((((()))()()))()()", "((((()))())((())))", "((((()))())(()()))", "((((()))())(())())", "((((()))())(()))()", "((((()))())()(()))", "((((()))())()()())", "((((()))())()())()", "((((()))())())(())", "((((()))())())()()", "((((()))()))((()))", "((((()))()))(()())", "((((()))()))(())()", "((((()))()))()(())", "((((()))()))()()()", "((((())))(((()))))", "((((())))((()())))", "((((())))((())()))", "((((())))((()))())", "((((())))((())))()", "((((())))(()(())))", "((((())))(()()()))", "((((())))(()())())", "((((())))(()()))()", "((((())))(())(()))", "((((())))(())()())", "((((())))(())())()", "((((())))(()))(())", "((((())))(()))()()", "((((())))()((())))", "((((())))()(()()))", "((((())))()(())())", "((((())))()(()))()", "((((())))()()(()))", "((((())))()()()())", "((((())))()()())()", "((((())))()())(())", "((((())))()())()()", "((((())))())((()))", "((((())))())(()())", "((((())))())(())()", "((((())))())()(())", "((((())))())()()()", "((((()))))(((())))", "((((()))))((()()))", "((((()))))((())())", "((((()))))((()))()", "((((()))))(()(()))", "((((()))))(()()())", "((((()))))(()())()", "((((()))))(())(())", "((((()))))(())()()", "((((()))))()((()))", "((((()))))()(()())", "((((()))))()(())()", "((((()))))()()(())", "((((()))))()()()()", "(((()((((())))))))", "(((()(((()()))))))", "(((()(((())())))))", "(((()(((()))()))))", "(((()(((())))())))", "(((()(((()))))()))", "(((()(((())))))())", "(((()(((()))))))()", "(((()((()(()))))))", "(((()((()()())))))", "(((()((()())()))))", "(((()((()()))())))", "(((()((()())))()))", "(((()((()()))))())", "(((()((()())))))()", "(((()((())(())))))", "(((()((())()()))))", "(((()((())())())))", "(((()((())()))()))", "(((()((())())))())", "(((()((())()))))()", "(((()((()))(()))))", "(((()((()))()())))", "(((()((()))())()))", "(((()((()))()))())", "(((()((()))())))()", "(((()((())))(())))", "(((()((())))()()))", "(((()((())))())())", "(((()((())))()))()", "(((()((()))))(()))", "(((()((()))))()())", "(((()((()))))())()", "(((()((())))))(())", "(((()((())))))()()", "(((()(()((()))))))", "(((()(()(()())))))", "(((()(()(())()))))", "(((()(()(()))())))", "(((()(()(())))()))", "(((()(()(()))))())", "(((()(()(())))))()", "(((()(()()(())))))", "(((()(()()()()))))", "(((()(()()())())))", "(((()(()()()))()))", "(((()(()()())))())", "(((()(()()()))))()", "(((()(()())(()))))", "(((()(()())()())))", "(((()(()())())()))", "(((()(()())()))())", "(((()(()())())))()", "(((()(()()))(())))", "(((()(()()))()()))", "(((()(()()))())())", "(((()(()()))()))()", "(((()(()())))(()))", "(((()(()())))()())", "(((()(()())))())()", "(((()(()()))))(())", "(((()(()()))))()()", "(((()(())((())))))", "(((()(())(()()))))", "(((()(())(())())))", "(((()(())(()))()))", "(((()(())(())))())", "(((()(())(()))))()", "(((()(())()(()))))", "(((()(())()()())))", "(((()(())()())()))", "(((()(())()()))())", "(((()(())()())))()", "(((()(())())(())))", "(((()(())())()()))", "(((()(())())())())", "(((()(())())()))()", "(((()(())()))(()))", "(((()(())()))()())", "(((()(())()))())()", "(((()(())())))(())", "(((()(())())))()()", "(((()(()))((()))))", "(((()(()))(()())))", "(((()(()))(())()))", "(((()(()))(()))())", "(((()(()))(())))()", "(((()(()))()(())))", "(((()(()))()()()))", "(((()(()))()())())", "(((()(()))()()))()", "(((()(()))())(()))", "(((()(()))())()())", "(((()(()))())())()", "(((()(()))()))(())", "(((()(()))()))()()", "(((()(())))((())))", "(((()(())))(()()))", "(((()(())))(())())", "(((()(())))(()))()", "(((()(())))()(()))", "(((()(())))()()())", "(((()(())))()())()", "(((()(())))())(())", "(((()(())))())()()", "(((()(()))))((()))", "(((()(()))))(()())", "(((()(()))))(())()", "(((()(()))))()(())", "(((()(()))))()()()", "(((()()(((()))))))", "(((()()((()())))))", "(((()()((())()))))", "(((()()((()))())))", "(((()()((())))()))", "(((()()((()))))())", "(((()()((())))))()", "(((()()(()(())))))", "(((()()(()()()))))", "(((()()(()())())))", "(((()()(()()))()))", "(((()()(()())))())", "(((()()(()()))))()", "(((()()(())(()))))", "(((()()(())()())))", "(((()()(())())()))", "(((()()(())()))())", "(((()()(())())))()", "(((()()(()))(())))", "(((()()(()))()()))", "(((()()(()))())())", "(((()()(()))()))()", "(((()()(())))(()))", "(((()()(())))()())", "(((()()(())))())()", "(((()()(()))))(())", "(((()()(()))))()()", "(((()()()((())))))", "(((()()()(()()))))", "(((()()()(())())))", "(((()()()(()))()))", "(((()()()(())))())", "(((()()()(()))))()", "(((()()()()(()))))", "(((()()()()()())))", "(((()()()()())()))", "(((()()()()()))())", "(((()()()()())))()", "(((()()()())(())))", "(((()()()())()()))", "(((()()()())())())", "(((()()()())()))()", "(((()()()()))(()))", "(((()()()()))()())", "(((()()()()))())()", "(((()()()())))(())", "(((()()()())))()()", "(((()()())((()))))", "(((()()())(()())))", "(((()()())(())()))", "(((()()())(()))())", "(((()()())(())))()", "(((()()())()(())))", "(((()()())()()()))", "(((()()())()())())", "(((()()())()()))()", "(((()()())())(()))", "(((()()())())()())", "(((()()())())())()", "(((()()())()))(())", "(((()()())()))()()", "(((()()()))((())))", "(((()()()))(()()))", "(((()()()))(())())", "(((()()()))(()))()", "(((()()()))()(()))", "(((()()()))()()())", "(((()()()))()())()", "(((()()()))())(())", "(((()()()))())()()", "(((()()())))((()))", "(((()()())))(()())", "(((()()())))(())()", "(((()()())))()(())", "(((()()())))()()()", "(((()())(((())))))", "(((()())((()()))))", "(((()())((())())))", "(((()())((()))()))", "(((()())((())))())", "(((()())((()))))()", "(((()())(()(()))))", "(((()())(()()())))", "(((()())(()())()))", "(((()())(()()))())", "(((()())(()())))()", "(((()())(())(())))", "(((()())(())()()))", "(((()())(())())())", "(((()())(())()))()", "(((()())(()))(()))", "(((()())(()))()())", "(((()())(()))())()", "(((()())(())))(())", "(((()())(())))()()", "(((()())()((()))))", "(((()())()(()())))", "(((()())()(())()))", "(((()())()(()))())", "(((()())()(())))()", "(((()())()()(())))", "(((()())()()()()))", "(((()())()()())())", "(((()())()()()))()", "(((()())()())(()))", "(((()())()())()())", "(((()())()())())()", "(((()())()()))(())", "(((()())()()))()()", "(((()())())((())))", "(((()())())(()()))", "(((()())())(())())", "(((()())())(()))()", "(((()())())()(()))", "(((()())())()()())", "(((()())())()())()", "(((()())())())(())", "(((()())())())()()", "(((()())()))((()))", "(((()())()))(()())", "(((()())()))(())()", "(((()())()))()(())", "(((()())()))()()()", "(((()()))(((()))))", "(((()()))((()())))", "(((()()))((())()))", "(((()()))((()))())", "(((()()))((())))()", "(((()()))(()(())))", "(((()()))(()()()))", "(((()()))(()())())", "(((()()))(()()))()", "(((()()))(())(()))", "(((()()))(())()())", "(((()()))(())())()", "(((()()))(()))(())", "(((()()))(()))()()", "(((()()))()((())))", "(((()()))()(()()))", "(((()()))()(())())", "(((()()))()(()))()", "(((()()))()()(()))", "(((()()))()()()())", "(((()()))()()())()", "(((()()))()())(())", "(((()()))()())()()", "(((()()))())((()))", "(((()()))())(()())", "(((()()))())(())()", "(((()()))())()(())", "(((()()))())()()()", "(((()())))(((())))", "(((()())))((()()))", "(((()())))((())())", "(((()())))((()))()", "(((()())))(()(()))", "(((()())))(()()())", "(((()())))(()())()", "(((()())))(())(())", "(((()())))(())()()", "(((()())))()((()))", "(((()())))()(()())", "(((()())))()(())()", "(((()())))()()(())", "(((()())))()()()()", "(((())((((()))))))", "(((())(((()())))))", "(((())(((())()))))", "(((())(((()))())))", "(((())(((())))()))", "(((())(((()))))())", "(((())(((())))))()", "(((())((()(())))))", "(((())((()()()))))", "(((())((()())())))", "(((())((()()))()))", "(((())((()())))())", "(((())((()()))))()", "(((())((())(()))))", "(((())((())()())))", "(((())((())())()))", "(((())((())()))())", "(((())((())())))()", "(((())((()))(())))", "(((())((()))()()))", "(((())((()))())())", "(((())((()))()))()", "(((())((())))(()))", "(((())((())))()())", "(((())((())))())()", "(((())((()))))(())", "(((())((()))))()()", "(((())(()((())))))", "(((())(()(()()))))", "(((())(()(())())))", "(((())(()(()))()))", "(((())(()(())))())", "(((())(()(()))))()", "(((())(()()(()))))", "(((())(()()()())))", "(((())(()()())()))", "(((())(()()()))())", "(((())(()()())))()", "(((())(()())(())))", "(((())(()())()()))", "(((())(()())())())", "(((())(()())()))()", "(((())(()()))(()))", "(((())(()()))()())", "(((())(()()))())()", "(((())(()())))(())", "(((())(()())))()()", "(((())(())((()))))", "(((())(())(()())))", "(((())(())(())()))", "(((())(())(()))())", "(((())(())(())))()", "(((())(())()(())))", "(((())(())()()()))", "(((())(())()())())", "(((())(())()()))()", "(((())(())())(()))", "(((())(())())()())", "(((())(())())())()", "(((())(())()))(())", "(((())(())()))()()", "(((())(()))((())))", "(((())(()))(()()))", "(((())(()))(())())", "(((())(()))(()))()", "(((())(()))()(()))", "(((())(()))()()())", "(((())(()))()())()", "(((())(()))())(())", "(((())(()))())()()", "(((())(())))((()))", "(((())(())))(()())", "(((())(())))(())()", "(((())(())))()(())", "(((())(())))()()()", "(((())()(((())))))", "(((())()((()()))))", "(((())()((())())))", "(((())()((()))()))", "(((())()((())))())", "(((())()((()))))()", "(((())()(()(()))))", "(((())()(()()())))", "(((())()(()())()))", "(((())()(()()))())", "(((())()(()())))()", "(((())()(())(())))", "(((())()(())()()))", "(((())()(())())())", "(((())()(())()))()", "(((())()(()))(()))", "(((())()(()))()())", "(((())()(()))())()", "(((())()(())))(())", "(((())()(())))()()", "(((())()()((()))))", "(((())()()(()())))", "(((())()()(())()))", "(((())()()(()))())", "(((())()()(())))()", "(((())()()()(())))", "(((())()()()()()))", "(((())()()()())())", "(((())()()()()))()", "(((())()()())(()))", "(((())()()())()())", "(((())()()())())()", "(((())()()()))(())", "(((())()()()))()()", "(((())()())((())))", "(((())()())(()()))", "(((())()())(())())", "(((())()())(()))()", "(((())()())()(()))", "(((())()())()()())", "(((())()())()())()", "(((())()())())(())", "(((())()())())()()", "(((())()()))((()))", "(((())()()))(()())", "(((())()()))(())()", "(((())()()))()(())", "(((())()()))()()()", "(((())())(((()))))", "(((())())((()())))", "(((())())((())()))", "(((())())((()))())", "(((())())((())))()", "(((())())(()(())))", "(((())())(()()()))", "(((())())(()())())", "(((())())(()()))()", "(((())())(())(()))", "(((())())(())()())", "(((())())(())())()", "(((())())(()))(())", "(((())())(()))()()", "(((())())()((())))", "(((())())()(()()))", "(((())())()(())())", "(((())())()(()))()", "(((())())()()(()))", "(((())())()()()())", "(((())())()()())()", "(((())())()())(())", "(((())())()())()()", "(((())())())((()))", "(((())())())(()())", "(((())())())(())()", "(((())())())()(())", "(((())())())()()()", "(((())()))(((())))", "(((())()))((()()))", "(((())()))((())())", "(((())()))((()))()", "(((())()))(()(()))", "(((())()))(()()())", "(((())()))(()())()", "(((())()))(())(())", "(((())()))(())()()", "(((())()))()((()))", "(((())()))()(()())", "(((())()))()(())()", "(((())()))()()(())", "(((())()))()()()()", "(((()))((((())))))", "(((()))(((()()))))", "(((()))(((())())))", "(((()))(((()))()))", "(((()))(((())))())", "(((()))(((()))))()", "(((()))((()(()))))", "(((()))((()()())))", "(((()))((()())()))", "(((()))((()()))())", "(((()))((()())))()", "(((()))((())(())))", "(((()))((())()()))", "(((()))((())())())", "(((()))((())()))()", "(((()))((()))(()))", "(((()))((()))()())", "(((()))((()))())()", "(((()))((())))(())", "(((()))((())))()()", "(((()))(()((()))))", "(((()))(()(()())))", "(((()))(()(())()))", "(((()))(()(()))())", "(((()))(()(())))()", "(((()))(()()(())))", "(((()))(()()()()))", "(((()))(()()())())", "(((()))(()()()))()", "(((()))(()())(()))", "(((()))(()())()())", "(((()))(()())())()", "(((()))(()()))(())", "(((()))(()()))()()", "(((()))(())((())))", "(((()))(())(()()))", "(((()))(())(())())", "(((()))(())(()))()", "(((()))(())()(()))", "(((()))(())()()())", "(((()))(())()())()", "(((()))(())())(())", "(((()))(())())()()", "(((()))(()))((()))", "(((()))(()))(()())", "(((()))(()))(())()", "(((()))(()))()(())", "(((()))(()))()()()", "(((()))()(((()))))", "(((()))()((()())))", "(((()))()((())()))", "(((()))()((()))())", "(((()))()((())))()", "(((()))()(()(())))", "(((()))()(()()()))", "(((()))()(()())())", "(((()))()(()()))()", "(((()))()(())(()))", "(((()))()(())()())", "(((()))()(())())()", "(((()))()(()))(())", "(((()))()(()))()()", "(((()))()()((())))", "(((()))()()(()()))", "(((()))()()(())())", "(((()))()()(()))()", "(((()))()()()(()))", "(((()))()()()()())", "(((()))()()()())()", "(((()))()()())(())", "(((()))()()())()()", "(((()))()())((()))", "(((()))()())(()())", "(((()))()())(())()", "(((()))()())()(())", "(((()))()())()()()", "(((()))())(((())))", "(((()))())((()()))", "(((()))())((())())", "(((()))())((()))()", "(((()))())(()(()))", "(((()))())(()()())", "(((()))())(()())()", "(((()))())(())(())", "(((()))())(())()()", "(((()))())()((()))", "(((()))())()(()())", "(((()))())()(())()", "(((()))())()()(())", "(((()))())()()()()", "(((())))((((()))))", "(((())))(((()())))", "(((())))(((())()))", "(((())))(((()))())", "(((())))(((())))()", "(((())))((()(())))", "(((())))((()()()))", "(((())))((()())())", "(((())))((()()))()", "(((())))((())(()))", "(((())))((())()())", "(((())))((())())()", "(((())))((()))(())", "(((())))((()))()()", "(((())))(()((())))", "(((())))(()(()()))", "(((())))(()(())())", "(((())))(()(()))()", "(((())))(()()(()))", "(((())))(()()()())", "(((())))(()()())()", "(((())))(()())(())", "(((())))(()())()()", "(((())))(())((()))", "(((())))(())(()())", "(((())))(())(())()", "(((())))(())()(())", "(((())))(())()()()", "(((())))()(((())))", "(((())))()((()()))", "(((())))()((())())", "(((())))()((()))()", "(((())))()(()(()))", "(((())))()(()()())", "(((())))()(()())()", "(((())))()(())(())", "(((())))()(())()()", "(((())))()()((()))", "(((())))()()(()())", "(((())))()()(())()", "(((())))()()()(())", "(((())))()()()()()", "((()(((((())))))))", "((()((((()()))))))", "((()((((())())))))", "((()((((()))()))))", "((()((((())))())))", "((()((((()))))()))", "((()((((())))))())", "((()((((()))))))()", "((()(((()(()))))))", "((()(((()()())))))", "((()(((()())()))))", "((()(((()()))())))", "((()(((()())))()))", "((()(((()()))))())", "((()(((()())))))()", "((()(((())(())))))", "((()(((())()()))))", "((()(((())())())))", "((()(((())()))()))", "((()(((())())))())", "((()(((())()))))()", "((()(((()))(()))))", "((()(((()))()())))", "((()(((()))())()))", "((()(((()))()))())", "((()(((()))())))()", "((()(((())))(())))", "((()(((())))()()))", "((()(((())))())())", "((()(((())))()))()", "((()(((()))))(()))", "((()(((()))))()())", "((()(((()))))())()", "((()(((())))))(())", "((()(((())))))()()", "((()((()((()))))))", "((()((()(()())))))", "((()((()(())()))))", "((()((()(()))())))", "((()((()(())))()))", "((()((()(()))))())", "((()((()(())))))()", "((()((()()(())))))", "((()((()()()()))))", "((()((()()())())))", "((()((()()()))()))", "((()((()()())))())", "((()((()()()))))()", "((()((()())(()))))", "((()((()())()())))", "((()((()())())()))", "((()((()())()))())", "((()((()())())))()", "((()((()()))(())))", "((()((()()))()()))", "((()((()()))())())", "((()((()()))()))()", "((()((()())))(()))", "((()((()())))()())", "((()((()())))())()", "((()((()()))))(())", "((()((()()))))()()", "((()((())((())))))", "((()((())(()()))))", "((()((())(())())))", "((()((())(()))()))", "((()((())(())))())", "((()((())(()))))()", "((()((())()(()))))", "((()((())()()())))", "((()((())()())()))", "((()((())()()))())", "((()((())()())))()", "((()((())())(())))", "((()((())())()()))", "((()((())())())())", "((()((())())()))()", "((()((())()))(()))", "((()((())()))()())", "((()((())()))())()", "((()((())())))(())", "((()((())())))()()", "((()((()))((()))))", "((()((()))(()())))", "((()((()))(())()))", "((()((()))(()))())", "((()((()))(())))()", "((()((()))()(())))", "((()((()))()()()))", "((()((()))()())())", "((()((()))()()))()", "((()((()))())(()))", "((()((()))())()())", "((()((()))())())()", "((()((()))()))(())", "((()((()))()))()()", "((()((())))((())))", "((()((())))(()()))", "((()((())))(())())", "((()((())))(()))()", "((()((())))()(()))", "((()((())))()()())", "((()((())))()())()", "((()((())))())(())", "((()((())))())()()", "((()((()))))((()))", "((()((()))))(()())", "((()((()))))(())()", "((()((()))))()(())", "((()((()))))()()()", "((()(()(((()))))))", "((()(()((()())))))", "((()(()((())()))))", "((()(()((()))())))", "((()(()((())))()))", "((()(()((()))))())", "((()(()((())))))()", "((()(()(()(())))))", "((()(()(()()()))))", "((()(()(()())())))", "((()(()(()()))()))", "((()(()(()())))())", "((()(()(()()))))()", "((()(()(())(()))))", "((()(()(())()())))", "((()(()(())())()))", "((()(()(())()))())", "((()(()(())())))()", "((()(()(()))(())))", "((()(()(()))()()))", "((()(()(()))())())", "((()(()(()))()))()", "((()(()(())))(()))", "((()(()(())))()())", "((()(()(())))())()", "((()(()(()))))(())", "((()(()(()))))()()", "((()(()()((())))))", "((()(()()(()()))))", "((()(()()(())())))", "((()(()()(()))()))", "((()(()()(())))())", "((()(()()(()))))()", "((()(()()()(()))))", "((()(()()()()())))", "((()(()()()())()))", "((()(()()()()))())", "((()(()()()())))()", "((()(()()())(())))", "((()(()()())()()))", "((()(()()())())())", "((()(()()())()))()", "((()(()()()))(()))", "((()(()()()))()())", "((()(()()()))())()", "((()(()()())))(())", "((()(()()())))()()", "((()(()())((()))))", "((()(()())(()())))", "((()(()())(())()))", "((()(()())(()))())", "((()(()())(())))()", "((()(()())()(())))", "((()(()())()()()))", "((()(()())()())())", "((()(()())()()))()", "((()(()())())(()))", "((()(()())())()())", "((()(()())())())()", "((()(()())()))(())", "((()(()())()))()()", "((()(()()))((())))", "((()(()()))(()()))", "((()(()()))(())())", "((()(()()))(()))()", "((()(()()))()(()))", "((()(()()))()()())", "((()(()()))()())()", "((()(()()))())(())", "((()(()()))())()()", "((()(()())))((()))", "((()(()())))(()())", "((()(()())))(())()", "((()(()())))()(())", "((()(()())))()()()", "((()(())(((())))))", "((()(())((()()))))", "((()(())((())())))", "((()(())((()))()))", "((()(())((())))())", "((()(())((()))))()", "((()(())(()(()))))", "((()(())(()()())))", "((()(())(()())()))", "((()(())(()()))())", "((()(())(()())))()", "((()(())(())(())))", "((()(())(())()()))", "((()(())(())())())", "((()(())(())()))()", "((()(())(()))(()))", "((()(())(()))()())", "((()(())(()))())()", "((()(())(())))(())", "((()(())(())))()()", "((()(())()((()))))", "((()(())()(()())))", "((()(())()(())()))", "((()(())()(()))())", "((()(())()(())))()", "((()(())()()(())))", "((()(())()()()()))", "((()(())()()())())", "((()(())()()()))()", "((()(())()())(()))", "((()(())()())()())", "((()(())()())())()", "((()(())()()))(())", "((()(())()()))()()", "((()(())())((())))", "((()(())())(()()))", "((()(())())(())())", "((()(())())(()))()", "((()(())())()(()))", "((()(())())()()())", "((()(())())()())()", "((()(())())())(())", "((()(())())())()()", "((()(())()))((()))", "((()(())()))(()())", "((()(())()))(())()", "((()(())()))()(())", "((()(())()))()()()", "((()(()))(((()))))", "((()(()))((()())))", "((()(()))((())()))", "((()(()))((()))())", "((()(()))((())))()", "((()(()))(()(())))", "((()(()))(()()()))", "((()(()))(()())())", "((()(()))(()()))()", "((()(()))(())(()))", "((()(()))(())()())", "((()(()))(())())()", "((()(()))(()))(())", "((()(()))(()))()()", "((()(()))()((())))", "((()(()))()(()()))", "((()(()))()(())())", "((()(()))()(()))()", "((()(()))()()(()))", "((()(()))()()()())", "((()(()))()()())()", "((()(()))()())(())", "((()(()))()())()()", "((()(()))())((()))", "((()(()))())(()())", "((()(()))())(())()", "((()(()))())()(())", "((()(()))())()()()", "((()(())))(((())))", "((()(())))((()()))", "((()(())))((())())", "((()(())))((()))()", "((()(())))(()(()))", "((()(())))(()()())", "((()(())))(()())()", "((()(())))(())(())", "((()(())))(())()()", "((()(())))()((()))", "((()(())))()(()())", "((()(())))()(())()", "((()(())))()()(())", "((()(())))()()()()", "((()()((((()))))))", "((()()(((()())))))", "((()()(((())()))))", "((()()(((()))())))", "((()()(((())))()))", "((()()(((()))))())", "((()()(((())))))()", "((()()((()(())))))", "((()()((()()()))))", "((()()((()())())))", "((()()((()()))()))", "((()()((()())))())", "((()()((()()))))()", "((()()((())(()))))", "((()()((())()())))", "((()()((())())()))", "((()()((())()))())", "((()()((())())))()", "((()()((()))(())))", "((()()((()))()()))", "((()()((()))())())", "((()()((()))()))()", "((()()((())))(()))", "((()()((())))()())", "((()()((())))())()", "((()()((()))))(())", "((()()((()))))()()", "((()()(()((())))))", "((()()(()(()()))))", "((()()(()(())())))", "((()()(()(()))()))", "((()()(()(())))())", "((()()(()(()))))()", "((()()(()()(()))))", "((()()(()()()())))", "((()()(()()())()))", "((()()(()()()))())", "((()()(()()())))()", "((()()(()())(())))", "((()()(()())()()))", "((()()(()())())())", "((()()(()())()))()", "((()()(()()))(()))", "((()()(()()))()())", "((()()(()()))())()", "((()()(()())))(())", "((()()(()())))()()", "((()()(())((()))))", "((()()(())(()())))", "((()()(())(())()))", "((()()(())(()))())", "((()()(())(())))()", "((()()(())()(())))", "((()()(())()()()))", "((()()(())()())())", "((()()(())()()))()", "((()()(())())(()))", "((()()(())())()())", "((()()(())())())()", "((()()(())()))(())", "((()()(())()))()()", "((()()(()))((())))", "((()()(()))(()()))", "((()()(()))(())())", "((()()(()))(()))()", "((()()(()))()(()))", "((()()(()))()()())", "((()()(()))()())()", "((()()(()))())(())", "((()()(()))())()()", "((()()(())))((()))", "((()()(())))(()())", "((()()(())))(())()", "((()()(())))()(())", "((()()(())))()()()", "((()()()(((())))))", "((()()()((()()))))", "((()()()((())())))", "((()()()((()))()))", "((()()()((())))())", "((()()()((()))))()", "((()()()(()(()))))", "((()()()(()()())))", "((()()()(()())()))", "((()()()(()()))())", "((()()()(()())))()", "((()()()(())(())))", "((()()()(())()()))", "((()()()(())())())", "((()()()(())()))()", "((()()()(()))(()))", "((()()()(()))()())", "((()()()(()))())()", "((()()()(())))(())", "((()()()(())))()()", "((()()()()((()))))", "((()()()()(()())))", "((()()()()(())()))", "((()()()()(()))())", "((()()()()(())))()", "((()()()()()(())))", "((()()()()()()()))", "((()()()()()())())", "((()()()()()()))()", "((()()()()())(()))", "((()()()()())()())", "((()()()()())())()", "((()()()()()))(())", "((()()()()()))()()", "((()()()())((())))", "((()()()())(()()))", "((()()()())(())())", "((()()()())(()))()", "((()()()())()(()))", "((()()()())()()())", "((()()()())()())()", "((()()()())())(())", "((()()()())())()()", "((()()()()))((()))", "((()()()()))(()())", "((()()()()))(())()", "((()()()()))()(())", "((()()()()))()()()", "((()()())(((()))))", "((()()())((()())))", "((()()())((())()))", "((()()())((()))())", "((()()())((())))()", "((()()())(()(())))", "((()()())(()()()))", "((()()())(()())())", "((()()())(()()))()", "((()()())(())(()))", "((()()())(())()())", "((()()())(())())()", "((()()())(()))(())", "((()()())(()))()()", "((()()())()((())))", "((()()())()(()()))", "((()()())()(())())", "((()()())()(()))()", "((()()())()()(()))", "((()()())()()()())", "((()()())()()())()", "((()()())()())(())", "((()()())()())()()", "((()()())())((()))", "((()()())())(()())", "((()()())())(())()", "((()()())())()(())", "((()()())())()()()", "((()()()))(((())))", "((()()()))((()()))", "((()()()))((())())", "((()()()))((()))()", "((()()()))(()(()))", "((()()()))(()()())", "((()()()))(()())()", "((()()()))(())(())", "((()()()))(())()()", "((()()()))()((()))", "((()()()))()(()())", "((()()()))()(())()", "((()()()))()()(())", "((()()()))()()()()", "((()())((((())))))", "((()())(((()()))))", "((()())(((())())))", "((()())(((()))()))", "((()())(((())))())", "((()())(((()))))()", "((()())((()(()))))", "((()())((()()())))", "((()())((()())()))", "((()())((()()))())", "((()())((()())))()", "((()())((())(())))", "((()())((())()()))", "((()())((())())())", "((()())((())()))()", "((()())((()))(()))", "((()())((()))()())", "((()())((()))())()", "((()())((())))(())", "((()())((())))()()", "((()())(()((()))))", "((()())(()(()())))", "((()())(()(())()))", "((()())(()(()))())", "((()())(()(())))()", "((()())(()()(())))", "((()())(()()()()))", "((()())(()()())())", "((()())(()()()))()", "((()())(()())(()))", "((()())(()())()())", "((()())(()())())()", "((()())(()()))(())", "((()())(()()))()()", "((()())(())((())))", "((()())(())(()()))", "((()())(())(())())", "((()())(())(()))()", "((()())(())()(()))", "((()())(())()()())", "((()())(())()())()", "((()())(())())(())", "((()())(())())()()", "((()())(()))((()))", "((()())(()))(()())", "((()())(()))(())()", "((()())(()))()(())", "((()())(()))()()()", "((()())()(((()))))", "((()())()((()())))", "((()())()((())()))", "((()())()((()))())", "((()())()((())))()", "((()())()(()(())))", "((()())()(()()()))", "((()())()(()())())", "((()())()(()()))()", "((()())()(())(()))", "((()())()(())()())", "((()())()(())())()", "((()())()(()))(())", "((()())()(()))()()", "((()())()()((())))", "((()())()()(()()))", "((()())()()(())())", "((()())()()(()))()", "((()())()()()(()))", "((()())()()()()())", "((()())()()()())()", "((()())()()())(())", "((()())()()())()()", "((()())()())((()))", "((()())()())(()())", "((()())()())(())()", "((()())()())()(())", "((()())()())()()()", "((()())())(((())))", "((()())())((()()))", "((()())())((())())", "((()())())((()))()", "((()())())(()(()))", "((()())())(()()())", "((()())())(()())()", "((()())())(())(())", "((()())())(())()()", "((()())())()((()))", "((()())())()(()())", "((()())())()(())()", "((()())())()()(())", "((()())())()()()()", "((()()))((((()))))", "((()()))(((()())))", "((()()))(((())()))", "((()()))(((()))())", "((()()))(((())))()", "((()()))((()(())))", "((()()))((()()()))", "((()()))((()())())", "((()()))((()()))()", "((()()))((())(()))", "((()()))((())()())", "((()()))((())())()", "((()()))((()))(())", "((()()))((()))()()", "((()()))(()((())))", "((()()))(()(()()))", "((()()))(()(())())", "((()()))(()(()))()", "((()()))(()()(()))", "((()()))(()()()())", "((()()))(()()())()", "((()()))(()())(())", "((()()))(()())()()", "((()()))(())((()))", "((()()))(())(()())", "((()()))(())(())()", "((()()))(())()(())", "((()()))(())()()()", "((()()))()(((())))", "((()()))()((()()))", "((()()))()((())())", "((()()))()((()))()", "((()()))()(()(()))", "((()()))()(()()())", "((()()))()(()())()", "((()()))()(())(())", "((()()))()(())()()", "((()()))()()((()))", "((()()))()()(()())", "((()()))()()(())()", "((()()))()()()(())", "((()()))()()()()()", "((())(((((()))))))", "((())((((()())))))", "((())((((())()))))", "((())((((()))())))", "((())((((())))()))", "((())((((()))))())", "((())((((())))))()", "((())(((()(())))))", "((())(((()()()))))", "((())(((()())())))", "((())(((()()))()))", "((())(((()())))())", "((())(((()()))))()", "((())(((())(()))))", "((())(((())()())))", "((())(((())())()))", "((())(((())()))())", "((())(((())())))()", "((())(((()))(())))", "((())(((()))()()))", "((())(((()))())())", "((())(((()))()))()", "((())(((())))(()))", "((())(((())))()())", "((())(((())))())()", "((())(((()))))(())", "((())(((()))))()()", "((())((()((())))))", "((())((()(()()))))", "((())((()(())())))", "((())((()(()))()))", "((())((()(())))())", "((())((()(()))))()", "((())((()()(()))))", "((())((()()()())))", "((())((()()())()))", "((())((()()()))())", "((())((()()())))()", "((())((()())(())))", "((())((()())()()))", "((())((()())())())", "((())((()())()))()", "((())((()()))(()))", "((())((()()))()())", "((())((()()))())()", "((())((()())))(())", "((())((()())))()()", "((())((())((()))))", "((())((())(()())))", "((())((())(())()))", "((())((())(()))())", "((())((())(())))()", "((())((())()(())))", "((())((())()()()))", "((())((())()())())", "((())((())()()))()", "((())((())())(()))", "((())((())())()())", "((())((())())())()", "((())((())()))(())", "((())((())()))()()", "((())((()))((())))", "((())((()))(()()))", "((())((()))(())())", "((())((()))(()))()", "((())((()))()(()))", "((())((()))()()())", "((())((()))()())()", "((())((()))())(())", "((())((()))())()()", "((())((())))((()))", "((())((())))(()())", "((())((())))(())()", "((())((())))()(())", "((())((())))()()()", "((())(()(((())))))", "((())(()((()()))))", "((())(()((())())))", "((())(()((()))()))", "((())(()((())))())", "((())(()((()))))()", "((())(()(()(()))))", "((())(()(()()())))", "((())(()(()())()))", "((())(()(()()))())", "((())(()(()())))()", "((())(()(())(())))", "((())(()(())()()))", "((())(()(())())())", "((())(()(())()))()", "((())(()(()))(()))", "((())(()(()))()())", "((())(()(()))())()", "((())(()(())))(())", "((())(()(())))()()", "((())(()()((()))))", "((())(()()(()())))", "((())(()()(())()))", "((())(()()(()))())", "((())(()()(())))()", "((())(()()()(())))", "((())(()()()()()))", "((())(()()()())())", "((())(()()()()))()", "((())(()()())(()))", "((())(()()())()())", "((())(()()())())()", "((())(()()()))(())", "((())(()()()))()()", "((())(()())((())))", "((())(()())(()()))", "((())(()())(())())", "((())(()())(()))()", "((())(()())()(()))", "((())(()())()()())", "((())(()())()())()", "((())(()())())(())", "((())(()())())()()", "((())(()()))((()))", "((())(()()))(()())", "((())(()()))(())()", "((())(()()))()(())", "((())(()()))()()()", "((())(())(((()))))", "((())(())((()())))", "((())(())((())()))", "((())(())((()))())", "((())(())((())))()", "((())(())(()(())))", "((())(())(()()()))", "((())(())(()())())", "((())(())(()()))()", "((())(())(())(()))", "((())(())(())()())", "((())(())(())())()", "((())(())(()))(())", "((())(())(()))()()", "((())(())()((())))", "((())(())()(()()))", "((())(())()(())())", "((())(())()(()))()", "((())(())()()(()))", "((())(())()()()())", "((())(())()()())()", "((())(())()())(())", "((())(())()())()()", "((())(())())((()))", "((())(())())(()())", "((())(())())(())()", "((())(())())()(())", "((())(())())()()()", "((())(()))(((())))", "((())(()))((()()))", "((())(()))((())())", "((())(()))((()))()", "((())(()))(()(()))", "((())(()))(()()())", "((())(()))(()())()", "((())(()))(())(())", "((())(()))(())()()", "((())(()))()((()))", "((())(()))()(()())", "((())(()))()(())()", "((())(()))()()(())", "((())(()))()()()()", "((())()((((())))))", "((())()(((()()))))", "((())()(((())())))", "((())()(((()))()))", "((())()(((())))())", "((())()(((()))))()", "((())()((()(()))))", "((())()((()()())))", "((())()((()())()))", "((())()((()()))())", "((())()((()())))()", "((())()((())(())))", "((())()((())()()))", "((())()((())())())", "((())()((())()))()", "((())()((()))(()))", "((())()((()))()())", "((())()((()))())()", "((())()((())))(())", "((())()((())))()()", "((())()(()((()))))", "((())()(()(()())))", "((())()(()(())()))", "((())()(()(()))())", "((())()(()(())))()", "((())()(()()(())))", "((())()(()()()()))", "((())()(()()())())", "((())()(()()()))()", "((())()(()())(()))", "((())()(()())()())", "((())()(()())())()", "((())()(()()))(())", "((())()(()()))()()", "((())()(())((())))", "((())()(())(()()))", "((())()(())(())())", "((())()(())(()))()", "((())()(())()(()))", "((())()(())()()())", "((())()(())()())()", "((())()(())())(())", "((())()(())())()()", "((())()(()))((()))", "((())()(()))(()())", "((())()(()))(())()", "((())()(()))()(())", "((())()(()))()()()", "((())()()(((()))))", "((())()()((()())))", "((())()()((())()))", "((())()()((()))())", "((())()()((())))()", "((())()()(()(())))", "((())()()(()()()))", "((())()()(()())())", "((())()()(()()))()", "((())()()(())(()))", "((())()()(())()())", "((())()()(())())()", "((())()()(()))(())", "((())()()(()))()()", "((())()()()((())))", "((())()()()(()()))", "((())()()()(())())", "((())()()()(()))()", "((())()()()()(()))", "((())()()()()()())", "((())()()()()())()", "((())()()()())(())", "((())()()()())()()", "((())()()())((()))", "((())()()())(()())", "((())()()())(())()", "((())()()())()(())", "((())()()())()()()", "((())()())(((())))", "((())()())((()()))", "((())()())((())())", "((())()())((()))()", "((())()())(()(()))", "((())()())(()()())", "((())()())(()())()", "((())()())(())(())", "((())()())(())()()", "((())()())()((()))", "((())()())()(()())", "((())()())()(())()", "((())()())()()(())", "((())()())()()()()", "((())())((((()))))", "((())())(((()())))", "((())())(((())()))", "((())())(((()))())", "((())())(((())))()", "((())())((()(())))", "((())())((()()()))", "((())())((()())())", "((())())((()()))()", "((())())((())(()))", "((())())((())()())", "((())())((())())()", "((())())((()))(())", "((())())((()))()()", "((())())(()((())))", "((())())(()(()()))", "((())())(()(())())", "((())())(()(()))()", "((())())(()()(()))", "((())())(()()()())", "((())())(()()())()", "((())())(()())(())", "((())())(()())()()", "((())())(())((()))", "((())())(())(()())", "((())())(())(())()", "((())())(())()(())", "((())())(())()()()", "((())())()(((())))", "((())())()((()()))", "((())())()((())())", "((())())()((()))()", "((())())()(()(()))", "((())())()(()()())", "((())())()(()())()", "((())())()(())(())", "((())())()(())()()", "((())())()()((()))", "((())())()()(()())", "((())())()()(())()", "((())())()()()(())", "((())())()()()()()", "((()))(((((())))))", "((()))((((()()))))", "((()))((((())())))", "((()))((((()))()))", "((()))((((())))())", "((()))((((()))))()", "((()))(((()(()))))", "((()))(((()()())))", "((()))(((()())()))", "((()))(((()()))())", "((()))(((()())))()", "((()))(((())(())))", "((()))(((())()()))", "((()))(((())())())", "((()))(((())()))()", "((()))(((()))(()))", "((()))(((()))()())", "((()))(((()))())()", "((()))(((())))(())", "((()))(((())))()()", "((()))((()((()))))", "((()))((()(()())))", "((()))((()(())()))", "((()))((()(()))())", "((()))((()(())))()", "((()))((()()(())))", "((()))((()()()()))", "((()))((()()())())", "((()))((()()()))()", "((()))((()())(()))", "((()))((()())()())", "((()))((()())())()", "((()))((()()))(())", "((()))((()()))()()", "((()))((())((())))", "((()))((())(()()))", "((()))((())(())())", "((()))((())(()))()", "((()))((())()(()))", "((()))((())()()())", "((()))((())()())()", "((()))((())())(())", "((()))((())())()()", "((()))((()))((()))", "((()))((()))(()())", "((()))((()))(())()", "((()))((()))()(())", "((()))((()))()()()", "((()))(()(((()))))", "((()))(()((()())))", "((()))(()((())()))", "((()))(()((()))())", "((()))(()((())))()", "((()))(()(()(())))", "((()))(()(()()()))", "((()))(()(()())())", "((()))(()(()()))()", "((()))(()(())(()))", "((()))(()(())()())", "((()))(()(())())()", "((()))(()(()))(())", "((()))(()(()))()()", "((()))(()()((())))", "((()))(()()(()()))", "((()))(()()(())())", "((()))(()()(()))()", "((()))(()()()(()))", "((()))(()()()()())", "((()))(()()()())()", "((()))(()()())(())", "((()))(()()())()()", "((()))(()())((()))", "((()))(()())(()())", "((()))(()())(())()", "((()))(()())()(())", "((()))(()())()()()", "((()))(())(((())))", "((()))(())((()()))", "((()))(())((())())", "((()))(())((()))()", "((()))(())(()(()))", "((()))(())(()()())", "((()))(())(()())()", "((()))(())(())(())", "((()))(())(())()()", "((()))(())()((()))", "((()))(())()(()())", "((()))(())()(())()", "((()))(())()()(())", "((()))(())()()()()", "((()))()((((()))))", "((()))()(((()())))", "((()))()(((())()))", "((()))()(((()))())", "((()))()(((())))()", "((()))()((()(())))", "((()))()((()()()))", "((()))()((()())())", "((()))()((()()))()", "((()))()((())(()))", "((()))()((())()())", "((()))()((())())()", "((()))()((()))(())", "((()))()((()))()()", "((()))()(()((())))", "((()))()(()(()()))", "((()))()(()(())())", "((()))()(()(()))()", "((()))()(()()(()))", "((()))()(()()()())", "((()))()(()()())()", "((()))()(()())(())", "((()))()(()())()()", "((()))()(())((()))", "((()))()(())(()())", "((()))()(())(())()", "((()))()(())()(())", "((()))()(())()()()", "((()))()()(((())))", "((()))()()((()()))", "((()))()()((())())", "((()))()()((()))()", "((()))()()(()(()))", "((()))()()(()()())", "((()))()()(()())()", "((()))()()(())(())", "((()))()()(())()()", "((()))()()()((()))", "((()))()()()(()())", "((()))()()()(())()", "((()))()()()()(())", "((()))()()()()()()", "(()((((((())))))))", "(()(((((()()))))))", "(()(((((())())))))", "(()(((((()))()))))", "(()(((((())))())))", "(()(((((()))))()))", "(()(((((())))))())", "(()(((((()))))))()", "(()((((()(()))))))", "(()((((()()())))))", "(()((((()())()))))", "(()((((()()))())))", "(()((((()())))()))", "(()((((()()))))())", "(()((((()())))))()", "(()((((())(())))))", "(()((((())()()))))", "(()((((())())())))", "(()((((())()))()))", "(()((((())())))())", "(()((((())()))))()", "(()((((()))(()))))", "(()((((()))()())))", "(()((((()))())()))", "(()((((()))()))())", "(()((((()))())))()", "(()((((())))(())))", "(()((((())))()()))", "(()((((())))())())", "(()((((())))()))()", "(()((((()))))(()))", "(()((((()))))()())", "(()((((()))))())()", "(()((((())))))(())", "(()((((())))))()()", "(()(((()((()))))))", "(()(((()(()())))))", "(()(((()(())()))))", "(()(((()(()))())))", "(()(((()(())))()))", "(()(((()(()))))())", "(()(((()(())))))()", "(()(((()()(())))))", "(()(((()()()()))))", "(()(((()()())())))", "(()(((()()()))()))", "(()(((()()())))())", "(()(((()()()))))()", "(()(((()())(()))))", "(()(((()())()())))", "(()(((()())())()))", "(()(((()())()))())", "(()(((()())())))()", "(()(((()()))(())))", "(()(((()()))()()))", "(()(((()()))())())", "(()(((()()))()))()", "(()(((()())))(()))", "(()(((()())))()())", "(()(((()())))())()", "(()(((()()))))(())", "(()(((()()))))()()", "(()(((())((())))))", "(()(((())(()()))))", "(()(((())(())())))", "(()(((())(()))()))", "(()(((())(())))())", "(()(((())(()))))()", "(()(((())()(()))))", "(()(((())()()())))", "(()(((())()())()))", "(()(((())()()))())", "(()(((())()())))()", "(()(((())())(())))", "(()(((())())()()))", "(()(((())())())())", "(()(((())())()))()", "(()(((())()))(()))", "(()(((())()))()())", "(()(((())()))())()", "(()(((())())))(())", "(()(((())())))()()", "(()(((()))((()))))", "(()(((()))(()())))", "(()(((()))(())()))", "(()(((()))(()))())", "(()(((()))(())))()", "(()(((()))()(())))", "(()(((()))()()()))", "(()(((()))()())())", "(()(((()))()()))()", "(()(((()))())(()))", "(()(((()))())()())", "(()(((()))())())()", "(()(((()))()))(())", "(()(((()))()))()()", "(()(((())))((())))", "(()(((())))(()()))", "(()(((())))(())())", "(()(((())))(()))()", "(()(((())))()(()))", "(()(((())))()()())", "(()(((())))()())()", "(()(((())))())(())", "(()(((())))())()()", "(()(((()))))((()))", "(()(((()))))(()())", "(()(((()))))(())()", "(()(((()))))()(())", "(()(((()))))()()()", "(()((()(((()))))))", "(()((()((()())))))", "(()((()((())()))))", "(()((()((()))())))", "(()((()((())))()))", "(()((()((()))))())", "(()((()((())))))()", "(()((()(()(())))))", "(()((()(()()()))))", "(()((()(()())())))", "(()((()(()()))()))", "(()((()(()())))())", "(()((()(()()))))()", "(()((()(())(()))))", "(()((()(())()())))", "(()((()(())())()))", "(()((()(())()))())", "(()((()(())())))()", "(()((()(()))(())))", "(()((()(()))()()))", "(()((()(()))())())", "(()((()(()))()))()", "(()((()(())))(()))", "(()((()(())))()())", "(()((()(())))())()", "(()((()(()))))(())", "(()((()(()))))()()", "(()((()()((())))))", "(()((()()(()()))))", "(()((()()(())())))", "(()((()()(()))()))", "(()((()()(())))())", "(()((()()(()))))()", "(()((()()()(()))))", "(()((()()()()())))", "(()((()()()())()))", "(()((()()()()))())", "(()((()()()())))()", "(()((()()())(())))", "(()((()()())()()))", "(()((()()())())())", "(()((()()())()))()", "(()((()()()))(()))", "(()((()()()))()())", "(()((()()()))())()", "(()((()()())))(())", "(()((()()())))()()", "(()((()())((()))))", "(()((()())(()())))", "(()((()())(())()))", "(()((()())(()))())", "(()((()())(())))()", "(()((()())()(())))", "(()((()())()()()))", "(()((()())()())())", "(()((()())()()))()", "(()((()())())(()))", "(()((()())())()())", "(()((()())())())()", "(()((()())()))(())", "(()((()())()))()()", "(()((()()))((())))", "(()((()()))(()()))", "(()((()()))(())())", "(()((()()))(()))()", "(()((()()))()(()))", "(()((()()))()()())", "(()((()()))()())()", "(()((()()))())(())", "(()((()()))())()()", "(()((()())))((()))", "(()((()())))(()())", "(()((()())))(())()", "(()((()())))()(())", "(()((()())))()()()", "(()((())(((())))))", "(()((())((()()))))", "(()((())((())())))", "(()((())((()))()))", "(()((())((())))())", "(()((())((()))))()", "(()((())(()(()))))", "(()((())(()()())))", "(()((())(()())()))", "(()((())(()()))())", "(()((())(()())))()", "(()((())(())(())))", "(()((())(())()()))", "(()((())(())())())", "(()((())(())()))()", "(()((())(()))(()))", "(()((())(()))()())", "(()((())(()))())()", "(()((())(())))(())", "(()((())(())))()()", "(()((())()((()))))", "(()((())()(()())))", "(()((())()(())()))", "(()((())()(()))())", "(()((())()(())))()", "(()((())()()(())))", "(()((())()()()()))", "(()((())()()())())", "(()((())()()()))()", "(()((())()())(()))", "(()((())()())()())", "(()((())()())())()", "(()((())()()))(())", "(()((())()()))()()", "(()((())())((())))", "(()((())())(()()))", "(()((())())(())())", "(()((())())(()))()", "(()((())())()(()))", "(()((())())()()())", "(()((())())()())()", "(()((())())())(())", "(()((())())())()()", "(()((())()))((()))", "(()((())()))(()())", "(()((())()))(())()", "(()((())()))()(())", "(()((())()))()()()", "(()((()))(((()))))", "(()((()))((()())))", "(()((()))((())()))", "(()((()))((()))())", "(()((()))((())))()", "(()((()))(()(())))", "(()((()))(()()()))", "(()((()))(()())())", "(()((()))(()()))()", "(()((()))(())(()))", "(()((()))(())()())", "(()((()))(())())()", "(()((()))(()))(())", "(()((()))(()))()()", "(()((()))()((())))", "(()((()))()(()()))", "(()((()))()(())())", "(()((()))()(()))()", "(()((()))()()(()))", "(()((()))()()()())", "(()((()))()()())()", "(()((()))()())(())", "(()((()))()())()()", "(()((()))())((()))", "(()((()))())(()())", "(()((()))())(())()", "(()((()))())()(())", "(()((()))())()()()", "(()((())))(((())))", "(()((())))((()()))", "(()((())))((())())", "(()((())))((()))()", "(()((())))(()(()))", "(()((())))(()()())", "(()((())))(()())()", "(()((())))(())(())", "(()((())))(())()()", "(()((())))()((()))", "(()((())))()(()())", "(()((())))()(())()", "(()((())))()()(())", "(()((())))()()()()", "(()(()((((()))))))", "(()(()(((()())))))", "(()(()(((())()))))", "(()(()(((()))())))", "(()(()(((())))()))", "(()(()(((()))))())", "(()(()(((())))))()", "(()(()((()(())))))", "(()(()((()()()))))", "(()(()((()())())))", "(()(()((()()))()))", "(()(()((()())))())", "(()(()((()()))))()", "(()(()((())(()))))", "(()(()((())()())))", "(()(()((())())()))", "(()(()((())()))())", "(()(()((())())))()", "(()(()((()))(())))", "(()(()((()))()()))", "(()(()((()))())())", "(()(()((()))()))()", "(()(()((())))(()))", "(()(()((())))()())", "(()(()((())))())()", "(()(()((()))))(())", "(()(()((()))))()()", "(()(()(()((())))))", "(()(()(()(()()))))", "(()(()(()(())())))", "(()(()(()(()))()))", "(()(()(()(())))())", "(()(()(()(()))))()", "(()(()(()()(()))))", "(()(()(()()()())))", "(()(()(()()())()))", "(()(()(()()()))())", "(()(()(()()())))()", "(()(()(()())(())))", "(()(()(()())()()))", "(()(()(()())())())", "(()(()(()())()))()", "(()(()(()()))(()))", "(()(()(()()))()())", "(()(()(()()))())()", "(()(()(()())))(())", "(()(()(()())))()()", "(()(()(())((()))))", "(()(()(())(()())))", "(()(()(())(())()))", "(()(()(())(()))())", "(()(()(())(())))()", "(()(()(())()(())))", "(()(()(())()()()))", "(()(()(())()())())", "(()(()(())()()))()", "(()(()(())())(()))", "(()(()(())())()())", "(()(()(())())())()", "(()(()(())()))(())", "(()(()(())()))()()", "(()(()(()))((())))", "(()(()(()))(()()))", "(()(()(()))(())())", "(()(()(()))(()))()", "(()(()(()))()(()))", "(()(()(()))()()())", "(()(()(()))()())()", "(()(()(()))())(())", "(()(()(()))())()()", "(()(()(())))((()))", "(()(()(())))(()())", "(()(()(())))(())()", "(()(()(())))()(())", "(()(()(())))()()()", "(()(()()(((())))))", "(()(()()((()()))))", "(()(()()((())())))", "(()(()()((()))()))", "(()(()()((())))())", "(()(()()((()))))()", "(()(()()(()(()))))", "(()(()()(()()())))", "(()(()()(()())()))", "(()(()()(()()))())", "(()(()()(()())))()", "(()(()()(())(())))", "(()(()()(())()()))", "(()(()()(())())())", "(()(()()(())()))()", "(()(()()(()))(()))", "(()(()()(()))()())", "(()(()()(()))())()", "(()(()()(())))(())", "(()(()()(())))()()", "(()(()()()((()))))", "(()(()()()(()())))", "(()(()()()(())()))", "(()(()()()(()))())", "(()(()()()(())))()", "(()(()()()()(())))", "(()(()()()()()()))", "(()(()()()()())())", "(()(()()()()()))()", "(()(()()()())(()))", "(()(()()()())()())", "(()(()()()())())()", "(()(()()()()))(())", "(()(()()()()))()()", "(()(()()())((())))", "(()(()()())(()()))", "(()(()()())(())())", "(()(()()())(()))()", "(()(()()())()(()))", "(()(()()())()()())", "(()(()()())()())()", "(()(()()())())(())", "(()(()()())())()()", "(()(()()()))((()))", "(()(()()()))(()())", "(()(()()()))(())()", "(()(()()()))()(())", "(()(()()()))()()()", "(()(()())(((()))))", "(()(()())((()())))", "(()(()())((())()))", "(()(()())((()))())", "(()(()())((())))()", "(()(()())(()(())))", "(()(()())(()()()))", "(()(()())(()())())", "(()(()())(()()))()", "(()(()())(())(()))", "(()(()())(())()())", "(()(()())(())())()", "(()(()())(()))(())", "(()(()())(()))()()", "(()(()())()((())))", "(()(()())()(()()))", "(()(()())()(())())", "(()(()())()(()))()", "(()(()())()()(()))", "(()(()())()()()())", "(()(()())()()())()", "(()(()())()())(())", "(()(()())()())()()", "(()(()())())((()))", "(()(()())())(()())", "(()(()())())(())()", "(()(()())())()(())", "(()(()())())()()()", "(()(()()))(((())))", "(()(()()))((()()))", "(()(()()))((())())", "(()(()()))((()))()", "(()(()()))(()(()))", "(()(()()))(()()())", "(()(()()))(()())()", "(()(()()))(())(())", "(()(()()))(())()()", "(()(()()))()((()))", "(()(()()))()(()())", "(()(()()))()(())()", "(()(()()))()()(())", "(()(()()))()()()()", "(()(())((((())))))", "(()(())(((()()))))", "(()(())(((())())))", "(()(())(((()))()))", "(()(())(((())))())", "(()(())(((()))))()", "(()(())((()(()))))", "(()(())((()()())))", "(()(())((()())()))", "(()(())((()()))())", "(()(())((()())))()", "(()(())((())(())))", "(()(())((())()()))", "(()(())((())())())", "(()(())((())()))()", "(()(())((()))(()))", "(()(())((()))()())", "(()(())((()))())()", "(()(())((())))(())", "(()(())((())))()()", "(()(())(()((()))))", "(()(())(()(()())))", "(()(())(()(())()))", "(()(())(()(()))())", "(()(())(()(())))()", "(()(())(()()(())))", "(()(())(()()()()))", "(()(())(()()())())", "(()(())(()()()))()", "(()(())(()())(()))", "(()(())(()())()())", "(()(())(()())())()", "(()(())(()()))(())", "(()(())(()()))()()", "(()(())(())((())))", "(()(())(())(()()))", "(()(())(())(())())", "(()(())(())(()))()", "(()(())(())()(()))", "(()(())(())()()())", "(()(())(())()())()", "(()(())(())())(())", "(()(())(())())()()", "(()(())(()))((()))", "(()(())(()))(()())", "(()(())(()))(())()", "(()(())(()))()(())", "(()(())(()))()()()", "(()(())()(((()))))", "(()(())()((()())))", "(()(())()((())()))", "(()(())()((()))())", "(()(())()((())))()", "(()(())()(()(())))", "(()(())()(()()()))", "(()(())()(()())())", "(()(())()(()()))()", "(()(())()(())(()))", "(()(())()(())()())", "(()(())()(())())()", "(()(())()(()))(())", "(()(())()(()))()()", "(()(())()()((())))", "(()(())()()(()()))", "(()(())()()(())())", "(()(())()()(()))()", "(()(())()()()(()))", "(()(())()()()()())", "(()(())()()()())()", "(()(())()()())(())", "(()(())()()())()()", "(()(())()())((()))", "(()(())()())(()())", "(()(())()())(())()", "(()(())()())()(())", "(()(())()())()()()", "(()(())())(((())))", "(()(())())((()()))", "(()(())())((())())", "(()(())())((()))()", "(()(())())(()(()))", "(()(())())(()()())", "(()(())())(()())()", "(()(())())(())(())", "(()(())())(())()()", "(()(())())()((()))", "(()(())())()(()())", "(()(())())()(())()", "(()(())())()()(())", "(()(())())()()()()", "(()(()))((((()))))", "(()(()))(((()())))", "(()(()))(((())()))", "(()(()))(((()))())", "(()(()))(((())))()", "(()(()))((()(())))", "(()(()))((()()()))", "(()(()))((()())())", "(()(()))((()()))()", "(()(()))((())(()))", "(()(()))((())()())", "(()(()))((())())()", "(()(()))((()))(())", "(()(()))((()))()()", "(()(()))(()((())))", "(()(()))(()(()()))", "(()(()))(()(())())", "(()(()))(()(()))()", "(()(()))(()()(()))", "(()(()))(()()()())", "(()(()))(()()())()", "(()(()))(()())(())", "(()(()))(()())()()", "(()(()))(())((()))", "(()(()))(())(()())", "(()(()))(())(())()", "(()(()))(())()(())", "(()(()))(())()()()", "(()(()))()(((())))", "(()(()))()((()()))", "(()(()))()((())())", "(()(()))()((()))()", "(()(()))()(()(()))", "(()(()))()(()()())", "(()(()))()(()())()", "(()(()))()(())(())", "(()(()))()(())()()", "(()(()))()()((()))", "(()(()))()()(()())", "(()(()))()()(())()", "(()(()))()()()(())", "(()(()))()()()()()", "(()()(((((()))))))", "(()()((((()())))))", "(()()((((())()))))", "(()()((((()))())))", "(()()((((())))()))", "(()()((((()))))())", "(()()((((())))))()", "(()()(((()(())))))", "(()()(((()()()))))", "(()()(((()())())))", "(()()(((()()))()))", "(()()(((()())))())", "(()()(((()()))))()", "(()()(((())(()))))", "(()()(((())()())))", "(()()(((())())()))", "(()()(((())()))())", "(()()(((())())))()", "(()()(((()))(())))", "(()()(((()))()()))", "(()()(((()))())())", "(()()(((()))()))()", "(()()(((())))(()))", "(()()(((())))()())", "(()()(((())))())()", "(()()(((()))))(())", "(()()(((()))))()()", "(()()((()((())))))", "(()()((()(()()))))", "(()()((()(())())))", "(()()((()(()))()))", "(()()((()(())))())", "(()()((()(()))))()", "(()()((()()(()))))", "(()()((()()()())))", "(()()((()()())()))", "(()()((()()()))())", "(()()((()()())))()", "(()()((()())(())))", "(()()((()())()()))", "(()()((()())())())", "(()()((()())()))()", "(()()((()()))(()))", "(()()((()()))()())", "(()()((()()))())()", "(()()((()())))(())", "(()()((()())))()()", "(()()((())((()))))", "(()()((())(()())))", "(()()((())(())()))", "(()()((())(()))())", "(()()((())(())))()", "(()()((())()(())))", "(()()((())()()()))", "(()()((())()())())", "(()()((())()()))()", "(()()((())())(()))", "(()()((())())()())", "(()()((())())())()", "(()()((())()))(())", "(()()((())()))()()", "(()()((()))((())))", "(()()((()))(()()))", "(()()((()))(())())", "(()()((()))(()))()", "(()()((()))()(()))", "(()()((()))()()())", "(()()((()))()())()", "(()()((()))())(())", "(()()((()))())()()", "(()()((())))((()))", "(()()((())))(()())", "(()()((())))(())()", "(()()((())))()(())", "(()()((())))()()()", "(()()(()(((())))))", "(()()(()((()()))))", "(()()(()((())())))", "(()()(()((()))()))", "(()()(()((())))())", "(()()(()((()))))()", "(()()(()(()(()))))", "(()()(()(()()())))", "(()()(()(()())()))", "(()()(()(()()))())", "(()()(()(()())))()", "(()()(()(())(())))", "(()()(()(())()()))", "(()()(()(())())())", "(()()(()(())()))()", "(()()(()(()))(()))", "(()()(()(()))()())", "(()()(()(()))())()", "(()()(()(())))(())", "(()()(()(())))()()", "(()()(()()((()))))", "(()()(()()(()())))", "(()()(()()(())()))", "(()()(()()(()))())", "(()()(()()(())))()", "(()()(()()()(())))", "(()()(()()()()()))", "(()()(()()()())())", "(()()(()()()()))()", "(()()(()()())(()))", "(()()(()()())()())", "(()()(()()())())()", "(()()(()()()))(())", "(()()(()()()))()()", "(()()(()())((())))", "(()()(()())(()()))", "(()()(()())(())())", "(()()(()())(()))()", "(()()(()())()(()))", "(()()(()())()()())", "(()()(()())()())()", "(()()(()())())(())", "(()()(()())())()()", "(()()(()()))((()))", "(()()(()()))(()())", "(()()(()()))(())()", "(()()(()()))()(())", "(()()(()()))()()()", "(()()(())(((()))))", "(()()(())((()())))", "(()()(())((())()))", "(()()(())((()))())", "(()()(())((())))()", "(()()(())(()(())))", "(()()(())(()()()))", "(()()(())(()())())", "(()()(())(()()))()", "(()()(())(())(()))", "(()()(())(())()())", "(()()(())(())())()", "(()()(())(()))(())", "(()()(())(()))()()", "(()()(())()((())))", "(()()(())()(()()))", "(()()(())()(())())", "(()()(())()(()))()", "(()()(())()()(()))", "(()()(())()()()())", "(()()(())()()())()", "(()()(())()())(())", "(()()(())()())()()", "(()()(())())((()))", "(()()(())())(()())", "(()()(())())(())()", "(()()(())())()(())", "(()()(())())()()()", "(()()(()))(((())))", "(()()(()))((()()))", "(()()(()))((())())", "(()()(()))((()))()", "(()()(()))(()(()))", "(()()(()))(()()())", "(()()(()))(()())()", "(()()(()))(())(())", "(()()(()))(())()()", "(()()(()))()((()))", "(()()(()))()(()())", "(()()(()))()(())()", "(()()(()))()()(())", "(()()(()))()()()()", "(()()()((((())))))", "(()()()(((()()))))", "(()()()(((())())))", "(()()()(((()))()))", "(()()()(((())))())", "(()()()(((()))))()", "(()()()((()(()))))", "(()()()((()()())))", "(()()()((()())()))", "(()()()((()()))())", "(()()()((()())))()", "(()()()((())(())))", "(()()()((())()()))", "(()()()((())())())", "(()()()((())()))()", "(()()()((()))(()))", "(()()()((()))()())", "(()()()((()))())()", "(()()()((())))(())", "(()()()((())))()()", "(()()()(()((()))))", "(()()()(()(()())))", "(()()()(()(())()))", "(()()()(()(()))())", "(()()()(()(())))()", "(()()()(()()(())))", "(()()()(()()()()))", "(()()()(()()())())", "(()()()(()()()))()", "(()()()(()())(()))", "(()()()(()())()())", "(()()()(()())())()", "(()()()(()()))(())", "(()()()(()()))()()", "(()()()(())((())))", "(()()()(())(()()))", "(()()()(())(())())", "(()()()(())(()))()", "(()()()(())()(()))", "(()()()(())()()())", "(()()()(())()())()", "(()()()(())())(())", "(()()()(())())()()", "(()()()(()))((()))", "(()()()(()))(()())", "(()()()(()))(())()", "(()()()(()))()(())", "(()()()(()))()()()", "(()()()()(((()))))", "(()()()()((()())))", "(()()()()((())()))", "(()()()()((()))())", "(()()()()((())))()", "(()()()()(()(())))", "(()()()()(()()()))", "(()()()()(()())())", "(()()()()(()()))()", "(()()()()(())(()))", "(()()()()(())()())", "(()()()()(())())()", "(()()()()(()))(())", "(()()()()(()))()()", "(()()()()()((())))", "(()()()()()(()()))", "(()()()()()(())())", "(()()()()()(()))()", "(()()()()()()(()))", "(()()()()()()()())", "(()()()()()()())()", "(()()()()()())(())", "(()()()()()())()()", "(()()()()())((()))", "(()()()()())(()())", "(()()()()())(())()", "(()()()()())()(())", "(()()()()())()()()", "(()()()())(((())))", "(()()()())((()()))", "(()()()())((())())", "(()()()())((()))()", "(()()()())(()(()))", "(()()()())(()()())", "(()()()())(()())()", "(()()()())(())(())", "(()()()())(())()()", "(()()()())()((()))", "(()()()())()(()())", "(()()()())()(())()", "(()()()())()()(())", "(()()()())()()()()", "(()()())((((()))))", "(()()())(((()())))", "(()()())(((())()))", "(()()())(((()))())", "(()()())(((())))()", "(()()())((()(())))", "(()()())((()()()))", "(()()())((()())())", "(()()())((()()))()", "(()()())((())(()))", "(()()())((())()())", "(()()())((())())()", "(()()())((()))(())", "(()()())((()))()()", "(()()())(()((())))", "(()()())(()(()()))", "(()()())(()(())())", "(()()())(()(()))()", "(()()())(()()(()))", "(()()())(()()()())", "(()()())(()()())()", "(()()())(()())(())", "(()()())(()())()()", "(()()())(())((()))", "(()()())(())(()())", "(()()())(())(())()", "(()()())(())()(())", "(()()())(())()()()", "(()()())()(((())))", "(()()())()((()()))", "(()()())()((())())", "(()()())()((()))()", "(()()())()(()(()))", "(()()())()(()()())", "(()()())()(()())()", "(()()())()(())(())", "(()()())()(())()()", "(()()())()()((()))", "(()()())()()(()())", "(()()())()()(())()", "(()()())()()()(())", "(()()())()()()()()", "(()())(((((())))))", "(()())((((()()))))", "(()())((((())())))", "(()())((((()))()))", "(()())((((())))())", "(()())((((()))))()", "(()())(((()(()))))", "(()())(((()()())))", "(()())(((()())()))", "(()())(((()()))())", "(()())(((()())))()", "(()())(((())(())))", "(()())(((())()()))", "(()())(((())())())", "(()())(((())()))()", "(()())(((()))(()))", "(()())(((()))()())", "(()())(((()))())()", "(()())(((())))(())", "(()())(((())))()()", "(()())((()((()))))", "(()())((()(()())))", "(()())((()(())()))", "(()())((()(()))())", "(()())((()(())))()", "(()())((()()(())))", "(()())((()()()()))", "(()())((()()())())", "(()())((()()()))()", "(()())((()())(()))", "(()())((()())()())", "(()())((()())())()", "(()())((()()))(())", "(()())((()()))()()", "(()())((())((())))", "(()())((())(()()))", "(()())((())(())())", "(()())((())(()))()", "(()())((())()(()))", "(()())((())()()())", "(()())((())()())()", "(()())((())())(())", "(()())((())())()()", "(()())((()))((()))", "(()())((()))(()())", "(()())((()))(())()", "(()())((()))()(())", "(()())((()))()()()", "(()())(()(((()))))", "(()())(()((()())))", "(()())(()((())()))", "(()())(()((()))())", "(()())(()((())))()", "(()())(()(()(())))", "(()())(()(()()()))", "(()())(()(()())())", "(()())(()(()()))()", "(()())(()(())(()))", "(()())(()(())()())", "(()())(()(())())()", "(()())(()(()))(())", "(()())(()(()))()()", "(()())(()()((())))", "(()())(()()(()()))", "(()())(()()(())())", "(()())(()()(()))()", "(()())(()()()(()))", "(()())(()()()()())", "(()())(()()()())()", "(()())(()()())(())", "(()())(()()())()()", "(()())(()())((()))", "(()())(()())(()())", "(()())(()())(())()", "(()())(()())()(())", "(()())(()())()()()", "(()())(())(((())))", "(()())(())((()()))", "(()())(())((())())", "(()())(())((()))()", "(()())(())(()(()))", "(()())(())(()()())", "(()())(())(()())()", "(()())(())(())(())", "(()())(())(())()()", "(()())(())()((()))", "(()())(())()(()())", "(()())(())()(())()", "(()())(())()()(())", "(()())(())()()()()", "(()())()((((()))))", "(()())()(((()())))", "(()())()(((())()))", "(()())()(((()))())", "(()())()(((())))()", "(()())()((()(())))", "(()())()((()()()))", "(()())()((()())())", "(()())()((()()))()", "(()())()((())(()))", "(()())()((())()())", "(()())()((())())()", "(()())()((()))(())", "(()())()((()))()()", "(()())()(()((())))", "(()())()(()(()()))", "(()())()(()(())())", "(()())()(()(()))()", "(()())()(()()(()))", "(()())()(()()()())", "(()())()(()()())()", "(()())()(()())(())", "(()())()(()())()()", "(()())()(())((()))", "(()())()(())(()())", "(()())()(())(())()", "(()())()(())()(())", "(()())()(())()()()", "(()())()()(((())))", "(()())()()((()()))", "(()())()()((())())", "(()())()()((()))()", "(()())()()(()(()))", "(()())()()(()()())", "(()())()()(()())()", "(()())()()(())(())", "(()())()()(())()()", "(()())()()()((()))", "(()())()()()(()())", "(()())()()()(())()", "(()())()()()()(())", "(()())()()()()()()", "(())((((((()))))))", "(())(((((()())))))", "(())(((((())()))))", "(())(((((()))())))", "(())(((((())))()))", "(())(((((()))))())", "(())(((((())))))()", "(())((((()(())))))", "(())((((()()()))))", "(())((((()())())))", "(())((((()()))()))", "(())((((()())))())", "(())((((()()))))()", "(())((((())(()))))", "(())((((())()())))", "(())((((())())()))", "(())((((())()))())", "(())((((())())))()", "(())((((()))(())))", "(())((((()))()()))", "(())((((()))())())", "(())((((()))()))()", "(())((((())))(()))", "(())((((())))()())", "(())((((())))())()", "(())((((()))))(())", "(())((((()))))()()", "(())(((()((())))))", "(())(((()(()()))))", "(())(((()(())())))", "(())(((()(()))()))", "(())(((()(())))())", "(())(((()(()))))()", "(())(((()()(()))))", "(())(((()()()())))", "(())(((()()())()))", "(())(((()()()))())", "(())(((()()())))()", "(())(((()())(())))", "(())(((()())()()))", "(())(((()())())())", "(())(((()())()))()", "(())(((()()))(()))", "(())(((()()))()())", "(())(((()()))())()", "(())(((()())))(())", "(())(((()())))()()", "(())(((())((()))))", "(())(((())(()())))", "(())(((())(())()))", "(())(((())(()))())", "(())(((())(())))()", "(())(((())()(())))", "(())(((())()()()))", "(())(((())()())())", "(())(((())()()))()", "(())(((())())(()))", "(())(((())())()())", "(())(((())())())()", "(())(((())()))(())", "(())(((())()))()()", "(())(((()))((())))", "(())(((()))(()()))", "(())(((()))(())())", "(())(((()))(()))()", "(())(((()))()(()))", "(())(((()))()()())", "(())(((()))()())()", "(())(((()))())(())", "(())(((()))())()()", "(())(((())))((()))", "(())(((())))(()())", "(())(((())))(())()", "(())(((())))()(())", "(())(((())))()()()", "(())((()(((())))))", "(())((()((()()))))", "(())((()((())())))", "(())((()((()))()))", "(())((()((())))())", "(())((()((()))))()", "(())((()(()(()))))", "(())((()(()()())))", "(())((()(()())()))", "(())((()(()()))())", "(())((()(()())))()", "(())((()(())(())))", "(())((()(())()()))", "(())((()(())())())", "(())((()(())()))()", "(())((()(()))(()))", "(())((()(()))()())", "(())((()(()))())()", "(())((()(())))(())", "(())((()(())))()()", "(())((()()((()))))", "(())((()()(()())))", "(())((()()(())()))", "(())((()()(()))())", "(())((()()(())))()", "(())((()()()(())))", "(())((()()()()()))", "(())((()()()())())", "(())((()()()()))()", "(())((()()())(()))", "(())((()()())()())", "(())((()()())())()", "(())((()()()))(())", "(())((()()()))()()", "(())((()())((())))", "(())((()())(()()))", "(())((()())(())())", "(())((()())(()))()", "(())((()())()(()))", "(())((()())()()())", "(())((()())()())()", "(())((()())())(())", "(())((()())())()()", "(())((()()))((()))", "(())((()()))(()())", "(())((()()))(())()", "(())((()()))()(())", "(())((()()))()()()", "(())((())(((()))))", "(())((())((()())))", "(())((())((())()))", "(())((())((()))())", "(())((())((())))()", "(())((())(()(())))", "(())((())(()()()))", "(())((())(()())())", "(())((())(()()))()", "(())((())(())(()))", "(())((())(())()())", "(())((())(())())()", "(())((())(()))(())", "(())((())(()))()()", "(())((())()((())))", "(())((())()(()()))", "(())((())()(())())", "(())((())()(()))()", "(())((())()()(()))", "(())((())()()()())", "(())((())()()())()", "(())((())()())(())", "(())((())()())()()", "(())((())())((()))", "(())((())())(()())", "(())((())())(())()", "(())((())())()(())", "(())((())())()()()", "(())((()))(((())))", "(())((()))((()()))", "(())((()))((())())", "(())((()))((()))()", "(())((()))(()(()))", "(())((()))(()()())", "(())((()))(()())()", "(())((()))(())(())", "(())((()))(())()()", "(())((()))()((()))", "(())((()))()(()())", "(())((()))()(())()", "(())((()))()()(())", "(())((()))()()()()", "(())(()((((())))))", "(())(()(((()()))))", "(())(()(((())())))", "(())(()(((()))()))", "(())(()(((())))())", "(())(()(((()))))()", "(())(()((()(()))))", "(())(()((()()())))", "(())(()((()())()))", "(())(()((()()))())", "(())(()((()())))()", "(())(()((())(())))", "(())(()((())()()))", "(())(()((())())())", "(())(()((())()))()", "(())(()((()))(()))", "(())(()((()))()())", "(())(()((()))())()", "(())(()((())))(())", "(())(()((())))()()", "(())(()(()((()))))", "(())(()(()(()())))", "(())(()(()(())()))", "(())(()(()(()))())", "(())(()(()(())))()", "(())(()(()()(())))", "(())(()(()()()()))", "(())(()(()()())())", "(())(()(()()()))()", "(())(()(()())(()))", "(())(()(()())()())", "(())(()(()())())()", "(())(()(()()))(())", "(())(()(()()))()()", "(())(()(())((())))", "(())(()(())(()()))", "(())(()(())(())())", "(())(()(())(()))()", "(())(()(())()(()))", "(())(()(())()()())", "(())(()(())()())()", "(())(()(())())(())", "(())(()(())())()()", "(())(()(()))((()))", "(())(()(()))(()())", "(())(()(()))(())()", "(())(()(()))()(())", "(())(()(()))()()()", "(())(()()(((()))))", "(())(()()((()())))", "(())(()()((())()))", "(())(()()((()))())", "(())(()()((())))()", "(())(()()(()(())))", "(())(()()(()()()))", "(())(()()(()())())", "(())(()()(()()))()", "(())(()()(())(()))", "(())(()()(())()())", "(())(()()(())())()", "(())(()()(()))(())", "(())(()()(()))()()", "(())(()()()((())))", "(())(()()()(()()))", "(())(()()()(())())", "(())(()()()(()))()", "(())(()()()()(()))", "(())(()()()()()())", "(())(()()()()())()", "(())(()()()())(())", "(())(()()()())()()", "(())(()()())((()))", "(())(()()())(()())", "(())(()()())(())()", "(())(()()())()(())", "(())(()()())()()()", "(())(()())(((())))", "(())(()())((()()))", "(())(()())((())())", "(())(()())((()))()", "(())(()())(()(()))", "(())(()())(()()())", "(())(()())(()())()", "(())(()())(())(())", "(())(()())(())()()", "(())(()())()((()))", "(())(()())()(()())", "(())(()())()(())()", "(())(()())()()(())", "(())(()())()()()()", "(())(())((((()))))", "(())(())(((()())))", "(())(())(((())()))", "(())(())(((()))())", "(())(())(((())))()", "(())(())((()(())))", "(())(())((()()()))", "(())(())((()())())", "(())(())((()()))()", "(())(())((())(()))", "(())(())((())()())", "(())(())((())())()", "(())(())((()))(())", "(())(())((()))()()", "(())(())(()((())))", "(())(())(()(()()))", "(())(())(()(())())", "(())(())(()(()))()", "(())(())(()()(()))", "(())(())(()()()())", "(())(())(()()())()", "(())(())(()())(())", "(())(())(()())()()", "(())(())(())((()))", "(())(())(())(()())", "(())(())(())(())()", "(())(())(())()(())", "(())(())(())()()()", "(())(())()(((())))", "(())(())()((()()))", "(())(())()((())())", "(())(())()((()))()", "(())(())()(()(()))", "(())(())()(()()())", "(())(())()(()())()", "(())(())()(())(())", "(())(())()(())()()", "(())(())()()((()))", "(())(())()()(()())", "(())(())()()(())()", "(())(())()()()(())", "(())(())()()()()()", "(())()(((((())))))", "(())()((((()()))))", "(())()((((())())))", "(())()((((()))()))", "(())()((((())))())", "(())()((((()))))()", "(())()(((()(()))))", "(())()(((()()())))", "(())()(((()())()))", "(())()(((()()))())", "(())()(((()())))()", "(())()(((())(())))", "(())()(((())()()))", "(())()(((())())())", "(())()(((())()))()", "(())()(((()))(()))", "(())()(((()))()())", "(())()(((()))())()", "(())()(((())))(())", "(())()(((())))()()", "(())()((()((()))))", "(())()((()(()())))", "(())()((()(())()))", "(())()((()(()))())", "(())()((()(())))()", "(())()((()()(())))", "(())()((()()()()))", "(())()((()()())())", "(())()((()()()))()", "(())()((()())(()))", "(())()((()())()())", "(())()((()())())()", "(())()((()()))(())", "(())()((()()))()()", "(())()((())((())))", "(())()((())(()()))", "(())()((())(())())", "(())()((())(()))()", "(())()((())()(()))", "(())()((())()()())", "(())()((())()())()", "(())()((())())(())", "(())()((())())()()", "(())()((()))((()))", "(())()((()))(()())", "(())()((()))(())()", "(())()((()))()(())", "(())()((()))()()()", "(())()(()(((()))))", "(())()(()((()())))", "(())()(()((())()))", "(())()(()((()))())", "(())()(()((())))()", "(())()(()(()(())))", "(())()(()(()()()))", "(())()(()(()())())", "(())()(()(()()))()", "(())()(()(())(()))", "(())()(()(())()())", "(())()(()(())())()", "(())()(()(()))(())", "(())()(()(()))()()", "(())()(()()((())))", "(())()(()()(()()))", "(())()(()()(())())", "(())()(()()(()))()", "(())()(()()()(()))", "(())()(()()()()())", "(())()(()()()())()", "(())()(()()())(())", "(())()(()()())()()", "(())()(()())((()))", "(())()(()())(()())", "(())()(()())(())()", "(())()(()())()(())", "(())()(()())()()()", "(())()(())(((())))", "(())()(())((()()))", "(())()(())((())())", "(())()(())((()))()", "(())()(())(()(()))", "(())()(())(()()())", "(())()(())(()())()", "(())()(())(())(())", "(())()(())(())()()", "(())()(())()((()))", "(())()(())()(()())", "(())()(())()(())()", "(())()(())()()(())", "(())()(())()()()()", "(())()()((((()))))", "(())()()(((()())))", "(())()()(((())()))", "(())()()(((()))())", "(())()()(((())))()", "(())()()((()(())))", "(())()()((()()()))", "(())()()((()())())", "(())()()((()()))()", "(())()()((())(()))", "(())()()((())()())", "(())()()((())())()", "(())()()((()))(())", "(())()()((()))()()", "(())()()(()((())))", "(())()()(()(()()))", "(())()()(()(())())", "(())()()(()(()))()", "(())()()(()()(()))", "(())()()(()()()())", "(())()()(()()())()", "(())()()(()())(())", "(())()()(()())()()", "(())()()(())((()))", "(())()()(())(()())", "(())()()(())(())()", "(())()()(())()(())", "(())()()(())()()()", "(())()()()(((())))", "(())()()()((()()))", "(())()()()((())())", "(())()()()((()))()", "(())()()()(()(()))", "(())()()()(()()())", "(())()()()(()())()", "(())()()()(())(())", "(())()()()(())()()", "(())()()()()((()))", "(())()()()()(()())", "(())()()()()(())()", "(())()()()()()(())", "(())()()()()()()()", "()(((((((())))))))", "()((((((()()))))))", "()((((((())())))))", "()((((((()))()))))", "()((((((())))())))", "()((((((()))))()))", "()((((((())))))())", "()((((((()))))))()", "()(((((()(()))))))", "()(((((()()())))))", "()(((((()())()))))", "()(((((()()))())))", "()(((((()())))()))", "()(((((()()))))())", "()(((((()())))))()", "()(((((())(())))))", "()(((((())()()))))", "()(((((())())())))", "()(((((())()))()))", "()(((((())())))())", "()(((((())()))))()", "()(((((()))(()))))", "()(((((()))()())))", "()(((((()))())()))", "()(((((()))()))())", "()(((((()))())))()", "()(((((())))(())))", "()(((((())))()()))", "()(((((())))())())", "()(((((())))()))()", "()(((((()))))(()))", "()(((((()))))()())", "()(((((()))))())()", "()(((((())))))(())", "()(((((())))))()()", "()((((()((()))))))", "()((((()(()())))))", "()((((()(())()))))", "()((((()(()))())))", "()((((()(())))()))", "()((((()(()))))())", "()((((()(())))))()", "()((((()()(())))))", "()((((()()()()))))", "()((((()()())())))", "()((((()()()))()))", "()((((()()())))())", "()((((()()()))))()", "()((((()())(()))))", "()((((()())()())))", "()((((()())())()))", "()((((()())()))())", "()((((()())())))()", "()((((()()))(())))", "()((((()()))()()))", "()((((()()))())())", "()((((()()))()))()", "()((((()())))(()))", "()((((()())))()())", "()((((()())))())()", "()((((()()))))(())", "()((((()()))))()()", "()((((())((())))))", "()((((())(()()))))", "()((((())(())())))", "()((((())(()))()))", "()((((())(())))())", "()((((())(()))))()", "()((((())()(()))))", "()((((())()()())))", "()((((())()())()))", "()((((())()()))())", "()((((())()())))()", "()((((())())(())))", "()((((())())()()))", "()((((())())())())", "()((((())())()))()", "()((((())()))(()))", "()((((())()))()())", "()((((())()))())()", "()((((())())))(())", "()((((())())))()()", "()((((()))((()))))", "()((((()))(()())))", "()((((()))(())()))", "()((((()))(()))())", "()((((()))(())))()", "()((((()))()(())))", "()((((()))()()()))", "()((((()))()())())", "()((((()))()()))()", "()((((()))())(()))", "()((((()))())()())", "()((((()))())())()", "()((((()))()))(())", "()((((()))()))()()", "()((((())))((())))", "()((((())))(()()))", "()((((())))(())())", "()((((())))(()))()", "()((((())))()(()))", "()((((())))()()())", "()((((())))()())()", "()((((())))())(())", "()((((())))())()()", "()((((()))))((()))", "()((((()))))(()())", "()((((()))))(())()", "()((((()))))()(())", "()((((()))))()()()", "()(((()(((()))))))", "()(((()((()())))))", "()(((()((())()))))", "()(((()((()))())))", "()(((()((())))()))", "()(((()((()))))())", "()(((()((())))))()", "()(((()(()(())))))", "()(((()(()()()))))", "()(((()(()())())))", "()(((()(()()))()))", "()(((()(()())))())", "()(((()(()()))))()", "()(((()(())(()))))", "()(((()(())()())))", "()(((()(())())()))", "()(((()(())()))())", "()(((()(())())))()", "()(((()(()))(())))", "()(((()(()))()()))", "()(((()(()))())())", "()(((()(()))()))()", "()(((()(())))(()))", "()(((()(())))()())", "()(((()(())))())()", "()(((()(()))))(())", "()(((()(()))))()()", "()(((()()((())))))", "()(((()()(()()))))", "()(((()()(())())))", "()(((()()(()))()))", "()(((()()(())))())", "()(((()()(()))))()", "()(((()()()(()))))", "()(((()()()()())))", "()(((()()()())()))", "()(((()()()()))())", "()(((()()()())))()", "()(((()()())(())))", "()(((()()())()()))", "()(((()()())())())", "()(((()()())()))()", "()(((()()()))(()))", "()(((()()()))()())", "()(((()()()))())()", "()(((()()())))(())", "()(((()()())))()()", "()(((()())((()))))", "()(((()())(()())))", "()(((()())(())()))", "()(((()())(()))())", "()(((()())(())))()", "()(((()())()(())))", "()(((()())()()()))", "()(((()())()())())", "()(((()())()()))()", "()(((()())())(()))", "()(((()())())()())", "()(((()())())())()", "()(((()())()))(())", "()(((()())()))()()", "()(((()()))((())))", "()(((()()))(()()))", "()(((()()))(())())", "()(((()()))(()))()", "()(((()()))()(()))", "()(((()()))()()())", "()(((()()))()())()", "()(((()()))())(())", "()(((()()))())()()", "()(((()())))((()))", "()(((()())))(()())", "()(((()())))(())()", "()(((()())))()(())", "()(((()())))()()()", "()(((())(((())))))", "()(((())((()()))))", "()(((())((())())))", "()(((())((()))()))", "()(((())((())))())", "()(((())((()))))()", "()(((())(()(()))))", "()(((())(()()())))", "()(((())(()())()))", "()(((())(()()))())", "()(((())(()())))()", "()(((())(())(())))", "()(((())(())()()))", "()(((())(())())())", "()(((())(())()))()", "()(((())(()))(()))", "()(((())(()))()())", "()(((())(()))())()", "()(((())(())))(())", "()(((())(())))()()", "()(((())()((()))))", "()(((())()(()())))", "()(((())()(())()))", "()(((())()(()))())", "()(((())()(())))()", "()(((())()()(())))", "()(((())()()()()))", "()(((())()()())())", "()(((())()()()))()", "()(((())()())(()))", "()(((())()())()())", "()(((())()())())()", "()(((())()()))(())", "()(((())()()))()()", "()(((())())((())))", "()(((())())(()()))", "()(((())())(())())", "()(((())())(()))()", "()(((())())()(()))", "()(((())())()()())", "()(((())())()())()", "()(((())())())(())", "()(((())())())()()", "()(((())()))((()))", "()(((())()))(()())", "()(((())()))(())()", "()(((())()))()(())", "()(((())()))()()()", "()(((()))(((()))))", "()(((()))((()())))", "()(((()))((())()))", "()(((()))((()))())", "()(((()))((())))()", "()(((()))(()(())))", "()(((()))(()()()))", "()(((()))(()())())", "()(((()))(()()))()", "()(((()))(())(()))", "()(((()))(())()())", "()(((()))(())())()", "()(((()))(()))(())", "()(((()))(()))()()", "()(((()))()((())))", "()(((()))()(()()))", "()(((()))()(())())", "()(((()))()(()))()", "()(((()))()()(()))", "()(((()))()()()())", "()(((()))()()())()", "()(((()))()())(())", "()(((()))()())()()", "()(((()))())((()))", "()(((()))())(()())", "()(((()))())(())()", "()(((()))())()(())", "()(((()))())()()()", "()(((())))(((())))", "()(((())))((()()))", "()(((())))((())())", "()(((())))((()))()", "()(((())))(()(()))", "()(((())))(()()())", "()(((())))(()())()", "()(((())))(())(())", "()(((())))(())()()", "()(((())))()((()))", "()(((())))()(()())", "()(((())))()(())()", "()(((())))()()(())", "()(((())))()()()()", "()((()((((()))))))", "()((()(((()())))))", "()((()(((())()))))", "()((()(((()))())))", "()((()(((())))()))", "()((()(((()))))())", "()((()(((())))))()", "()((()((()(())))))", "()((()((()()()))))", "()((()((()())())))", "()((()((()()))()))", "()((()((()())))())", "()((()((()()))))()", "()((()((())(()))))", "()((()((())()())))", "()((()((())())()))", "()((()((())()))())", "()((()((())())))()", "()((()((()))(())))", "()((()((()))()()))", "()((()((()))())())", "()((()((()))()))()", "()((()((())))(()))", "()((()((())))()())", "()((()((())))())()", "()((()((()))))(())", "()((()((()))))()()", "()((()(()((())))))", "()((()(()(()()))))", "()((()(()(())())))", "()((()(()(()))()))", "()((()(()(())))())", "()((()(()(()))))()", "()((()(()()(()))))", "()((()(()()()())))", "()((()(()()())()))", "()((()(()()()))())", "()((()(()()())))()", "()((()(()())(())))", "()((()(()())()()))", "()((()(()())())())", "()((()(()())()))()", "()((()(()()))(()))", "()((()(()()))()())", "()((()(()()))())()", "()((()(()())))(())", "()((()(()())))()()", "()((()(())((()))))", "()((()(())(()())))", "()((()(())(())()))", "()((()(())(()))())", "()((()(())(())))()", "()((()(())()(())))", "()((()(())()()()))", "()((()(())()())())", "()((()(())()()))()", "()((()(())())(()))", "()((()(())())()())", "()((()(())())())()", "()((()(())()))(())", "()((()(())()))()()", "()((()(()))((())))", "()((()(()))(()()))", "()((()(()))(())())", "()((()(()))(()))()", "()((()(()))()(()))", "()((()(()))()()())", "()((()(()))()())()", "()((()(()))())(())", "()((()(()))())()()", "()((()(())))((()))", "()((()(())))(()())", "()((()(())))(())()", "()((()(())))()(())", "()((()(())))()()()", "()((()()(((())))))", "()((()()((()()))))", "()((()()((())())))", "()((()()((()))()))", "()((()()((())))())", "()((()()((()))))()", "()((()()(()(()))))", "()((()()(()()())))", "()((()()(()())()))", "()((()()(()()))())", "()((()()(()())))()", "()((()()(())(())))", "()((()()(())()()))", "()((()()(())())())", "()((()()(())()))()", "()((()()(()))(()))", "()((()()(()))()())", "()((()()(()))())()", "()((()()(())))(())", "()((()()(())))()()", "()((()()()((()))))", "()((()()()(()())))", "()((()()()(())()))", "()((()()()(()))())", "()((()()()(())))()", "()((()()()()(())))", "()((()()()()()()))", "()((()()()()())())", "()((()()()()()))()", "()((()()()())(()))", "()((()()()())()())", "()((()()()())())()", "()((()()()()))(())", "()((()()()()))()()", "()((()()())((())))", "()((()()())(()()))", "()((()()())(())())", "()((()()())(()))()", "()((()()())()(()))", "()((()()())()()())", "()((()()())()())()", "()((()()())())(())", "()((()()())())()()", "()((()()()))((()))", "()((()()()))(()())", "()((()()()))(())()", "()((()()()))()(())", "()((()()()))()()()", "()((()())(((()))))", "()((()())((()())))", "()((()())((())()))", "()((()())((()))())", "()((()())((())))()", "()((()())(()(())))", "()((()())(()()()))", "()((()())(()())())", "()((()())(()()))()", "()((()())(())(()))", "()((()())(())()())", "()((()())(())())()", "()((()())(()))(())", "()((()())(()))()()", "()((()())()((())))", "()((()())()(()()))", "()((()())()(())())", "()((()())()(()))()", "()((()())()()(()))", "()((()())()()()())", "()((()())()()())()", "()((()())()())(())", "()((()())()())()()", "()((()())())((()))", "()((()())())(()())", "()((()())())(())()", "()((()())())()(())", "()((()())())()()()", "()((()()))(((())))", "()((()()))((()()))", "()((()()))((())())", "()((()()))((()))()", "()((()()))(()(()))", "()((()()))(()()())", "()((()()))(()())()", "()((()()))(())(())", "()((()()))(())()()", "()((()()))()((()))", "()((()()))()(()())", "()((()()))()(())()", "()((()()))()()(())", "()((()()))()()()()", "()((())((((())))))", "()((())(((()()))))", "()((())(((())())))", "()((())(((()))()))", "()((())(((())))())", "()((())(((()))))()", "()((())((()(()))))", "()((())((()()())))", "()((())((()())()))", "()((())((()()))())", "()((())((()())))()", "()((())((())(())))", "()((())((())()()))", "()((())((())())())", "()((())((())()))()", "()((())((()))(()))", "()((())((()))()())", "()((())((()))())()", "()((())((())))(())", "()((())((())))()()", "()((())(()((()))))", "()((())(()(()())))", "()((())(()(())()))", "()((())(()(()))())", "()((())(()(())))()", "()((())(()()(())))", "()((())(()()()()))", "()((())(()()())())", "()((())(()()()))()", "()((())(()())(()))", "()((())(()())()())", "()((())(()())())()", "()((())(()()))(())", "()((())(()()))()()", "()((())(())((())))", "()((())(())(()()))", "()((())(())(())())", "()((())(())(()))()", "()((())(())()(()))", "()((())(())()()())", "()((())(())()())()", "()((())(())())(())", "()((())(())())()()", "()((())(()))((()))", "()((())(()))(()())", "()((())(()))(())()", "()((())(()))()(())", "()((())(()))()()()", "()((())()(((()))))", "()((())()((()())))", "()((())()((())()))", "()((())()((()))())", "()((())()((())))()", "()((())()(()(())))", "()((())()(()()()))", "()((())()(()())())", "()((())()(()()))()", "()((())()(())(()))", "()((())()(())()())", "()((())()(())())()", "()((())()(()))(())", "()((())()(()))()()", "()((())()()((())))", "()((())()()(()()))", "()((())()()(())())", "()((())()()(()))()", "()((())()()()(()))", "()((())()()()()())", "()((())()()()())()", "()((())()()())(())", "()((())()()())()()", "()((())()())((()))", "()((())()())(()())", "()((())()())(())()", "()((())()())()(())", "()((())()())()()()", "()((())())(((())))", "()((())())((()()))", "()((())())((())())", "()((())())((()))()", "()((())())(()(()))", "()((())())(()()())", "()((())())(()())()", "()((())())(())(())", "()((())())(())()()", "()((())())()((()))", "()((())())()(()())", "()((())())()(())()", "()((())())()()(())", "()((())())()()()()", "()((()))((((()))))", "()((()))(((()())))", "()((()))(((())()))", "()((()))(((()))())", "()((()))(((())))()", "()((()))((()(())))", "()((()))((()()()))", "()((()))((()())())", "()((()))((()()))()", "()((()))((())(()))", "()((()))((())()())", "()((()))((())())()", "()((()))((()))(())", "()((()))((()))()()", "()((()))(()((())))", "()((()))(()(()()))", "()((()))(()(())())", "()((()))(()(()))()", "()((()))(()()(()))", "()((()))(()()()())", "()((()))(()()())()", "()((()))(()())(())", "()((()))(()())()()", "()((()))(())((()))", "()((()))(())(()())", "()((()))(())(())()", "()((()))(())()(())", "()((()))(())()()()", "()((()))()(((())))", "()((()))()((()()))", "()((()))()((())())", "()((()))()((()))()", "()((()))()(()(()))", "()((()))()(()()())", "()((()))()(()())()", "()((()))()(())(())", "()((()))()(())()()", "()((()))()()((()))", "()((()))()()(()())", "()((()))()()(())()", "()((()))()()()(())", "()((()))()()()()()", "()(()(((((()))))))", "()(()((((()())))))", "()(()((((())()))))", "()(()((((()))())))", "()(()((((())))()))", "()(()((((()))))())", "()(()((((())))))()", "()(()(((()(())))))", "()(()(((()()()))))", "()(()(((()())())))", "()(()(((()()))()))", "()(()(((()())))())", "()(()(((()()))))()", "()(()(((())(()))))", "()(()(((())()())))", "()(()(((())())()))", "()(()(((())()))())", "()(()(((())())))()", "()(()(((()))(())))", "()(()(((()))()()))", "()(()(((()))())())", "()(()(((()))()))()", "()(()(((())))(()))", "()(()(((())))()())", "()(()(((())))())()", "()(()(((()))))(())", "()(()(((()))))()()", "()(()((()((())))))", "()(()((()(()()))))", "()(()((()(())())))", "()(()((()(()))()))", "()(()((()(())))())", "()(()((()(()))))()", "()(()((()()(()))))", "()(()((()()()())))", "()(()((()()())()))", "()(()((()()()))())", "()(()((()()())))()", "()(()((()())(())))", "()(()((()())()()))", "()(()((()())())())", "()(()((()())()))()", "()(()((()()))(()))", "()(()((()()))()())", "()(()((()()))())()", "()(()((()())))(())", "()(()((()())))()()", "()(()((())((()))))", "()(()((())(()())))", "()(()((())(())()))", "()(()((())(()))())", "()(()((())(())))()", "()(()((())()(())))", "()(()((())()()()))", "()(()((())()())())", "()(()((())()()))()", "()(()((())())(()))", "()(()((())())()())", "()(()((())())())()", "()(()((())()))(())", "()(()((())()))()()", "()(()((()))((())))", "()(()((()))(()()))", "()(()((()))(())())", "()(()((()))(()))()", "()(()((()))()(()))", "()(()((()))()()())", "()(()((()))()())()", "()(()((()))())(())", "()(()((()))())()()", "()(()((())))((()))", "()(()((())))(()())", "()(()((())))(())()", "()(()((())))()(())", "()(()((())))()()()", "()(()(()(((())))))", "()(()(()((()()))))", "()(()(()((())())))", "()(()(()((()))()))", "()(()(()((())))())", "()(()(()((()))))()", "()(()(()(()(()))))", "()(()(()(()()())))", "()(()(()(()())()))", "()(()(()(()()))())", "()(()(()(()())))()", "()(()(()(())(())))", "()(()(()(())()()))", "()(()(()(())())())", "()(()(()(())()))()", "()(()(()(()))(()))", "()(()(()(()))()())", "()(()(()(()))())()", "()(()(()(())))(())", "()(()(()(())))()()", "()(()(()()((()))))", "()(()(()()(()())))", "()(()(()()(())()))", "()(()(()()(()))())", "()(()(()()(())))()", "()(()(()()()(())))", "()(()(()()()()()))", "()(()(()()()())())", "()(()(()()()()))()", "()(()(()()())(()))", "()(()(()()())()())", "()(()(()()())())()", "()(()(()()()))(())", "()(()(()()()))()()", "()(()(()())((())))", "()(()(()())(()()))", "()(()(()())(())())", "()(()(()())(()))()", "()(()(()())()(()))", "()(()(()())()()())", "()(()(()())()())()", "()(()(()())())(())", "()(()(()())())()()", "()(()(()()))((()))", "()(()(()()))(()())", "()(()(()()))(())()", "()(()(()()))()(())", "()(()(()()))()()()", "()(()(())(((()))))", "()(()(())((()())))", "()(()(())((())()))", "()(()(())((()))())", "()(()(())((())))()", "()(()(())(()(())))", "()(()(())(()()()))", "()(()(())(()())())", "()(()(())(()()))()", "()(()(())(())(()))", "()(()(())(())()())", "()(()(())(())())()", "()(()(())(()))(())", "()(()(())(()))()()", "()(()(())()((())))", "()(()(())()(()()))", "()(()(())()(())())", "()(()(())()(()))()", "()(()(())()()(()))", "()(()(())()()()())", "()(()(())()()())()", "()(()(())()())(())", "()(()(())()())()()", "()(()(())())((()))", "()(()(())())(()())", "()(()(())())(())()", "()(()(())())()(())", "()(()(())())()()()", "()(()(()))(((())))", "()(()(()))((()()))", "()(()(()))((())())", "()(()(()))((()))()", "()(()(()))(()(()))", "()(()(()))(()()())", "()(()(()))(()())()", "()(()(()))(())(())", "()(()(()))(())()()", "()(()(()))()((()))", "()(()(()))()(()())", "()(()(()))()(())()", "()(()(()))()()(())", "()(()(()))()()()()", "()(()()((((())))))", "()(()()(((()()))))", "()(()()(((())())))", "()(()()(((()))()))", "()(()()(((())))())", "()(()()(((()))))()", "()(()()((()(()))))", "()(()()((()()())))", "()(()()((()())()))", "()(()()((()()))())", "()(()()((()())))()", "()(()()((())(())))", "()(()()((())()()))", "()(()()((())())())", "()(()()((())()))()", "()(()()((()))(()))", "()(()()((()))()())", "()(()()((()))())()", "()(()()((())))(())", "()(()()((())))()()", "()(()()(()((()))))", "()(()()(()(()())))", "()(()()(()(())()))", "()(()()(()(()))())", "()(()()(()(())))()", "()(()()(()()(())))", "()(()()(()()()()))", "()(()()(()()())())", "()(()()(()()()))()", "()(()()(()())(()))", "()(()()(()())()())", "()(()()(()())())()", "()(()()(()()))(())", "()(()()(()()))()()", "()(()()(())((())))", "()(()()(())(()()))", "()(()()(())(())())", "()(()()(())(()))()", "()(()()(())()(()))", "()(()()(())()()())", "()(()()(())()())()", "()(()()(())())(())", "()(()()(())())()()", "()(()()(()))((()))", "()(()()(()))(()())", "()(()()(()))(())()", "()(()()(()))()(())", "()(()()(()))()()()", "()(()()()(((()))))", "()(()()()((()())))", "()(()()()((())()))", "()(()()()((()))())", "()(()()()((())))()", "()(()()()(()(())))", "()(()()()(()()()))", "()(()()()(()())())", "()(()()()(()()))()", "()(()()()(())(()))", "()(()()()(())()())", "()(()()()(())())()", "()(()()()(()))(())", "()(()()()(()))()()", "()(()()()()((())))", "()(()()()()(()()))", "()(()()()()(())())", "()(()()()()(()))()", "()(()()()()()(()))", "()(()()()()()()())", "()(()()()()()())()", "()(()()()()())(())", "()(()()()()())()()", "()(()()()())((()))", "()(()()()())(()())", "()(()()()())(())()", "()(()()()())()(())", "()(()()()())()()()", "()(()()())(((())))", "()(()()())((()()))", "()(()()())((())())", "()(()()())((()))()", "()(()()())(()(()))", "()(()()())(()()())", "()(()()())(()())()", "()(()()())(())(())", "()(()()())(())()()", "()(()()())()((()))", "()(()()())()(()())", "()(()()())()(())()", "()(()()())()()(())", "()(()()())()()()()", "()(()())((((()))))", "()(()())(((()())))", "()(()())(((())()))", "()(()())(((()))())", "()(()())(((())))()", "()(()())((()(())))", "()(()())((()()()))", "()(()())((()())())", "()(()())((()()))()", "()(()())((())(()))", "()(()())((())()())", "()(()())((())())()", "()(()())((()))(())", "()(()())((()))()()", "()(()())(()((())))", "()(()())(()(()()))", "()(()())(()(())())", "()(()())(()(()))()", "()(()())(()()(()))", "()(()())(()()()())", "()(()())(()()())()", "()(()())(()())(())", "()(()())(()())()()", "()(()())(())((()))", "()(()())(())(()())", "()(()())(())(())()", "()(()())(())()(())", "()(()())(())()()()", "()(()())()(((())))", "()(()())()((()()))", "()(()())()((())())", "()(()())()((()))()", "()(()())()(()(()))", "()(()())()(()()())", "()(()())()(()())()", "()(()())()(())(())", "()(()())()(())()()", "()(()())()()((()))", "()(()())()()(()())", "()(()())()()(())()", "()(()())()()()(())", "()(()())()()()()()", "()(())(((((())))))", "()(())((((()()))))", "()(())((((())())))", "()(())((((()))()))", "()(())((((())))())", "()(())((((()))))()", "()(())(((()(()))))", "()(())(((()()())))", "()(())(((()())()))", "()(())(((()()))())", "()(())(((()())))()", "()(())(((())(())))", "()(())(((())()()))", "()(())(((())())())", "()(())(((())()))()", "()(())(((()))(()))", "()(())(((()))()())", "()(())(((()))())()", "()(())(((())))(())", "()(())(((())))()()", "()(())((()((()))))", "()(())((()(()())))", "()(())((()(())()))", "()(())((()(()))())", "()(())((()(())))()", "()(())((()()(())))", "()(())((()()()()))", "()(())((()()())())", "()(())((()()()))()", "()(())((()())(()))", "()(())((()())()())", "()(())((()())())()", "()(())((()()))(())", "()(())((()()))()()", "()(())((())((())))", "()(())((())(()()))", "()(())((())(())())", "()(())((())(()))()", "()(())((())()(()))", "()(())((())()()())", "()(())((())()())()", "()(())((())())(())", "()(())((())())()()", "()(())((()))((()))", "()(())((()))(()())", "()(())((()))(())()", "()(())((()))()(())", "()(())((()))()()()", "()(())(()(((()))))", "()(())(()((()())))", "()(())(()((())()))", "()(())(()((()))())", "()(())(()((())))()", "()(())(()(()(())))", "()(())(()(()()()))", "()(())(()(()())())", "()(())(()(()()))()", "()(())(()(())(()))", "()(())(()(())()())", "()(())(()(())())()", "()(())(()(()))(())", "()(())(()(()))()()", "()(())(()()((())))", "()(())(()()(()()))", "()(())(()()(())())", "()(())(()()(()))()", "()(())(()()()(()))", "()(())(()()()()())", "()(())(()()()())()", "()(())(()()())(())", "()(())(()()())()()", "()(())(()())((()))", "()(())(()())(()())", "()(())(()())(())()", "()(())(()())()(())", "()(())(()())()()()", "()(())(())(((())))", "()(())(())((()()))", "()(())(())((())())", "()(())(())((()))()", "()(())(())(()(()))", "()(())(())(()()())", "()(())(())(()())()", "()(())(())(())(())", "()(())(())(())()()", "()(())(())()((()))", "()(())(())()(()())", "()(())(())()(())()", "()(())(())()()(())", "()(())(())()()()()", "()(())()((((()))))", "()(())()(((()())))", "()(())()(((())()))", "()(())()(((()))())", "()(())()(((())))()", "()(())()((()(())))", "()(())()((()()()))", "()(())()((()())())", "()(())()((()()))()", "()(())()((())(()))", "()(())()((())()())", "()(())()((())())()", "()(())()((()))(())", "()(())()((()))()()", "()(())()(()((())))", "()(())()(()(()()))", "()(())()(()(())())", "()(())()(()(()))()", "()(())()(()()(()))", "()(())()(()()()())", "()(())()(()()())()", "()(())()(()())(())", "()(())()(()())()()", "()(())()(())((()))", "()(())()(())(()())", "()(())()(())(())()", "()(())()(())()(())", "()(())()(())()()()", "()(())()()(((())))", "()(())()()((()()))", "()(())()()((())())", "()(())()()((()))()", "()(())()()(()(()))", "()(())()()(()()())", "()(())()()(()())()", "()(())()()(())(())", "()(())()()(())()()", "()(())()()()((()))", "()(())()()()(()())", "()(())()()()(())()", "()(())()()()()(())", "()(())()()()()()()", "()()((((((()))))))", "()()(((((()())))))", "()()(((((())()))))", "()()(((((()))())))", "()()(((((())))()))", "()()(((((()))))())", "()()(((((())))))()", "()()((((()(())))))", "()()((((()()()))))", "()()((((()())())))", "()()((((()()))()))", "()()((((()())))())", "()()((((()()))))()", "()()((((())(()))))", "()()((((())()())))", "()()((((())())()))", "()()((((())()))())", "()()((((())())))()", "()()((((()))(())))", "()()((((()))()()))", "()()((((()))())())", "()()((((()))()))()", "()()((((())))(()))", "()()((((())))()())", "()()((((())))())()", "()()((((()))))(())", "()()((((()))))()()", "()()(((()((())))))", "()()(((()(()()))))", "()()(((()(())())))", "()()(((()(()))()))", "()()(((()(())))())", "()()(((()(()))))()", "()()(((()()(()))))", "()()(((()()()())))", "()()(((()()())()))", "()()(((()()()))())", "()()(((()()())))()", "()()(((()())(())))", "()()(((()())()()))", "()()(((()())())())", "()()(((()())()))()", "()()(((()()))(()))", "()()(((()()))()())", "()()(((()()))())()", "()()(((()())))(())", "()()(((()())))()()", "()()(((())((()))))", "()()(((())(()())))", "()()(((())(())()))", "()()(((())(()))())", "()()(((())(())))()", "()()(((())()(())))", "()()(((())()()()))", "()()(((())()())())", "()()(((())()()))()", "()()(((())())(()))", "()()(((())())()())", "()()(((())())())()", "()()(((())()))(())", "()()(((())()))()()", "()()(((()))((())))", "()()(((()))(()()))", "()()(((()))(())())", "()()(((()))(()))()", "()()(((()))()(()))", "()()(((()))()()())", "()()(((()))()())()", "()()(((()))())(())", "()()(((()))())()()", "()()(((())))((()))", "()()(((())))(()())", "()()(((())))(())()", "()()(((())))()(())", "()()(((())))()()()", "()()((()(((())))))", "()()((()((()()))))", "()()((()((())())))", "()()((()((()))()))", "()()((()((())))())", "()()((()((()))))()", "()()((()(()(()))))", "()()((()(()()())))", "()()((()(()())()))", "()()((()(()()))())", "()()((()(()())))()", "()()((()(())(())))", "()()((()(())()()))", "()()((()(())())())", "()()((()(())()))()", "()()((()(()))(()))", "()()((()(()))()())", "()()((()(()))())()", "()()((()(())))(())", "()()((()(())))()()", "()()((()()((()))))", "()()((()()(()())))", "()()((()()(())()))", "()()((()()(()))())", "()()((()()(())))()", "()()((()()()(())))", "()()((()()()()()))", "()()((()()()())())", "()()((()()()()))()", "()()((()()())(()))", "()()((()()())()())", "()()((()()())())()", "()()((()()()))(())", "()()((()()()))()()", "()()((()())((())))", "()()((()())(()()))", "()()((()())(())())", "()()((()())(()))()", "()()((()())()(()))", "()()((()())()()())", "()()((()())()())()", "()()((()())())(())", "()()((()())())()()", "()()((()()))((()))", "()()((()()))(()())", "()()((()()))(())()", "()()((()()))()(())", "()()((()()))()()()", "()()((())(((()))))", "()()((())((()())))", "()()((())((())()))", "()()((())((()))())", "()()((())((())))()", "()()((())(()(())))", "()()((())(()()()))", "()()((())(()())())", "()()((())(()()))()", "()()((())(())(()))", "()()((())(())()())", "()()((())(())())()", "()()((())(()))(())", "()()((())(()))()()", "()()((())()((())))", "()()((())()(()()))", "()()((())()(())())", "()()((())()(()))()", "()()((())()()(()))", "()()((())()()()())", "()()((())()()())()", "()()((())()())(())", "()()((())()())()()", "()()((())())((()))", "()()((())())(()())", "()()((())())(())()", "()()((())())()(())", "()()((())())()()()", "()()((()))(((())))", "()()((()))((()()))", "()()((()))((())())", "()()((()))((()))()", "()()((()))(()(()))", "()()((()))(()()())", "()()((()))(()())()", "()()((()))(())(())", "()()((()))(())()()", "()()((()))()((()))", "()()((()))()(()())", "()()((()))()(())()", "()()((()))()()(())", "()()((()))()()()()", "()()(()((((())))))", "()()(()(((()()))))", "()()(()(((())())))", "()()(()(((()))()))", "()()(()(((())))())", "()()(()(((()))))()", "()()(()((()(()))))", "()()(()((()()())))", "()()(()((()())()))", "()()(()((()()))())", "()()(()((()())))()", "()()(()((())(())))", "()()(()((())()()))", "()()(()((())())())", "()()(()((())()))()", "()()(()((()))(()))", "()()(()((()))()())", "()()(()((()))())()", "()()(()((())))(())", "()()(()((())))()()", "()()(()(()((()))))", "()()(()(()(()())))", "()()(()(()(())()))", "()()(()(()(()))())", "()()(()(()(())))()", "()()(()(()()(())))", "()()(()(()()()()))", "()()(()(()()())())", "()()(()(()()()))()", "()()(()(()())(()))", "()()(()(()())()())", "()()(()(()())())()", "()()(()(()()))(())", "()()(()(()()))()()", "()()(()(())((())))", "()()(()(())(()()))", "()()(()(())(())())", "()()(()(())(()))()", "()()(()(())()(()))", "()()(()(())()()())", "()()(()(())()())()", "()()(()(())())(())", "()()(()(())())()()", "()()(()(()))((()))", "()()(()(()))(()())", "()()(()(()))(())()", "()()(()(()))()(())", "()()(()(()))()()()", "()()(()()(((()))))", "()()(()()((()())))", "()()(()()((())()))", "()()(()()((()))())", "()()(()()((())))()", "()()(()()(()(())))", "()()(()()(()()()))", "()()(()()(()())())", "()()(()()(()()))()", "()()(()()(())(()))", "()()(()()(())()())", "()()(()()(())())()", "()()(()()(()))(())", "()()(()()(()))()()", "()()(()()()((())))", "()()(()()()(()()))", "()()(()()()(())())", "()()(()()()(()))()", "()()(()()()()(()))", "()()(()()()()()())", "()()(()()()()())()", "()()(()()()())(())", "()()(()()()())()()", "()()(()()())((()))", "()()(()()())(()())", "()()(()()())(())()", "()()(()()())()(())", "()()(()()())()()()", "()()(()())(((())))", "()()(()())((()()))", "()()(()())((())())", "()()(()())((()))()", "()()(()())(()(()))", "()()(()())(()()())", "()()(()())(()())()", "()()(()())(())(())", "()()(()())(())()()", "()()(()())()((()))", "()()(()())()(()())", "()()(()())()(())()", "()()(()())()()(())", "()()(()())()()()()", "()()(())((((()))))", "()()(())(((()())))", "()()(())(((())()))", "()()(())(((()))())", "()()(())(((())))()", "()()(())((()(())))", "()()(())((()()()))", "()()(())((()())())", "()()(())((()()))()", "()()(())((())(()))", "()()(())((())()())", "()()(())((())())()", "()()(())((()))(())", "()()(())((()))()()", "()()(())(()((())))", "()()(())(()(()()))", "()()(())(()(())())", "()()(())(()(()))()", "()()(())(()()(()))", "()()(())(()()()())", "()()(())(()()())()", "()()(())(()())(())", "()()(())(()())()()", "()()(())(())((()))", "()()(())(())(()())", "()()(())(())(())()", "()()(())(())()(())", "()()(())(())()()()", "()()(())()(((())))", "()()(())()((()()))", "()()(())()((())())", "()()(())()((()))()", "()()(())()(()(()))", "()()(())()(()()())", "()()(())()(()())()", "()()(())()(())(())", "()()(())()(())()()", "()()(())()()((()))", "()()(())()()(()())", "()()(())()()(())()", "()()(())()()()(())", "()()(())()()()()()", "()()()(((((())))))", "()()()((((()()))))", "()()()((((())())))", "()()()((((()))()))", "()()()((((())))())", "()()()((((()))))()", "()()()(((()(()))))", "()()()(((()()())))", "()()()(((()())()))", "()()()(((()()))())", "()()()(((()())))()", "()()()(((())(())))", "()()()(((())()()))", "()()()(((())())())", "()()()(((())()))()", "()()()(((()))(()))", "()()()(((()))()())", "()()()(((()))())()", "()()()(((())))(())", "()()()(((())))()()", "()()()((()((()))))", "()()()((()(()())))", "()()()((()(())()))", "()()()((()(()))())", "()()()((()(())))()", "()()()((()()(())))", "()()()((()()()()))", "()()()((()()())())", "()()()((()()()))()", "()()()((()())(()))", "()()()((()())()())", "()()()((()())())()", "()()()((()()))(())", "()()()((()()))()()", "()()()((())((())))", "()()()((())(()()))", "()()()((())(())())", "()()()((())(()))()", "()()()((())()(()))", "()()()((())()()())", "()()()((())()())()", "()()()((())())(())", "()()()((())())()()", "()()()((()))((()))", "()()()((()))(()())", "()()()((()))(())()", "()()()((()))()(())", "()()()((()))()()()", "()()()(()(((()))))", "()()()(()((()())))", "()()()(()((())()))", "()()()(()((()))())", "()()()(()((())))()", "()()()(()(()(())))", "()()()(()(()()()))", "()()()(()(()())())", "()()()(()(()()))()", "()()()(()(())(()))", "()()()(()(())()())", "()()()(()(())())()", "()()()(()(()))(())", "()()()(()(()))()()", "()()()(()()((())))", "()()()(()()(()()))", "()()()(()()(())())", "()()()(()()(()))()", "()()()(()()()(()))", "()()()(()()()()())", "()()()(()()()())()", "()()()(()()())(())", "()()()(()()())()()", "()()()(()())((()))", "()()()(()())(()())", "()()()(()())(())()", "()()()(()())()(())", "()()()(()())()()()", "()()()(())(((())))", "()()()(())((()()))", "()()()(())((())())", "()()()(())((()))()", "()()()(())(()(()))", "()()()(())(()()())", "()()()(())(()())()", "()()()(())(())(())", "()()()(())(())()()", "()()()(())()((()))", "()()()(())()(()())", "()()()(())()(())()", "()()()(())()()(())", "()()()(())()()()()", "()()()()((((()))))", "()()()()(((()())))", "()()()()(((())()))", "()()()()(((()))())", "()()()()(((())))()", "()()()()((()(())))", "()()()()((()()()))", "()()()()((()())())", "()()()()((()()))()", "()()()()((())(()))", "()()()()((())()())", "()()()()((())())()", "()()()()((()))(())", "()()()()((()))()()", "()()()()(()((())))", "()()()()(()(()()))", "()()()()(()(())())", "()()()()(()(()))()", "()()()()(()()(()))", "()()()()(()()()())", "()()()()(()()())()", "()()()()(()())(())", "()()()()(()())()()", "()()()()(())((()))", "()()()()(())(()())", "()()()()(())(())()", "()()()()(())()(())", "()()()()(())()()()", "()()()()()(((())))", "()()()()()((()()))", "()()()()()((())())", "()()()()()((()))()", "()()()()()(()(()))", "()()()()()(()()())", "()()()()()(()())()", "()()()()()(())(())", "()()()()()(())()()", "()()()()()()((()))", "()()()()()()(()())", "()()()()()()(())()", "()()()()()()()(())", "()()()()()()()()()"] TODO
10 ["(((((((((())))))))))", "((((((((()()))))))))", "((((((((())())))))))", "((((((((()))()))))))", "((((((((())))())))))", "((((((((()))))()))))", "((((((((())))))())))", "((((((((()))))))()))", "((((((((())))))))())", "((((((((()))))))))()", "(((((((()(()))))))))", "(((((((()()())))))))", "(((((((()())()))))))", "(((((((()()))())))))", "(((((((()())))()))))", "(((((((()()))))())))", "(((((((()())))))()))", "(((((((()()))))))())", "(((((((()())))))))()", "(((((((())(())))))))", "(((((((())()()))))))", "(((((((())())())))))", "(((((((())()))()))))", "(((((((())())))())))", "(((((((())()))))()))", "(((((((())())))))())", "(((((((())()))))))()", "(((((((()))(()))))))", "(((((((()))()())))))", "(((((((()))())()))))", "(((((((()))()))())))", "(((((((()))())))()))", "(((((((()))()))))())", "(((((((()))())))))()", "(((((((())))(())))))", "(((((((())))()()))))", "(((((((())))())())))", "(((((((())))()))()))", "(((((((())))())))())", "(((((((())))()))))()", "(((((((()))))(()))))", "(((((((()))))()())))", "(((((((()))))())()))", "(((((((()))))()))())", "(((((((()))))())))()", "(((((((())))))(())))", "(((((((())))))()()))", "(((((((())))))())())", "(((((((())))))()))()", "(((((((()))))))(()))", "(((((((()))))))()())", "(((((((()))))))())()", "(((((((())))))))(())", "(((((((())))))))()()", "((((((()((()))))))))", "((((((()(()())))))))", "((((((()(())()))))))", "((((((()(()))())))))", "((((((()(())))()))))", "((((((()(()))))())))", "((((((()(())))))()))", "((((((()(()))))))())", "((((((()(())))))))()", "((((((()()(())))))))", "((((((()()()()))))))", "((((((()()())())))))", "((((((()()()))()))))", "((((((()()())))())))", "((((((()()()))))()))", "((((((()()())))))())", "((((((()()()))))))()", "((((((()())(()))))))", "((((((()())()())))))", "((((((()())())()))))", "((((((()())()))())))", "((((((()())())))()))", "((((((()())()))))())", "((((((()())())))))()", "((((((()()))(())))))", "((((((()()))()()))))", "((((((()()))())())))", "((((((()()))()))()))", "((((((()()))())))())", "((((((()()))()))))()", "((((((()())))(()))))", "((((((()())))()())))", "((((((()())))())()))", "((((((()())))()))())", "((((((()())))())))()", "((((((()()))))(())))", "((((((()()))))()()))", "((((((()()))))())())", "((((((()()))))()))()", "((((((()())))))(()))", "((((((()())))))()())", "((((((()())))))())()", "((((((()()))))))(())", "((((((()()))))))()()", "((((((())((())))))))", "((((((())(()()))))))", "((((((())(())())))))", "((((((())(()))()))))", "((((((())(())))())))", "((((((())(()))))()))", "((((((())(())))))())", "((((((())(()))))))()", "((((((())()(()))))))", "((((((())()()())))))", "((((((())()())()))))", "((((((())()()))())))", "((((((())()())))()))", "((((((())()()))))())", "((((((())()())))))()", "((((((())())(())))))", "((((((())())()()))))", "((((((())())())())))", "((((((())())()))()))", "((((((())())())))())", "((((((())())()))))()", "((((((())()))(()))))", "((((((())()))()())))", "((((((())()))())()))", "((((((())()))()))())", "((((((())()))())))()", "((((((())())))(())))", "((((((())())))()()))", "((((((())())))())())", "((((((())())))()))()", "((((((())()))))(()))", "((((((())()))))()())", "((((((())()))))())()", "((((((())())))))(())", "((((((())())))))()()", "((((((()))((()))))))", "((((((()))(()())))))", "((((((()))(())()))))", "((((((()))(()))())))", "((((((()))(())))()))", "((((((()))(()))))())", "((((((()))(())))))()", "((((((()))()(())))))", "((((((()))()()()))))", "((((((()))()())())))", "((((((()))()()))()))", "((((((()))()())))())", "((((((()))()()))))()", "((((((()))())(()))))", "((((((()))())()())))", "((((((()))())())()))", "((((((()))())()))())", "((((((()))())())))()", "((((((()))()))(())))", "((((((()))()))()()))", "((((((()))()))())())", "((((((()))()))()))()", "((((((()))())))(()))", "((((((()))())))()())", "((((((()))())))())()", "((((((()))()))))(())", "((((((()))()))))()()", "((((((())))((())))))", "((((((())))(()()))))", "((((((())))(())())))", "((((((())))(()))()))", "((((((())))(())))())", "((((((())))(()))))()", "((((((())))()(()))))", "((((((())))()()())))", "((((((())))()())()))", "((((((())))()()))())", "((((((())))()())))()", "((((((())))())(())))", "((((((())))())()()))", "((((((())))())())())", "((((((())))())()))()", "((((((())))()))(()))", "((((((())))()))()())", "((((((())))()))())()", "((((((())))())))(())", "((((((())))())))()()", "((((((()))))((()))))", "((((((()))))(()())))", "((((((()))))(())()))", "((((((()))))(()))())", "((((((()))))(())))()", "((((((()))))()(())))", "((((((()))))()()()))", "((((((()))))()())())", "((((((()))))()()))()", "((((((()))))())(()))", "((((((()))))())()())", "((((((()))))())())()", "((((((()))))()))(())", "((((((()))))()))()()", "((((((())))))((())))", "((((((())))))(()()))", "((((((())))))(())())", "((((((())))))(()))()", "((((((())))))()(()))", "((((((())))))()()())", "((((((())))))()())()", "((((((())))))())(())", "((((((())))))())()()", "((((((()))))))((()))", "((((((()))))))(()())", "((((((()))))))(())()", "((((((()))))))()(())", "((((((()))))))()()()", "(((((()(((()))))))))", "(((((()((()())))))))", "(((((()((())()))))))", "(((((()((()))())))))", "(((((()((())))()))))", "(((((()((()))))())))", "(((((()((())))))()))", "(((((()((()))))))())", "(((((()((())))))))()", "(((((()(()(())))))))", "(((((()(()()()))))))", "(((((()(()())())))))", "(((((()(()()))()))))", "(((((()(()())))())))", "(((((()(()()))))()))", "(((((()(()())))))())", "(((((()(()()))))))()", "(((((()(())(()))))))", "(((((()(())()())))))", "(((((()(())())()))))", "(((((()(())()))())))", "(((((()(())())))()))", "(((((()(())()))))())", "(((((()(())())))))()", "(((((()(()))(())))))", "(((((()(()))()()))))", "(((((()(()))())())))", "(((((()(()))()))()))", "(((((()(()))())))())", "(((((()(()))()))))()", "(((((()(())))(()))))", "(((((()(())))()())))", "(((((()(())))())()))", "(((((()(())))()))())", "(((((()(())))())))()", "(((((()(()))))(())))", "(((((()(()))))()()))", "(((((()(()))))())())", "(((((()(()))))()))()", "(((((()(())))))(()))", "(((((()(())))))()())", "(((((()(())))))())()", "(((((()(()))))))(())", "(((((()(()))))))()()", "(((((()()((())))))))", "(((((()()(()()))))))", "(((((()()(())())))))", "(((((()()(()))()))))", "(((((()()(())))())))", "(((((()()(()))))()))", "(((((()()(())))))())", "(((((()()(()))))))()", "(((((()()()(()))))))", "(((((()()()()())))))", "(((((()()()())()))))", "(((((()()()()))())))", "(((((()()()())))()))", "(((((()()()()))))())", "(((((()()()())))))()", "(((((()()())(())))))", "(((((()()())()()))))", "(((((()()())())())))", "(((((()()())()))()))", "(((((()()())())))())", "(((((()()())()))))()", "(((((()()()))(()))))", "(((((()()()))()())))", "(((((()()()))())()))", "(((((()()()))()))())", "(((((()()()))())))()", "(((((()()())))(())))", "(((((()()())))()()))", "(((((()()())))())())", "(((((()()())))()))()", "(((((()()()))))(()))", "(((((()()()))))()())", "(((((()()()))))())()", "(((((()()())))))(())", "(((((()()())))))()()", "(((((()())((()))))))", "(((((()())(()())))))", "(((((()())(())()))))", "(((((()())(()))())))", "(((((()())(())))()))", "(((((()())(()))))())", "(((((()())(())))))()", "(((((()())()(())))))", "(((((()())()()()))))", "(((((()())()())())))", "(((((()())()()))()))", "(((((()())()())))())", "(((((()())()()))))()", "(((((()())())(()))))", "(((((()())())()())))", "(((((()())())())()))", "(((((()())())()))())", "(((((()())())())))()", "(((((()())()))(())))", "(((((()())()))()()))", "(((((()())()))())())", "(((((()())()))()))()", "(((((()())())))(()))", "(((((()())())))()())", "(((((()())())))())()", "(((((()())()))))(())", "(((((()())()))))()()", "(((((()()))((())))))", "(((((()()))(()()))))", "(((((()()))(())())))", "(((((()()))(()))()))", "(((((()()))(())))())", "(((((()()))(()))))()", "(((((()()))()(()))))", "(((((()()))()()())))", "(((((()()))()())()))", "(((((()()))()()))())", "(((((()()))()())))()", "(((((()()))())(())))", "(((((()()))())()()))", "(((((()()))())())())", "(((((()()))())()))()", "(((((()()))()))(()))", "(((((()()))()))()())", "(((((()()))()))())()", "(((((()()))())))(())", "(((((()()))())))()()", "(((((()())))((()))))", "(((((()())))(()())))", "(((((()())))(())()))", "(((((()())))(()))())", "(((((()())))(())))()", "(((((()())))()(())))", "(((((()())))()()()))", "(((((()())))()())())", "(((((()())))()()))()", "(((((()())))())(()))", "(((((()())))())()())", "(((((()())))())())()", "(((((()())))()))(())", "(((((()())))()))()()", "(((((()()))))((())))", "(((((()()))))(()()))", "(((((()()))))(())())", "(((((()()))))(()))()", "(((((()()))))()(()))", "(((((()()))))()()())", "(((((()()))))()())()", "(((((()()))))())(())", "(((((()()))))())()()", "(((((()())))))((()))", "(((((()())))))(()())", "(((((()())))))(())()", "(((((()())))))()(())", "(((((()())))))()()()", "(((((())(((())))))))", "(((((())((()()))))))", "(((((())((())())))))", "(((((())((()))()))))", "(((((())((())))())))", "(((((())((()))))()))", "(((((())((())))))())", "(((((())((()))))))()", "(((((())(()(()))))))", "(((((())(()()())))))", "(((((())(()())()))))", "(((((())(()()))())))", "(((((())(()())))()))", "(((((())(()()))))())", "(((((())(()())))))()", "(((((())(())(())))))", "(((((())(())()()))))", "(((((())(())())())))", "(((((())(())()))()))", "(((((())(())())))())", "(((((())(())()))))()", "(((((())(()))(()))))", "(((((())(()))()())))", "(((((())(()))())()))", "(((((())(()))()))())", "(((((())(()))())))()", "(((((())(())))(())))", "(((((())(())))()()))", "(((((())(())))())())", "(((((())(())))()))()", "(((((())(()))))(()))", "(((((())(()))))()())", "(((((())(()))))())()", "(((((())(())))))(())", "(((((())(())))))()()", "(((((())()((()))))))", "(((((())()(()())))))", "(((((())()(())()))))", "(((((())()(()))())))", "(((((())()(())))()))", "(((((())()(()))))())", "(((((())()(())))))()", "(((((())()()(())))))", "(((((())()()()()))))", "(((((())()()())())))", "(((((())()()()))()))", "(((((())()()())))())", "(((((())()()()))))()", "(((((())()())(()))))", "(((((())()())()())))", "(((((())()())())()))", "(((((())()())()))())", "(((((())()())())))()", "(((((())()()))(())))", "(((((())()()))()()))", "(((((())()()))())())", "(((((())()()))()))()", "(((((())()())))(()))", "(((((())()())))()())", "(((((())()())))())()", "(((((())()()))))(())", "(((((())()()))))()()", "(((((())())((())))))", "(((((())())(()()))))", "(((((())())(())())))", "(((((())())(()))()))", "(((((())())(())))())", "(((((())())(()))))()", "(((((())())()(()))))", "(((((())())()()())))", "(((((())())()())()))", "(((((())())()()))())", "(((((())())()())))()", "(((((())())())(())))", "(((((())())())()()))", "(((((())())())())())", "(((((())())())()))()", "(((((())())()))(()))", "(((((())())()))()())", "(((((())())()))())()", "(((((())())())))(())", "(((((())())())))()()", "(((((())()))((()))))", "(((((())()))(()())))", "(((((())()))(())()))", "(((((())()))(()))())", "(((((())()))(())))()", "(((((())()))()(())))", "(((((())()))()()()))", "(((((())()))()())())", "(((((())()))()()))()", "(((((())()))())(()))", "(((((())()))())()())", "(((((())()))())())()", "(((((())()))()))(())", "(((((())()))()))()()", "(((((())())))((())))", "(((((())())))(()()))", "(((((())())))(())())", "(((((())())))(()))()", "(((((())())))()(()))", "(((((())())))()()())", "(((((())())))()())()", "(((((())())))())(())", "(((((())())))())()()", "(((((())()))))((()))", "(((((())()))))(()())", "(((((())()))))(())()", "(((((())()))))()(())", "(((((())()))))()()()", "(((((()))(((()))))))", "(((((()))((()())))))", "(((((()))((())()))))", "(((((()))((()))())))", "(((((()))((())))()))", "(((((()))((()))))())", "(((((()))((())))))()", "(((((()))(()(())))))", "(((((()))(()()()))))", "(((((()))(()())())))", "(((((()))(()()))()))", "(((((()))(()())))())", "(((((()))(()()))))()", "(((((()))(())(()))))", "(((((()))(())()())))", "(((((()))(())())()))", "(((((()))(())()))())", "(((((()))(())())))()", "(((((()))(()))(())))", "(((((()))(()))()()))", "(((((()))(()))())())", "(((((()))(()))()))()", "(((((()))(())))(()))", "(((((()))(())))()())", "(((((()))(())))())()", "(((((()))(()))))(())", "(((((()))(()))))()()", "(((((()))()((())))))", "(((((()))()(()()))))", "(((((()))()(())())))", "(((((()))()(()))()))", "(((((()))()(())))())", "(((((()))()(()))))()", "(((((()))()()(()))))", "(((((()))()()()())))", "(((((()))()()())()))", "(((((()))()()()))())", "(((((()))()()())))()", "(((((()))()())(())))", "(((((()))()())()()))", "(((((()))()())())())", "(((((()))()())()))()", "(((((()))()()))(()))", "(((((()))()()))()())", "(((((()))()()))())()", "(((((()))()())))(())", "(((((()))()())))()()", "(((((()))())((()))))", "(((((()))())(()())))", "(((((()))())(())()))", "(((((()))())(()))())", "(((((()))())(())))()", "(((((()))())()(())))", "(((((()))())()()()))", "(((((()))())()())())", "(((((()))())()()))()", "(((((()))())())(()))", "(((((()))())())()())", "(((((()))())())())()", "(((((()))())()))(())", "(((((()))())()))()()", "(((((()))()))((())))", "(((((()))()))(()()))", "(((((()))()))(())())", "(((((()))()))(()))()", "(((((()))()))()(()))", "(((((()))()))()()())", "(((((()))()))()())()", "(((((()))()))())(())", "(((((()))()))())()()", "(((((()))())))((()))", "(((((()))())))(()())", "(((((()))())))(())()", "(((((()))())))()(())", "(((((()))())))()()()", "(((((())))(((())))))", "(((((())))((()()))))", "(((((())))((())())))", "(((((())))((()))()))", "(((((())))((())))())", "(((((())))((()))))()", "(((((())))(()(()))))", "(((((())))(()()())))", "(((((())))(()())()))", "(((((())))(()()))())", "(((((())))(()())))()", "(((((())))(())(())))", "(((((())))(())()()))", "(((((())))(())())())", "(((((())))(())()))()", "(((((())))(()))(()))", "(((((())))(()))()())", "(((((())))(()))())()", "(((((())))(())))(())", "(((((())))(())))()()", "(((((())))()((()))))", "(((((())))()(()())))", "(((((())))()(())()))", "(((((())))()(()))())", "(((((())))()(())))()", "(((((())))()()(())))", "(((((())))()()()()))", "(((((())))()()())())", "(((((())))()()()))()", "(((((())))()())(()))", "(((((())))()())()())", "(((((())))()())())()", "(((((())))()()))(())", "(((((())))()()))()()", "(((((())))())((())))", "(((((())))())(()()))", "(((((())))())(())())", "(((((())))())(()))()", "(((((())))())()(()))", "(((((())))())()()())", "(((((())))())()())()", "(((((())))())())(())", "(((((())))())())()()", "(((((())))()))((()))", "(((((())))()))(()())", "(((((())))()))(())()", "(((((())))()))()(())", "(((((())))()))()()()", "(((((()))))(((()))))", "(((((()))))((()())))", "(((((()))))((())()))", "(((((()))))((()))())", "(((((()))))((())))()", "(((((()))))(()(())))", "(((((()))))(()()()))", "(((((()))))(()())())", "(((((()))))(()()))()", "(((((()))))(())(()))", "(((((()))))(())()())", "(((((()))))(())())()", "(((((()))))(()))(())", "(((((()))))(()))()()", "(((((()))))()((())))", "(((((()))))()(()()))", "(((((()))))()(())())", "(((((()))))()(()))()", "(((((()))))()()(()))", "(((((()))))()()()())", "(((((()))))()()())()", "(((((()))))()())(())", "(((((()))))()())()()", "(((((()))))())((()))", "(((((()))))())(()())", "(((((()))))())(())()", "(((((()))))())()(())", "(((((()))))())()()()", "(((((())))))(((())))", "(((((())))))((()()))", "(((((())))))((())())", "(((((())))))((()))()", "(((((())))))(()(()))", "(((((())))))(()()())", "(((((())))))(()())()", "(((((())))))(())(())", "(((((())))))(())()()", "(((((())))))()((()))", "(((((())))))()(()())", "(((((())))))()(())()", "(((((())))))()()(())", "(((((())))))()()()()", "((((()((((()))))))))", "((((()(((()())))))))", "((((()(((())()))))))", "((((()(((()))())))))", "((((()(((())))()))))", "((((()(((()))))())))", "((((()(((())))))()))", "((((()(((()))))))())", "((((()(((())))))))()", "((((()((()(())))))))", "((((()((()()()))))))", "((((()((()())())))))", "((((()((()()))()))))", "((((()((()())))())))", "((((()((()()))))()))", "((((()((()())))))())", "((((()((()()))))))()", "((((()((())(()))))))", "((((()((())()())))))", "((((()((())())()))))", "((((()((())()))())))", "((((()((())())))()))", "((((()((())()))))())", "((((()((())())))))()", "((((()((()))(())))))", "((((()((()))()()))))", "((((()((()))())())))", "((((()((()))()))()))", "((((()((()))())))())", "((((()((()))()))))()", "((((()((())))(()))))", "((((()((())))()())))", "((((()((())))())()))", "((((()((())))()))())", "((((()((())))())))()", "((((()((()))))(())))", "((((()((()))))()()))", "((((()((()))))())())", "((((()((()))))()))()", "((((()((())))))(()))", "((((()((())))))()())", "((((()((())))))())()", "((((()((()))))))(())", "((((()((()))))))()()", "((((()(()((())))))))", "((((()(()(()()))))))", "((((()(()(())())))))", "((((()(()(()))()))))", "((((()(()(())))())))", "((((()(()(()))))()))", "((((()(()(())))))())", "((((()(()(()))))))()", "((((()(()()(()))))))", "((((()(()()()())))))", "((((()(()()())()))))", "((((()(()()()))())))", "((((()(()()())))()))", "((((()(()()()))))())", "((((()(()()())))))()", "((((()(()())(())))))", "((((()(()())()()))))", "((((()(()())())())))", "((((()(()())()))()))", "((((()(()())())))())", "((((()(()())()))))()", "((((()(()()))(()))))", "((((()(()()))()())))", "((((()(()()))())()))", "((((()(()()))()))())", "((((()(()()))())))()", "((((()(()())))(())))", "((((()(()())))()()))", "((((()(()())))())())", "((((()(()())))()))()", "((((()(()()))))(()))", "((((()(()()))))()())", "((((()(()()))))())()", "((((()(()())))))(())", "((((()(()())))))()()", "((((()(())((()))))))", "((((()(())(()())))))", "((((()(())(())()))))", "((((()(())(()))())))", "((((()(())(())))()))", "((((()(())(()))))())", "((((()(())(())))))()", "((((()(())()(())))))", "((((()(())()()()))))", "((((()(())()())())))", "((((()(())()()))()))", "((((()(())()())))())", "((((()(())()()))))()", "((((()(())())(()))))", "((((()(())())()())))", "((((()(())())())()))", "((((()(())())()))())", "((((()(())())())))()", "((((()(())()))(())))", "((((()(())()))()()))", "((((()(())()))())())", "((((()(())()))()))()", "((((()(())())))(()))", "((((()(())())))()())", "((((()(())())))())()", "((((()(())()))))(())", "((((()(())()))))()()", "((((()(()))((())))))", "((((()(()))(()()))))", "((((()(()))(())())))", "((((()(()))(()))()))", "((((()(()))(())))())", "((((()(()))(()))))()", "((((()(()))()(()))))", "((((()(()))()()())))", "((((()(()))()())()))", "((((()(()))()()))())", "((((()(()))()())))()", "((((()(()))())(())))", "((((()(()))())()()))", "((((()(()))())())())", "((((()(()))())()))()", "((((()(()))()))(()))", "((((()(()))()))()())", "((((()(()))()))())()", "((((()(()))())))(())", "((((()(()))())))()()", "((((()(())))((()))))", "((((()(())))(()())))", "((((()(())))(())()))", "((((()(())))(()))())", "((((()(())))(())))()", "((((()(())))()(())))", "((((()(())))()()()))", "((((()(())))()())())", "((((()(())))()()))()", "((((()(())))())(()))", "((((()(())))())()())", "((((()(())))())())()", "((((()(())))()))(())", "((((()(())))()))()()", "((((()(()))))((())))", "((((()(()))))(()()))", "((((()(()))))(())())", "((((()(()))))(()))()", "((((()(()))))()(()))", "((((()(()))))()()())", "((((()(()))))()())()", "((((()(()))))())(())", "((((()(()))))())()()", "((((()(())))))((()))", "((((()(())))))(()())", "((((()(())))))(())()", "((((()(())))))()(())", "((((()(())))))()()()", "((((()()(((())))))))", "((((()()((()()))))))", "((((()()((())())))))", "((((()()((()))()))))", "((((()()((())))())))", "((((()()((()))))()))", "((((()()((())))))())", "((((()()((()))))))()", "((((()()(()(()))))))", "((((()()(()()())))))", "((((()()(()())()))))", "((((()()(()()))())))", "((((()()(()())))()))", "((((()()(()()))))())", "((((()()(()())))))()", "((((()()(())(())))))", "((((()()(())()()))))", "((((()()(())())())))", "((((()()(())()))()))", "((((()()(())())))())", "((((()()(())()))))()", "((((()()(()))(()))))", "((((()()(()))()())))", "((((()()(()))())()))", "((((()()(()))()))())", "((((()()(()))())))()", "((((()()(())))(())))", "((((()()(())))()()))", "((((()()(())))())())", "((((()()(())))()))()", "((((()()(()))))(()))", "((((()()(()))))()())", "((((()()(()))))())()", "((((()()(())))))(())", "((((()()(())))))()()", "((((()()()((()))))))", "((((()()()(()())))))", "((((()()()(())()))))", "((((()()()(()))())))", "((((()()()(())))()))", "((((()()()(()))))())", "((((()()()(())))))()", "((((()()()()(())))))", "((((()()()()()()))))", "((((()()()()())())))", "((((()()()()()))()))", "((((()()()()())))())", "((((()()()()()))))()", "((((()()()())(()))))", "((((()()()())()())))", "((((()()()())())()))", "((((()()()())()))())", "((((()()()())())))()", "((((()()()()))(())))", "((((()()()()))()()))", "((((()()()()))())())", "((((()()()()))()))()", "((((()()()())))(()))", "((((()()()())))()())", "((((()()()())))())()", "((((()()()()))))(())", "((((()()()()))))()()", "((((()()())((())))))", "((((()()())(()()))))", "((((()()())(())())))", "((((()()())(()))()))", "((((()()())(())))())", "((((()()())(()))))()", "((((()()())()(()))))", "((((()()())()()())))", "((((()()())()())()))", "((((()()())()()))())", "((((()()())()())))()", "((((()()())())(())))", "((((()()())())()()))", "((((()()())())())())", "((((()()())())()))()", "((((()()())()))(()))", "((((()()())()))()())", "((((()()())()))())()", "((((()()())())))(())", "((((()()())())))()()", "((((()()()))((()))))", "((((()()()))(()())))", "((((()()()))(())()))", "((((()()()))(()))())", "((((()()()))(())))()", "((((()()()))()(())))", "((((()()()))()()()))", "((((()()()))()())())", "((((()()()))()()))()", "((((()()()))())(()))", "((((()()()))())()())", "((((()()()))())())()", "((((()()()))()))(())", "((((()()()))()))()()", "((((()()())))((())))", "((((()()())))(()()))", "((((()()())))(())())", "((((()()())))(()))()", "((((()()())))()(()))", "((((()()())))()()())", "((((()()())))()())()", "((((()()())))())(())", "((((()()())))())()()", "((((()()()))))((()))", "((((()()()))))(()())", "((((()()()))))(())()", "((((()()()))))()(())", "((((()()()))))()()()", "((((()())(((()))))))", "((((()())((()())))))", "((((()())((())()))))", "((((()())((()))())))", "((((()())((())))()))", "((((()())((()))))())", "((((()())((())))))()", "((((()())(()(())))))", "((((()())(()()()))))", "((((()())(()())())))", "((((()())(()()))()))", "((((()())(()())))())", "((((()())(()()))))()", "((((()())(())(()))))", "((((()())(())()())))", "((((()())(())())()))", "((((()())(())()))())", "((((()())(())())))()", "((((()())(()))(())))", "((((()())(()))()()))", "((((()())(()))())())", "((((()())(()))()))()", "((((()())(())))(()))", "((((()())(())))()())", "((((()())(())))())()", "((((()())(()))))(())", "((((()())(()))))()()", "((((()())()((())))))", "((((()())()(()()))))", "((((()())()(())())))", "((((()())()(()))()))", "((((()())()(())))())", "((((()())()(()))))()", "((((()())()()(()))))", "((((()())()()()())))", "((((()())()()())()))", "((((()())()()()))())", "((((()())()()())))()", "((((()())()())(())))", "((((()())()())()()))", "((((()())()())())())", "((((()())()())()))()", "((((()())()()))(()))", "((((()())()()))()())", "((((()())()()))())()", "((((()())()())))(())", "((((()())()())))()()", "((((()())())((()))))", "((((()())())(()())))", "((((()())())(())()))", "((((()())())(()))())", "((((()())())(())))()", "((((()())())()(())))", "((((()())())()()()))", "((((()())())()())())", "((((()())())()()))()", "((((()())())())(()))", "((((()())())())()())", "((((()())())())())()", "((((()())())()))(())", "((((()())())()))()()", "((((()())()))((())))", "((((()())()))(()()))", "((((()())()))(())())", "((((()())()))(()))()", "((((()())()))()(()))", "((((()())()))()()())", "((((()())()))()())()", "((((()())()))())(())", "((((()())()))())()()", "((((()())())))((()))", "((((()())())))(()())", "((((()())())))(())()", "((((()())())))()(())", "((((()())())))()()()", "((((()()))(((())))))", "((((()()))((()()))))", "((((()()))((())())))", "((((()()))((()))()))", "((((()()))((())))())", "((((()()))((()))))()", "((((()()))(()(()))))", "((((()()))(()()())))", "((((()()))(()())()))", "((((()()))(()()))())", "((((()()))(()())))()", "((((()()))(())(())))", "((((()()))(())()()))", "((((()()))(())())())", "((((()()))(())()))()", "((((()()))(()))(()))", "((((()()))(()))()())", "((((()()))(()))())()", "((((()()))(())))(())", "((((()()))(())))()()", "((((()()))()((()))))", "((((()()))()(()())))", "((((()()))()(())()))", "((((()()))()(()))())", "((((()()))()(())))()", "((((()()))()()(())))", "((((()()))()()()()))", "((((()()))()()())())", "((((()()))()()()))()", "((((()()))()())(()))", "((((()()))()())()())", "((((()()))()())())()", "((((()()))()()))(())", "((((()()))()()))()()", "((((()()))())((())))", "((((()()))())(()()))", "((((()()))())(())())", "((((()()))())(()))()", "((((()()))())()(()))", "((((()()))())()()())", "((((()()))())()())()", "((((()()))())())(())", "((((()()))())())()()", "((((()()))()))((()))", "((((()()))()))(()())", "((((()()))()))(())()", "((((()()))()))()(())", "((((()()))()))()()()", "((((()())))(((()))))", "((((()())))((()())))", "((((()())))((())()))", "((((()())))((()))())", "((((()())))((())))()", "((((()())))(()(())))", "((((()())))(()()()))", "((((()())))(()())())", "((((()())))(()()))()", "((((()())))(())(()))", "((((()())))(())()())", "((((()())))(())())()", "((((()())))(()))(())", "((((()())))(()))()()", "((((()())))()((())))", "((((()())))()(()()))", "((((()())))()(())())", "((((()())))()(()))()", "((((()())))()()(()))", "((((()())))()()()())", "((((()())))()()())()", "((((()())))()())(())", "((((()())))()())()()", "((((()())))())((()))", "((((()())))())(()())", "((((()())))())(())()", "((((()())))())()(())", "((((()())))())()()()", "((((()()))))(((())))", "((((()()))))((()()))", "((((()()))))((())())", "((((()()))))((()))()", "((((()()))))(()(()))", "((((()()))))(()()())", "((((()()))))(()())()", "((((()()))))(())(())", "((((()()))))(())()()", "((((()()))))()((()))", "((((()()))))()(()())", "((((()()))))()(())()", "((((()()))))()()(())", "((((()()))))()()()()", "((((())((((())))))))", "((((())(((()()))))))", "((((())(((())())))))", "((((())(((()))()))))", "((((())(((())))())))", "((((())(((()))))()))", "((((())(((())))))())", "((((())(((()))))))()", "((((())((()(()))))))", "((((())((()()())))))", "((((())((()())()))))", "((((())((()()))())))", "((((())((()())))()))", "((((())((()()))))())", "((((())((()())))))()", "((((())((())(())))))", "((((())((())()()))))", "((((())((())())())))", "((((())((())()))()))", "((((())((())())))())", "((((())((())()))))()", "((((())((()))(()))))", "((((())((()))()())))", "((((())((()))())()))", "((((())((()))()))())", "((((())((()))())))()", "((((())((())))(())))", "((((())((())))()()))", "((((())((())))())())", "((((())((())))()))()", "((((())((()))))(()))", "((((())((()))))()())", "((((())((()))))())()", "((((())((())))))(())", "((((())((())))))()()", "((((())(()((()))))))", "((((())(()(()())))))", "((((())(()(())()))))", "((((())(()(()))())))", "((((())(()(())))()))", "((((())(()(()))))())", "((((())(()(())))))()", "((((())(()()(())))))", "((((())(()()()()))))", "((((())(()()())())))", "((((())(()()()))()))", "((((())(()()())))())", "((((())(()()()))))()", "((((())(()())(()))))", "((((())(()())()())))", "((((())(()())())()))", "((((())(()())()))())", "((((())(()())())))()", "((((())(()()))(())))", "((((())(()()))()()))", "((((())(()()))())())", "((((())(()()))()))()", "((((())(()())))(()))", "((((())(()())))()())", "((((())(()())))())()", "((((())(()()))))(())", "((((())(()()))))()()", "((((())(())((())))))", "((((())(())(()()))))", "((((())(())(())())))", "((((())(())(()))()))", "((((())(())(())))())", "((((())(())(()))))()", "((((())(())()(()))))", "((((())(())()()())))", "((((())(())()())()))", "((((())(())()()))())", "((((())(())()())))()", "((((())(())())(())))", "((((())(())())()()))", "((((())(())())())())", "((((())(())())()))()", "((((())(())()))(()))", "((((())(())()))()())", "((((())(())()))())()", "((((())(())())))(())", "((((())(())())))()()", "((((())(()))((()))))", "((((())(()))(()())))", "((((())(()))(())()))", "((((())(()))(()))())", "((((())(()))(())))()", "((((())(()))()(())))", "((((())(()))()()()))", "((((())(()))()())())", "((((())(()))()()))()", "((((())(()))())(()))", "((((())(()))())()())", "((((())(()))())())()", "((((())(()))()))(())", "((((())(()))()))()()", "((((())(())))((())))", "((((())(())))(()()))", "((((())(())))(())())", "((((())(())))(()))()", "((((())(())))()(()))", "((((())(())))()()())", "((((())(())))()())()", "((((())(())))())(())", "((((())(())))())()()", "((((())(()))))((()))", "((((())(()))))(()())", "((((())(()))))(())()", "((((())(()))))()(())", "((((())(()))))()()()", "((((())()(((()))))))", "((((())()((()())))))", "((((())()((())()))))", "((((())()((()))())))", "((((())()((())))()))", "((((())()((()))))())", "((((())()((())))))()", "((((())()(()(())))))", "((((())()(()()()))))", "((((())()(()())())))", "((((())()(()()))()))", "((((())()(()())))())", "((((())()(()()))))()", "((((())()(())(()))))", "((((())()(())()())))", "((((())()(())())()))", "((((())()(())()))())", "((((())()(())())))()", "((((())()(()))(())))", "((((())()(()))()()))", "((((())()(()))())())", "((((())()(()))()))()", "((((())()(())))(()))", "((((())()(())))()())", "((((())()(())))())()", "((((())()(()))))(())", "((((())()(()))))()()", "((((())()()((())))))", "((((())()()(()()))))", "((((())()()(())())))", "((((())()()(()))()))", "((((())()()(())))())", "((((())()()(()))))()", "((((())()()()(()))))", "((((())()()()()())))", "((((())()()()())()))", "((((())()()()()))())", "((((())()()()())))()", "((((())()()())(())))", "((((())()()())()()))", "((((())()()())())())", "((((())()()())()))()", "((((())()()()))(()))", "((((())()()()))()())", "((((())()()()))())()", "((((())()()())))(())", "((((())()()())))()()", "((((())()())((()))))", "((((())()())(()())))", "((((())()())(())()))", "((((())()())(()))())", "((((())()())(())))()", "((((())()())()(())))", "((((())()())()()()))", "((((())()())()())())", "((((())()())()()))()", "((((())()())())(()))", "((((())()())())()())", "((((())()())())())()", "((((())()())()))(())", "((((())()())()))()()", "((((())()()))((())))", "((((())()()))(()()))", "((((())()()))(())())", "((((())()()))(()))()", "((((())()()))()(()))", "((((())()()))()()())", "((((())()()))()())()", "((((())()()))())(())", "((((())()()))())()()", "((((())()())))((()))", "((((())()())))(()())", "((((())()())))(())()", "((((())()())))()(())", "((((())()())))()()()", "((((())())(((())))))", "((((())())((()()))))", "((((())())((())())))", "((((())())((()))()))", "((((())())((())))())", "((((())())((()))))()", "((((())())(()(()))))", "((((())())(()()())))", "((((())())(()())()))", "((((())())(()()))())", "((((())())(()())))()", "((((())())(())(())))", "((((())())(())()()))", "((((())())(())())())", "((((())())(())()))()", "((((())())(()))(()))", "((((())())(()))()())", "((((())())(()))())()", "((((())())(())))(())", "((((())())(())))()()", "((((())())()((()))))", "((((())())()(()())))", "((((())())()(())()))", "((((())())()(()))())", "((((())())()(())))()", "((((())())()()(())))", "((((())())()()()()))", "((((())())()()())())", "((((())())()()()))()", "((((())())()())(()))", "((((())())()())()())", "((((())())()())())()", "((((())())()()))(())", "((((())())()()))()()", "((((())())())((())))", "((((())())())(()()))", "((((())())())(())())", "((((())())())(()))()", "((((())())())()(()))", "((((())())())()()())", "((((())())())()())()", "((((())())())())(())", "((((())())())())()()", "((((())())()))((()))", "((((())())()))(()())", "((((())())()))(())()", "((((())())()))()(())", "((((())())()))()()()", "((((())()))(((()))))", "((((())()))((()())))", "((((())()))((())()))", "((((())()))((()))())", "((((())()))((())))()", "((((())()))(()(())))", "((((())()))(()()()))", "((((())()))(()())())", "((((())()))(()()))()", "((((())()))(())(()))", "((((())()))(())()())", "((((())()))(())())()", "((((())()))(()))(())", "((((())()))(()))()()", "((((())()))()((())))", "((((())()))()(()()))", "((((())()))()(())())", "((((())()))()(()))()", "((((())()))()()(()))", "((((())()))()()()())", "((((())()))()()())()", "((((())()))()())(())", "((((())()))()())()()", "((((())()))())((()))", "((((())()))())(()())", "((((())()))())(())()", "((((())()))())()(())", "((((())()))())()()()", "((((())())))(((())))", "((((())())))((()()))", "((((())())))((())())", "((((())())))((()))()", "((((())())))(()(()))", "((((())())))(()()())", "((((())())))(()())()", "((((())())))(())(())", "((((())())))(())()()", "((((())())))()((()))", "((((())())))()(()())", "((((())())))()(())()", "((((())())))()()(())", "((((())())))()()()()", "((((()))((((()))))))", "((((()))(((()())))))", "((((()))(((())()))))", "((((()))(((()))())))", "((((()))(((())))()))", "((((()))(((()))))())", "((((()))(((())))))()", "((((()))((()(())))))", "((((()))((()()()))))", "((((()))((()())())))", "((((()))((()()))()))", "((((()))((()())))())", "((((()))((()()))))()", "((((()))((())(()))))", "((((()))((())()())))", "((((()))((())())()))", "((((()))((())()))())", "((((()))((())())))()", "((((()))((()))(())))", "((((()))((()))()()))", "((((()))((()))())())", "((((()))((()))()))()", "((((()))((())))(()))", "((((()))((())))()())", "((((()))((())))())()", "((((()))((()))))(())", "((((()))((()))))()()", "((((()))(()((())))))", "((((()))(()(()()))))", "((((()))(()(())())))", "((((()))(()(()))()))", "((((()))(()(())))())", "((((()))(()(()))))()", "((((()))(()()(()))))", "((((()))(()()()())))", "((((()))(()()())()))", "((((()))(()()()))())", "((((()))(()()())))()", "((((()))(()())(())))", "((((()))(()())()()))", "((((()))(()())())())", "((((()))(()())()))()", "((((()))(()()))(()))", "((((()))(()()))()())", "((((()))(()()))())()", "((((()))(()())))(())", "((((()))(()())))()()", "((((()))(())((()))))", "((((()))(())(()())))", "((((()))(())(())()))", "((((()))(())(()))())", "((((()))(())(())))()", "((((()))(())()(())))", "((((()))(())()()()))", "((((()))(())()())())", "((((()))(())()()))()", "((((()))(())())(()))", "((((()))(())())()())", "((((()))(())())())()", "((((()))(())()))(())", "((((()))(())()))()()", "((((()))(()))((())))", "((((()))(()))(()()))", "((((()))(()))(())())", "((((()))(()))(()))()", "((((()))(()))()(()))", "((((()))(()))()()())", "((((()))(()))()())()", "((((()))(()))())(())", "((((()))(()))())()()", "((((()))(())))((()))", "((((()))(())))(()())", "((((()))(())))(())()", "((((()))(())))()(())", "((((()))(())))()()()", "((((()))()(((())))))", "((((()))()((()()))))", "((((()))()((())())))", "((((()))()((()))()))", "((((()))()((())))())", "((((()))()((()))))()", "((((()))()(()(()))))", "((((()))()(()()())))", "((((()))()(()())()))", "((((()))()(()()))())", "((((()))()(()())))()", "((((()))()(())(())))", "((((()))()(())()()))", "((((()))()(())())())", "((((()))()(())()))()", "((((()))()(()))(()))", "((((()))()(()))()())", "((((()))()(()))())()", "((((()))()(())))(())", "((((()))()(())))()()", "((((()))()()((()))))", "((((()))()()(()())))", "((((()))()()(())()))", "((((()))()()(()))())", "((((()))()()(())))()", "((((()))()()()(())))", "((((()))()()()()()))", "((((()))()()()())())", "((((()))()()()()))()", "((((()))()()())(()))", "((((()))()()())()())", "((((()))()()())())()", "((((()))()()()))(())", "((((()))()()()))()()", "((((()))()())((())))", "((((()))()())(()()))", "((((()))()())(())())", "((((()))()())(()))()", "((((()))()())()(()))", "((((()))()())()()())", "((((()))()())()())()", "((((()))()())())(())", "((((()))()())())()()", "((((()))()()))((()))", "((((()))()()))(()())", "((((()))()()))(())()", "((((()))()()))()(())", "((((()))()()))()()()", "((((()))())(((()))))", "((((()))())((()())))", "((((()))())((())()))", "((((()))())((()))())", "((((()))())((())))()", "((((()))())(()(())))", "((((()))())(()()()))", "((((()))())(()())())", "((((()))())(()()))()", "((((()))())(())(()))", "((((()))())(())()())", "((((()))())(())())()", "((((()))())(()))(())", "((((()))())(()))()()", "((((()))())()((())))", "((((()))())()(()()))", "((((()))())()(())())", "((((()))())()(()))()", "((((()))())()()(()))", "((((()))())()()()())", "((((()))())()()())()", "((((()))())()())(())", "((((()))())()())()()", "((((()))())())((()))", "((((()))())())(()())", "((((()))())())(())()", "((((()))())())()(())", "((((()))())())()()()", "((((()))()))(((())))", "((((()))()))((()()))", "((((()))()))((())())", "((((()))()))((()))()", "((((()))()))(()(()))", "((((()))()))(()()())", "((((()))()))(()())()", "((((()))()))(())(())", "((((()))()))(())()()", "((((()))()))()((()))", "((((()))()))()(()())", "((((()))()))()(())()", "((((()))()))()()(())", "((((()))()))()()()()", "((((())))((((())))))", "((((())))(((()()))))", "((((())))(((())())))", "((((())))(((()))()))", "((((())))(((())))())", "((((())))(((()))))()", "((((())))((()(()))))", "((((())))((()()())))", "((((())))((()())()))", "((((())))((()()))())", "((((())))((()())))()", "((((())))((())(())))", "((((())))((())()()))", "((((())))((())())())", "((((())))((())()))()", "((((())))((()))(()))", "((((())))((()))()())", "((((())))((()))())()", "((((())))((())))(())", "((((())))((())))()()", "((((())))(()((()))))", "((((())))(()(()())))", "((((())))(()(())()))", "((((())))(()(()))())", "((((())))(()(())))()", "((((())))(()()(())))", "((((())))(()()()()))", "((((())))(()()())())", "((((())))(()()()))()", "((((())))(()())(()))", "((((())))(()())()())", "((((())))(()())())()", "((((())))(()()))(())", "((((())))(()()))()()", "((((())))(())((())))", "((((())))(())(()()))", "((((())))(())(())())", "((((())))(())(()))()", "((((())))(())()(()))", "((((())))(())()()())", "((((())))(())()())()", "((((())))(())())(())", "((((())))(())())()()", "((((())))(()))((()))", "((((())))(()))(()())", "((((())))(()))(())()", "((((())))(()))()(())", "((((())))(()))()()()", "((((())))()(((()))))", "((((())))()((()())))", "((((())))()((())()))", "((((())))()((()))())", "((((())))()((())))()", "((((())))()(()(())))", "((((())))()(()()()))", "((((())))()(()())())", "((((())))()(()()))()", "((((())))()(())(()))", "((((())))()(())()())", "((((())))()(())())()", "((((())))()(()))(())", "((((())))()(()))()()", "((((())))()()((())))", "((((())))()()(()()))", "((((())))()()(())())", "((((())))()()(()))()", "((((())))()()()(()))", "((((())))()()()()())", "((((())))()()()())()", "((((())))()()())(())", "((((())))()()())()()", "((((())))()())((()))", "((((())))()())(()())", "((((())))()())(())()", "((((())))()())()(())", "((((())))()())()()()", "((((())))())(((())))", "((((())))())((()()))", "((((())))())((())())", "((((())))())((()))()", "((((())))())(()(()))", "((((())))())(()()())", "((((())))())(()())()", "((((())))())(())(())", "((((())))())(())()()", "((((())))())()((()))", "((((())))())()(()())", "((((())))())()(())()", "((((())))())()()(())", "((((())))())()()()()", "((((()))))((((()))))", "((((()))))(((()())))", "((((()))))(((())()))", "((((()))))(((()))())", "((((()))))(((())))()", "((((()))))((()(())))", "((((()))))((()()()))", "((((()))))((()())())", "((((()))))((()()))()", "((((()))))((())(()))", "((((()))))((())()())", "((((()))))((())())()", "((((()))))((()))(())", "((((()))))((()))()()", "((((()))))(()((())))", "((((()))))(()(()()))", "((((()))))(()(())())", "((((()))))(()(()))()", "((((()))))(()()(()))", "((((()))))(()()()())", "((((()))))(()()())()", "((((()))))(()())(())", "((((()))))(()())()()", "((((()))))(())((()))", "((((()))))(())(()())", "((((()))))(())(())()", "((((()))))(())()(())", "((((()))))(())()()()", "((((()))))()(((())))", "((((()))))()((()()))", "((((()))))()((())())", "((((()))))()((()))()", "((((()))))()(()(()))", "((((()))))()(()()())", "((((()))))()(()())()", "((((()))))()(())(())", "((((()))))()(())()()", "((((()))))()()((()))", "((((()))))()()(()())", "((((()))))()()(())()", "((((()))))()()()(())", "((((()))))()()()()()", "(((()(((((()))))))))", "(((()((((()())))))))", "(((()((((())()))))))", "(((()((((()))())))))", "(((()((((())))()))))", "(((()((((()))))())))", "(((()((((())))))()))", "(((()((((()))))))())", "(((()((((())))))))()", "(((()(((()(())))))))", "(((()(((()()()))))))", "(((()(((()())())))))", "(((()(((()()))()))))", "(((()(((()())))())))", "(((()(((()()))))()))", "(((()(((()())))))())", "(((()(((()()))))))()", "(((()(((())(()))))))", "(((()(((())()())))))", "(((()(((())())()))))", "(((()(((())()))())))", "(((()(((())())))()))", "(((()(((())()))))())", "(((()(((())())))))()", "(((()(((()))(())))))", "(((()(((()))()()))))", "(((()(((()))())())))", "(((()(((()))()))()))", "(((()(((()))())))())", "(((()(((()))()))))()", "(((()(((())))(()))))", "(((()(((())))()())))", "(((()(((())))())()))", "(((()(((())))()))())", "(((()(((())))())))()", "(((()(((()))))(())))", "(((()(((()))))()()))", "(((()(((()))))())())", "(((()(((()))))()))()", "(((()(((())))))(()))", "(((()(((())))))()())", "(((()(((())))))())()", "(((()(((()))))))(())", "(((()(((()))))))()()", "(((()((()((())))))))", "(((()((()(()()))))))", "(((()((()(())())))))", "(((()((()(()))()))))", "(((()((()(())))())))", "(((()((()(()))))()))", "(((()((()(())))))())", "(((()((()(()))))))()", "(((()((()()(()))))))", "(((()((()()()())))))", "(((()((()()())()))))", "(((()((()()()))())))", "(((()((()()())))()))", "(((()((()()()))))())", "(((()((()()())))))()", "(((()((()())(())))))", "(((()((()())()()))))", "(((()((()())())())))", "(((()((()())()))()))", "(((()((()())())))())", "(((()((()())()))))()", "(((()((()()))(()))))", "(((()((()()))()())))", "(((()((()()))())()))", "(((()((()()))()))())", "(((()((()()))())))()", "(((()((()())))(())))", "(((()((()())))()()))", "(((()((()())))())())", "(((()((()())))()))()", "(((()((()()))))(()))", "(((()((()()))))()())", "(((()((()()))))())()", "(((()((()())))))(())", "(((()((()())))))()()", "(((()((())((()))))))", "(((()((())(()())))))", "(((()((())(())()))))", "(((()((())(()))())))", "(((()((())(())))()))", "(((()((())(()))))())", "(((()((())(())))))()", "(((()((())()(())))))", "(((()((())()()()))))", "(((()((())()())())))", "(((()((())()()))()))", "(((()((())()())))())", "(((()((())()()))))()", "(((()((())())(()))))", "(((()((())())()())))", "(((()((())())())()))", "(((()((())())()))())", "(((()((())())())))()", "(((()((())()))(())))", "(((()((())()))()()))", "(((()((())()))())())", "(((()((())()))()))()", "(((()((())())))(()))", "(((()((())())))()())", "(((()((())())))())()", "(((()((())()))))(())", "(((()((())()))))()()", "(((()((()))((())))))", "(((()((()))(()()))))", "(((()((()))(())())))", "(((()((()))(()))()))", "(((()((()))(())))())", "(((()((()))(()))))()", "(((()((()))()(()))))", "(((()((()))()()())))", "(((()((()))()())()))", "(((()((()))()()))())", "(((()((()))()())))()", "(((()((()))())(())))", "(((()((()))())()()))", "(((()((()))())())())", "(((()((()))())()))()", "(((()((()))()))(()))", "(((()((()))()))()())", "(((()((()))()))())()", "(((()((()))())))(())", "(((()((()))())))()()", "(((()((())))((()))))", "(((()((())))(()())))", "(((()((())))(())()))", "(((()((())))(()))())", "(((()((())))(())))()", "(((()((())))()(())))", "(((()((())))()()()))", "(((()((())))()())())", "(((()((())))()()))()", "(((()((())))())(()))", "(((()((())))())()())", "(((()((())))())())()", "(((()((())))()))(())", "(((()((())))()))()()", "(((()((()))))((())))", "(((()((()))))(()()))", "(((()((()))))(())())", "(((()((()))))(()))()", "(((()((()))))()(()))", "(((()((()))))()()())", "(((()((()))))()())()", "(((()((()))))())(())", "(((()((()))))())()()", "(((()((())))))((()))", "(((()((())))))(()())", "(((()((())))))(())()", "(((()((())))))()(())", "(((()((())))))()()()", "(((()(()(((())))))))", "(((()(()((()()))))))", "(((()(()((())())))))", "(((()(()((()))()))))", "(((()(()((())))())))", "(((()(()((()))))()))", "(((()(()((())))))())", "(((()(()((()))))))()", "(((()(()(()(()))))))", "(((()(()(()()())))))", "(((()(()(()())()))))", "(((()(()(()()))())))", "(((()(()(()())))()))", "(((()(()(()()))))())", "(((()(()(()())))))()", "(((()(()(())(())))))", "(((()(()(())()()))))", "(((()(()(())())())))", "(((()(()(())()))()))", "(((()(()(())())))())", "(((()(()(())()))))()", "(((()(()(()))(()))))", "(((()(()(()))()())))", "(((()(()(()))())()))", "(((()(()(()))()))())", "(((()(()(()))())))()", "(((()(()(())))(())))", "(((()(()(())))()()))", "(((()(()(())))())())", "(((()(()(())))()))()", "(((()(()(()))))(()))", "(((()(()(()))))()())", "(((()(()(()))))())()", "(((()(()(())))))(())", "(((()(()(())))))()()", "(((()(()()((()))))))", "(((()(()()(()())))))", "(((()(()()(())()))))", "(((()(()()(()))())))", "(((()(()()(())))()))", "(((()(()()(()))))())", "(((()(()()(())))))()", "(((()(()()()(())))))", "(((()(()()()()()))))", "(((()(()()()())())))", "(((()(()()()()))()))", "(((()(()()()())))())", "(((()(()()()()))))()", "(((()(()()())(()))))", "(((()(()()())()())))", "(((()(()()())())()))", "(((()(()()())()))())", "(((()(()()())())))()", "(((()(()()()))(())))", "(((()(()()()))()()))", "(((()(()()()))())())", "(((()(()()()))()))()", "(((()(()()())))(()))", "(((()(()()())))()())", "(((()(()()())))())()", "(((()(()()()))))(())", "(((()(()()()))))()()", "(((()(()())((())))))", "(((()(()())(()()))))", "(((()(()())(())())))", "(((()(()())(()))()))", "(((()(()())(())))())", "(((()(()())(()))))()", "(((()(()())()(()))))", "(((()(()())()()())))", "(((()(()())()())()))", "(((()(()())()()))())", "(((()(()())()())))()", "(((()(()())())(())))", "(((()(()())())()()))", "(((()(()())())())())", "(((()(()())())()))()", "(((()(()())()))(()))", "(((()(()())()))()())", "(((()(()())()))())()", "(((()(()())())))(())", "(((()(()())())))()()", "(((()(()()))((()))))", "(((()(()()))(()())))", "(((()(()()))(())()))", "(((()(()()))(()))())", "(((()(()()))(())))()", "(((()(()()))()(())))", "(((()(()()))()()()))", "(((()(()()))()())())", "(((()(()()))()()))()", "(((()(()()))())(()))", "(((()(()()))())()())", "(((()(()()))())())()", "(((()(()()))()))(())", "(((()(()()))()))()()", "(((()(()())))((())))", "(((()(()())))(()()))", "(((()(()())))(())())", "(((()(()())))(()))()", "(((()(()())))()(()))", "(((()(()())))()()())", "(((()(()())))()())()", "(((()(()())))())(())", "(((()(()())))())()()", "(((()(()()))))((()))", "(((()(()()))))(()())", "(((()(()()))))(())()", "(((()(()()))))()(())", "(((()(()()))))()()()", "(((()(())(((()))))))", "(((()(())((()())))))", "(((()(())((())()))))", "(((()(())((()))())))", "(((()(())((())))()))", "(((()(())((()))))())", "(((()(())((())))))()", "(((()(())(()(())))))", "(((()(())(()()()))))", "(((()(())(()())())))", "(((()(())(()()))()))", "(((()(())(()())))())", "(((()(())(()()))))()", "(((()(())(())(()))))", "(((()(())(())()())))", "(((()(())(())())()))", "(((()(())(())()))())", "(((()(())(())())))()", "(((()(())(()))(())))", "(((()(())(()))()()))", "(((()(())(()))())())", "(((()(())(()))()))()", "(((()(())(())))(()))", "(((()(())(())))()())", "(((()(())(())))())()", "(((()(())(()))))(())", "(((()(())(()))))()()", "(((()(())()((())))))", "(((()(())()(()()))))", "(((()(())()(())())))", "(((()(())()(()))()))", "(((()(())()(())))())", "(((()(())()(()))))()", "(((()(())()()(()))))", "(((()(())()()()())))", "(((()(())()()())()))", "(((()(())()()()))())", "(((()(())()()())))()", "(((()(())()())(())))", "(((()(())()())()()))", "(((()(())()())())())", "(((()(())()())()))()", "(((()(())()()))(()))", "(((()(())()()))()())", "(((()(())()()))())()", "(((()(())()())))(())", "(((()(())()())))()()", "(((()(())())((()))))", "(((()(())())(()())))", "(((()(())())(())()))", "(((()(())())(()))())", "(((()(())())(())))()", "(((()(())())()(())))", "(((()(())())()()()))", "(((()(())())()())())", "(((()(())())()()))()", "(((()(())())())(()))", "(((()(())())())()())", "(((()(())())())())()", "(((()(())())()))(())", "(((()(())())()))()()", "(((()(())()))((())))", "(((()(())()))(()()))", "(((()(())()))(())())", "(((()(())()))(()))()", "(((()(())()))()(()))", "(((()(())()))()()())", "(((()(())()))()())()", "(((()(())()))())(())", "(((()(())()))())()()", "(((()(())())))((()))", "(((()(())())))(()())", "(((()(())())))(())()", "(((()(())())))()(())", "(((()(())())))()()()", "(((()(()))(((())))))", "(((()(()))((()()))))", "(((()(()))((())())))", "(((()(()))((()))()))", "(((()(()))((())))())", "(((()(()))((()))))()", "(((()(()))(()(()))))", "(((()(()))(()()())))", "(((()(()))(()())()))", "(((()(()))(()()))())", "(((()(()))(()())))()", "(((()(()))(())(())))", "(((()(()))(())()()))", "(((()(()))(())())())", "(((()(()))(())()))()", "(((()(()))(()))(()))", "(((()(()))(()))()())", "(((()(()))(()))())()", "(((()(()))(())))(())", "(((()(()))(())))()()", "(((()(()))()((()))))", "(((()(()))()(()())))", "(((()(()))()(())()))", "(((()(()))()(()))())", "(((()(()))()(())))()", "(((()(()))()()(())))", "(((()(()))()()()()))", "(((()(()))()()())())", "(((()(()))()()()))()", "(((()(()))()())(()))", "(((()(()))()())()())", "(((()(()))()())())()", "(((()(()))()()))(())", "(((()(()))()()))()()", "(((()(()))())((())))", "(((()(()))())(()()))", "(((()(()))())(())())", "(((()(()))())(()))()", "(((()(()))())()(()))", "(((()(()))())()()())", "(((()(()))())()())()", "(((()(()))())())(())", "(((()(()))())())()()", "(((()(()))()))((()))", "(((()(()))()))(()())", "(((()(()))()))(())()", "(((()(()))()))()(())", "(((()(()))()))()()()", "(((()(())))(((()))))", "(((()(())))((()())))", "(((()(())))((())()))", "(((()(())))((()))())", "(((()(())))((())))()", "(((()(())))(()(())))", "(((()(())))(()()()))", "(((()(())))(()())())", "(((()(())))(()()))()", "(((()(())))(())(()))", "(((()(())))(())()())", "(((()(())))(())())()", "(((()(())))(()))(())", "(((()(())))(()))()()", "(((()(())))()((())))", "(((()(())))()(()()))", "(((()(())))()(())())", "(((()(())))()(()))()", "(((()(())))()()(()))", "(((()(())))()()()())", "(((()(())))()()())()", "(((()(())))()())(())", "(((()(())))()())()()", "(((()(())))())((()))", "(((()(())))())(()())", "(((()(())))())(())()", "(((()(())))())()(())", "(((()(())))())()()()", "(((()(()))))(((())))", "(((()(()))))((()()))", "(((()(()))))((())())", "(((()(()))))((()))()", "(((()(()))))(()(()))", "(((()(()))))(()()())", "(((()(()))))(()())()", "(((()(()))))(())(())", "(((()(()))))(())()()", "(((()(()))))()((()))", "(((()(()))))()(()())", "(((()(()))))()(())()", "(((()(()))))()()(())", "(((()(()))))()()()()", "(((()()((((())))))))", "(((()()(((()()))))))", "(((()()(((())())))))", "(((()()(((()))()))))", "(((()()(((())))())))", "(((()()(((()))))()))", "(((()()(((())))))())", "(((()()(((()))))))()", "(((()()((()(()))))))", "(((()()((()()())))))", "(((()()((()())()))))", "(((()()((()()))())))", "(((()()((()())))()))", "(((()()((()()))))())", "(((()()((()())))))()", "(((()()((())(())))))", "(((()()((())()()))))", "(((()()((())())())))", "(((()()((())()))()))", "(((()()((())())))())", "(((()()((())()))))()", "(((()()((()))(()))))", "(((()()((()))()())))", "(((()()((()))())()))", "(((()()((()))()))())", "(((()()((()))())))()", "(((()()((())))(())))", "(((()()((())))()()))", "(((()()((())))())())", "(((()()((())))()))()", "(((()()((()))))(()))", "(((()()((()))))()())", "(((()()((()))))())()", "(((()()((())))))(())", "(((()()((())))))()()", "(((()()(()((()))))))", "(((()()(()(()())))))", "(((()()(()(())()))))", "(((()()(()(()))())))", "(((()()(()(())))()))", "(((()()(()(()))))())", "(((()()(()(())))))()", "(((()()(()()(())))))", "(((()()(()()()()))))", "(((()()(()()())())))", "(((()()(()()()))()))", "(((()()(()()())))())", "(((()()(()()()))))()", "(((()()(()())(()))))", "(((()()(()())()())))", "(((()()(()())())()))", "(((()()(()())()))())", "(((()()(()())())))()", "(((()()(()()))(())))", "(((()()(()()))()()))", "(((()()(()()))())())", "(((()()(()()))()))()", "(((()()(()())))(()))", "(((()()(()())))()())", "(((()()(()())))())()", "(((()()(()()))))(())", "(((()()(()()))))()()", "(((()()(())((())))))", "(((()()(())(()()))))", "(((()()(())(())())))", "(((()()(())(()))()))", "(((()()(())(())))())", "(((()()(())(()))))()", "(((()()(())()(()))))", "(((()()(())()()())))", "(((()()(())()())()))", "(((()()(())()()))())", "(((()()(())()())))()", "(((()()(())())(())))", "(((()()(())())()()))", "(((()()(())())())())", "(((()()(())())()))()", "(((()()(())()))(()))", "(((()()(())()))()())", "(((()()(())()))())()", "(((()()(())())))(())", "(((()()(())())))()()", "(((()()(()))((()))))", "(((()()(()))(()())))", "(((()()(()))(())()))", "(((()()(()))(()))())", "(((()()(()))(())))()", "(((()()(()))()(())))", "(((()()(()))()()()))", "(((()()(()))()())())", "(((()()(()))()()))()", "(((()()(()))())(()))", "(((()()(()))())()())", "(((()()(()))())())()", "(((()()(()))()))(())", "(((()()(()))()))()()", "(((()()(())))((())))", "(((()()(())))(()()))", "(((()()(())))(())())", "(((()()(())))(()))()", "(((()()(())))()(()))", "(((()()(())))()()())", "(((()()(())))()())()", "(((()()(())))())(())", "(((()()(())))())()()", "(((()()(()))))((()))", "(((()()(()))))(()())", "(((()()(()))))(())()", "(((()()(()))))()(())", "(((()()(()))))()()()", "(((()()()(((()))))))", "(((()()()((()())))))", "(((()()()((())()))))", "(((()()()((()))())))", "(((()()()((())))()))", "(((()()()((()))))())", "(((()()()((())))))()", "(((()()()(()(())))))", "(((()()()(()()()))))", "(((()()()(()())())))", "(((()()()(()()))()))", "(((()()()(()())))())", "(((()()()(()()))))()", "(((()()()(())(()))))", "(((()()()(())()())))", "(((()()()(())())()))", "(((()()()(())()))())", "(((()()()(())())))()", "(((()()()(()))(())))", "(((()()()(()))()()))", "(((()()()(()))())())", "(((()()()(()))()))()", "(((()()()(())))(()))", "(((()()()(())))()())", "(((()()()(())))())()", "(((()()()(()))))(())", "(((()()()(()))))()()", "(((()()()()((())))))", "(((()()()()(()()))))", "(((()()()()(())())))", "(((()()()()(()))()))", "(((()()()()(())))())", "(((()()()()(()))))()", "(((()()()()()(()))))", "(((()()()()()()())))", "(((()()()()()())()))", "(((()()()()()()))())", "(((()()()()()())))()", "(((()()()()())(())))", "(((()()()()())()()))", "(((()()()()())())())", "(((()()()()())()))()", "(((()()()()()))(()))", "(((()()()()()))()())", "(((()()()()()))())()", "(((()()()()())))(())", "(((()()()()())))()()", "(((()()()())((()))))", "(((()()()())(()())))", "(((()()()())(())()))", "(((()()()())(()))())", "(((()()()())(())))()", "(((()()()())()(())))", "(((()()()())()()()))", "(((()()()())()())())", "(((()()()())()()))()", "(((()()()())())(()))", "(((()()()())())()())", "(((()()()())())())()", "(((()()()())()))(())", "(((()()()())()))()()", "(((()()()()))((())))", "(((()()()()))(()()))", "(((()()()()))(())())", "(((()()()()))(()))()", "(((()()()()))()(()))", "(((()()()()))()()())", "(((()()()()))()())()", "(((()()()()))())(())", "(((()()()()))())()()", "(((()()()())))((()))", "(((()()()())))(()())", "(((()()()())))(())()", "(((()()()())))()(())", "(((()()()())))()()()", "(((()()())(((())))))", "(((()()())((()()))))", "(((()()())((())())))", "(((()()())((()))()))", "(((()()())((())))())", "(((()()())((()))))()", "(((()()())(()(()))))", "(((()()())(()()())))", "(((()()())(()())()))", "(((()()())(()()))())", "(((()()())(()())))()", "(((()()())(())(())))", "(((()()())(())()()))", "(((()()())(())())())", "(((()()())(())()))()", "(((()()())(()))(()))", "(((()()())(()))()())", "(((()()())(()))())()", "(((()()())(())))(())", "(((()()())(())))()()", "(((()()())()((()))))", "(((()()())()(()())))", "(((()()())()(())()))", "(((()()())()(()))())", "(((()()())()(())))()", "(((()()())()()(())))", "(((()()())()()()()))", "(((()()())()()())())", "(((()()())()()()))()", "(((()()())()())(()))", "(((()()())()())()())", "(((()()())()())())()", "(((()()())()()))(())", "(((()()())()()))()()", "(((()()())())((())))", "(((()()())())(()()))", "(((()()())())(())())", "(((()()())())(()))()", "(((()()())())()(()))", "(((()()())())()()())", "(((()()())())()())()", "(((()()())())())(())", "(((()()())())())()()", "(((()()())()))((()))", "(((()()())()))(()())", "(((()()())()))(())()", "(((()()())()))()(())", "(((()()())()))()()()", "(((()()()))(((()))))", "(((()()()))((()())))", "(((()()()))((())()))", "(((()()()))((()))())", "(((()()()))((())))()", "(((()()()))(()(())))", "(((()()()))(()()()))", "(((()()()))(()())())", "(((()()()))(()()))()", "(((()()()))(())(()))", "(((()()()))(())()())", "(((()()()))(())())()", "(((()()()))(()))(())", "(((()()()))(()))()()", "(((()()()))()((())))", "(((()()()))()(()()))", "(((()()()))()(())())", "(((()()()))()(()))()", "(((()()()))()()(()))", "(((()()()))()()()())", "(((()()()))()()())()", "(((()()()))()())(())", "(((()()()))()())()()", "(((()()()))())((()))", "(((()()()))())(()())", "(((()()()))())(())()", "(((()()()))())()(())", "(((()()()))())()()()", "(((()()())))(((())))", "(((()()())))((()()))", "(((()()())))((())())", "(((()()())))((()))()", "(((()()())))(()(()))", "(((()()())))(()()())", "(((()()())))(()())()", "(((()()())))(())(())", "(((()()())))(())()()", "(((()()())))()((()))", "(((()()())))()(()())", "(((()()())))()(())()", "(((()()())))()()(())", "(((()()())))()()()()", "(((()())((((()))))))", "(((()())(((()())))))", "(((()())(((())()))))", "(((()())(((()))())))", "(((()())(((())))()))", "(((()())(((()))))())", "(((()())(((())))))()", "(((()())((()(())))))", "(((()())((()()()))))", "(((()())((()())())))", "(((()())((()()))()))", "(((()())((()())))())", "(((()())((()()))))()", "(((()())((())(()))))", "(((()())((())()())))", "(((()())((())())()))", "(((()())((())()))())", "(((()())((())())))()", "(((()())((()))(())))", "(((()())((()))()()))", "(((()())((()))())())", "(((()())((()))()))()", "(((()())((())))(()))", "(((()())((())))()())", "(((()())((())))())()", "(((()())((()))))(())", "(((()())((()))))()()", "(((()())(()((())))))", "(((()())(()(()()))))", "(((()())(()(())())))", "(((()())(()(()))()))", "(((()())(()(())))())", "(((()())(()(()))))()", "(((()())(()()(()))))", "(((()())(()()()())))", "(((()())(()()())()))", "(((()())(()()()))())", "(((()())(()()())))()", "(((()())(()())(())))", "(((()())(()())()()))", "(((()())(()())())())", "(((()())(()())()))()", "(((()())(()()))(()))", "(((()())(()()))()())", "(((()())(()()))())()", "(((()())(()())))(())", "(((()())(()())))()()", "(((()())(())((()))))", "(((()())(())(()())))", "(((()())(())(())()))", "(((()())(())(()))())", "(((()())(())(())))()", "(((()())(())()(())))", "(((()())(())()()()))", "(((()())(())()())())", "(((()())(())()()))()", "(((()())(())())(()))", "(((()())(())())()())", "(((()())(())())())()", "(((()())(())()))(())", "(((()())(())()))()()", "(((()())(()))((())))", "(((()())(()))(()()))", "(((()())(()))(())())", "(((()())(()))(()))()", "(((()())(()))()(()))", "(((()())(()))()()())", "(((()())(()))()())()", "(((()())(()))())(())", "(((()())(()))())()()", "(((()())(())))((()))", "(((()())(())))(()())", "(((()())(())))(())()", "(((()())(())))()(())", "(((()())(())))()()()", "(((()())()(((())))))", "(((()())()((()()))))", "(((()())()((())())))", "(((()())()((()))()))", "(((()())()((())))())", "(((()())()((()))))()", "(((()())()(()(()))))", "(((()())()(()()())))", "(((()())()(()())()))", "(((()())()(()()))())", "(((()())()(()())))()", "(((()())()(())(())))", "(((()())()(())()()))", "(((()())()(())())())", "(((()())()(())()))()", "(((()())()(()))(()))", "(((()())()(()))()())", "(((()())()(()))())()", "(((()())()(())))(())", "(((()())()(())))()()", "(((()())()()((()))))", "(((()())()()(()())))", "(((()())()()(())()))", "(((()())()()(()))())", "(((()())()()(())))()", "(((()())()()()(())))", "(((()())()()()()()))", "(((()())()()()())())", "(((()())()()()()))()", "(((()())()()())(()))", "(((()())()()())()())", "(((()())()()())())()", "(((()())()()()))(())", "(((()())()()()))()()", "(((()())()())((())))", "(((()())()())(()()))", "(((()())()())(())())", "(((()())()())(()))()", "(((()())()())()(()))", "(((()())()())()()())", "(((()())()())()())()", "(((()())()())())(())", "(((()())()())())()()", "(((()())()()))((()))", "(((()())()()))(()())", "(((()())()()))(())()", "(((()())()()))()(())", "(((()())()()))()()()", "(((()())())(((()))))", "(((()())())((()())))", "(((()())())((())()))", "(((()())())((()))())", "(((()())())((())))()", "(((()())())(()(())))", "(((()())())(()()()))", "(((()())())(()())())", "(((()())())(()()))()", "(((()())())(())(()))", "(((()())())(())()())", "(((()())())(())())()", "(((()())())(()))(())", "(((()())())(()))()()", "(((()())())()((())))", "(((()())())()(()()))", "(((()())())()(())())", "(((()())())()(()))()", "(((()())())()()(()))", "(((()())())()()()())", "(((()())())()()())()", "(((()())())()())(())", "(((()())())()())()()", "(((()())())())((()))", "(((()())())())(()())", "(((()())())())(())()", "(((()())())())()(())", "(((()())())())()()()", "(((()())()))(((())))", "(((()())()))((()()))", "(((()())()))((())())", "(((()())()))((()))()", "(((()())()))(()(()))", "(((()())()))(()()())", "(((()())()))(()())()", "(((()())()))(())(())", "(((()())()))(())()()", "(((()())()))()((()))", "(((()())()))()(()())", "(((()())()))()(())()", "(((()())()))()()(())", "(((()())()))()()()()", "(((()()))((((())))))", "(((()()))(((()()))))", "(((()()))(((())())))", "(((()()))(((()))()))", "(((()()))(((())))())", "(((()()))(((()))))()", "(((()()))((()(()))))", "(((()()))((()()())))", "(((()()))((()())()))", "(((()()))((()()))())", "(((()()))((()())))()", "(((()()))((())(())))", "(((()()))((())()()))", "(((()()))((())())())", "(((()()))((())()))()", "(((()()))((()))(()))", "(((()()))((()))()())", "(((()()))((()))())()", "(((()()))((())))(())", "(((()()))((())))()()", "(((()()))(()((()))))", "(((()()))(()(()())))", "(((()()))(()(())()))", "(((()()))(()(()))())", "(((()()))(()(())))()", "(((()()))(()()(())))", "(((()()))(()()()()))", "(((()()))(()()())())", "(((()()))(()()()))()", "(((()()))(()())(()))", "(((()()))(()())()())", "(((()()))(()())())()", "(((()()))(()()))(())", "(((()()))(()()))()()", "(((()()))(())((())))", "(((()()))(())(()()))", "(((()()))(())(())())", "(((()()))(())(()))()", "(((()()))(())()(()))", "(((()()))(())()()())", "(((()()))(())()())()", "(((()()))(())())(())", "(((()()))(())())()()", "(((()()))(()))((()))", "(((()()))(()))(()())", "(((()()))(()))(())()", "(((()()))(()))()(())", "(((()()))(()))()()()", "(((()()))()(((()))))", "(((()()))()((()())))", "(((()()))()((())()))", "(((()()))()((()))())", "(((()()))()((())))()", "(((()()))()(()(())))", "(((()()))()(()()()))", "(((()()))()(()())())", "(((()()))()(()()))()", "(((()()))()(())(()))", "(((()()))()(())()())", "(((()()))()(())())()", "(((()()))()(()))(())", "(((()()))()(()))()()", "(((()()))()()((())))", "(((()()))()()(()()))", "(((()()))()()(())())", "(((()()))()()(()))()", "(((()()))()()()(()))", "(((()()))()()()()())", "(((()()))()()()())()", "(((()()))()()())(())", "(((()()))()()())()()", "(((()()))()())((()))", "(((()()))()())(()())", "(((()()))()())(())()", "(((()()))()())()(())", "(((()()))()())()()()", "(((()()))())(((())))", "(((()()))())((()()))", "(((()()))())((())())", "(((()()))())((()))()", "(((()()))())(()(()))", "(((()()))())(()()())", "(((()()))())(()())()", "(((()()))())(())(())", "(((()()))())(())()()", "(((()()))())()((()))", "(((()()))())()(()())", "(((()()))())()(())()", "(((()()))())()()(())", "(((()()))())()()()()", "(((()())))((((()))))", "(((()())))(((()())))", "(((()())))(((())()))", "(((()())))(((()))())", "(((()())))(((())))()", "(((()())))((()(())))", "(((()())))((()()()))", "(((()())))((()())())", "(((()())))((()()))()", "(((()())))((())(()))", "(((()())))((())()())", "(((()())))((())())()", "(((()())))((()))(())", "(((()())))((()))()()", "(((()())))(()((())))", "(((()())))(()(()()))", "(((()())))(()(())())", "(((()())))(()(()))()", "(((()())))(()()(()))", "(((()())))(()()()())", "(((()())))(()()())()", "(((()())))(()())(())", "(((()())))(()())()()", "(((()())))(())((()))", "(((()())))(())(()())", "(((()())))(())(())()", "(((()())))(())()(())", "(((()())))(())()()()", "(((()())))()(((())))", "(((()())))()((()()))", "(((()())))()((())())", "(((()())))()((()))()", "(((()())))()(()(()))", "(((()())))()(()()())", "(((()())))()(()())()", "(((()())))()(())(())", "(((()())))()(())()()", "(((()())))()()((()))", "(((()())))()()(()())", "(((()())))()()(())()", "(((()())))()()()(())", "(((()())))()()()()()", "(((())(((((())))))))", "(((())((((()()))))))", "(((())((((())())))))", "(((())((((()))()))))", "(((())((((())))())))", "(((())((((()))))()))", "(((())((((())))))())", "(((())((((()))))))()", "(((())(((()(()))))))", "(((())(((()()())))))", "(((())(((()())()))))", "(((())(((()()))())))", "(((())(((()())))()))", "(((())(((()()))))())", "(((())(((()())))))()", "(((())(((())(())))))", "(((())(((())()()))))", "(((())(((())())())))", "(((())(((())()))()))", "(((())(((())())))())", "(((())(((())()))))()", "(((())(((()))(()))))", "(((())(((()))()())))", "(((())(((()))())()))", "(((())(((()))()))())", "(((())(((()))())))()", "(((())(((())))(())))", "(((())(((())))()()))", "(((())(((())))())())", "(((())(((())))()))()", "(((())(((()))))(()))", "(((())(((()))))()())", "(((())(((()))))())()", "(((())(((())))))(())", "(((())(((())))))()()", "(((())((()((()))))))", "(((())((()(()())))))", "(((())((()(())()))))", "(((())((()(()))())))", "(((())((()(())))()))", "(((())((()(()))))())", "(((())((()(())))))()", "(((())((()()(())))))", "(((())((()()()()))))", "(((())((()()())())))", "(((())((()()()))()))", "(((())((()()())))())", "(((())((()()()))))()", "(((())((()())(()))))", "(((())((()())()())))", "(((())((()())())()))", "(((())((()())()))())", "(((())((()())())))()", "(((())((()()))(())))", "(((())((()()))()()))", "(((())((()()))())())", "(((())((()()))()))()", "(((())((()())))(()))", "(((())((()())))()())", "(((())((()())))())()", "(((())((()()))))(())", "(((())((()()))))()()", "(((())((())((())))))", "(((())((())(()()))))", "(((())((())(())())))", "(((())((())(()))()))", "(((())((())(())))())", "(((())((())(()))))()", "(((())((())()(()))))", "(((())((())()()())))", "(((())((())()())()))", "(((())((())()()))())", "(((())((())()())))()", "(((())((())())(())))", "(((())((())())()()))", "(((())((())())())())", "(((())((())())()))()", "(((())((())()))(()))", "(((())((())()))()())", "(((())((())()))())()", "(((())((())())))(())", "(((())((())())))()()", "(((())((()))((()))))", "(((())((()))(()())))", "(((())((()))(())()))", "(((())((()))(()))())", "(((())((()))(())))()", "(((())((()))()(())))", "(((())((()))()()()))", "(((())((()))()())())", "(((())((()))()()))()", "(((())((()))())(()))", "(((())((()))())()())", "(((())((()))())())()", "(((())((()))()))(())", "(((())((()))()))()()", "(((())((())))((())))", "(((())((())))(()()))", "(((())((())))(())())", "(((())((())))(()))()", "(((())((())))()(()))", "(((())((())))()()())", "(((())((())))()())()", "(((())((())))())(())", "(((())((())))())()()", "(((())((()))))((()))", "(((())((()))))(()())", "(((())((()))))(())()", "(((())((()))))()(())", "(((())((()))))()()()", "(((())(()(((()))))))", "(((())(()((()())))))", "(((())(()((())()))))", "(((())(()((()))())))", "(((())(()((())))()))", "(((())(()((()))))())", "(((())(()((())))))()", "(((())(()(()(())))))", "(((())(()(()()()))))", "(((())(()(()())())))", "(((())(()(()()))()))", "(((())(()(()())))())", "(((())(()(()()))))()", "(((())(()(())(()))))", "(((())(()(())()())))", "(((())(()(())())()))", "(((())(()(())()))())", "(((())(()(())())))()", "(((())(()(()))(())))", "(((())(()(()))()()))", "(((())(()(()))())())", "(((())(()(()))()))()", "(((())(()(())))(()))", "(((())(()(())))()())", "(((())(()(())))())()", "(((())(()(()))))(())", "(((())(()(()))))()()", "(((())(()()((())))))", "(((())(()()(()()))))", "(((())(()()(())())))", "(((())(()()(()))()))", "(((())(()()(())))())", "(((())(()()(()))))()", "(((())(()()()(()))))", "(((())(()()()()())))", "(((())(()()()())()))", "(((())(()()()()))())", "(((())(()()()())))()", "(((())(()()())(())))", "(((())(()()())()()))", "(((())(()()())())())", "(((())(()()())()))()", "(((())(()()()))(()))", "(((())(()()()))()())", "(((())(()()()))())()", "(((())(()()())))(())", "(((())(()()())))()()", "(((())(()())((()))))", "(((())(()())(()())))", "(((())(()())(())()))", "(((())(()())(()))())", "(((())(()())(())))()", "(((())(()())()(())))", "(((())(()())()()()))", "(((())(()())()())())", "(((())(()())()()))()", "(((())(()())())(()))", "(((())(()())())()())", "(((())(()())())())()", "(((())(()())()))(())", "(((())(()())()))()()", "(((())(()()))((())))", "(((())(()()))(()()))", "(((())(()()))(())())", "(((())(()()))(()))()", "(((())(()()))()(()))", "(((())(()()))()()())", "(((())(()()))()())()", "(((())(()()))())(())", "(((())(()()))())()()", "(((())(()())))((()))", "(((())(()())))(()())", "(((())(()())))(())()", "(((())(()())))()(())", "(((())(()())))()()()", "(((())(())(((())))))", "(((())(())((()()))))", "(((())(())((())())))", "(((())(())((()))()))", "(((())(())((())))())", "(((())(())((()))))()", "(((())(())(()(()))))", "(((())(())(()()())))", "(((())(())(()())()))", "(((())(())(()()))())", "(((())(())(()())))()", "(((())(())(())(())))", "(((())(())(())()()))", "(((())(())(())())())", "(((())(())(())()))()", "(((())(())(()))(()))", "(((())(())(()))()())", "(((())(())(()))())()", "(((())(())(())))(())", "(((())(())(())))()()", "(((())(())()((()))))", "(((())(())()(()())))", "(((())(())()(())()))", "(((())(())()(()))())", "(((())(())()(())))()", "(((())(())()()(())))", "(((())(())()()()()))", "(((())(())()()())())", "(((())(())()()()))()", "(((())(())()())(()))", "(((())(())()())()())", "(((())(())()())())()", "(((())(())()()))(())", "(((())(())()()))()()", "(((())(())())((())))", "(((())(())())(()()))", "(((())(())())(())())", "(((())(())())(()))()", "(((())(())())()(()))", "(((())(())())()()())", "(((())(())())()())()", "(((())(())())())(())", "(((())(())())())()()", "(((())(())()))((()))", "(((())(())()))(()())", "(((())(())()))(())()", "(((())(())()))()(())", "(((())(())()))()()()", "(((())(()))(((()))))", "(((())(()))((()())))", "(((())(()))((())()))", "(((())(()))((()))())", "(((())(()))((())))()", "(((())(()))(()(())))", "(((())(()))(()()()))", "(((())(()))(()())())", "(((())(()))(()()))()", "(((())(()))(())(()))", "(((())(()))(())()())", "(((())(()))(())())()", "(((())(()))(()))(())", "(((())(()))(()))()()", "(((())(()))()((())))", "(((())(()))()(()()))", "(((())(()))()(())())", "(((())(()))()(()))()", "(((())(()))()()(()))", "(((())(()))()()()())", "(((())(()))()()())()", "(((())(()))()())(())", "(((())(()))()())()()", "(((())(()))())((()))", "(((())(()))())(()())", "(((())(()))())(())()", "(((())(()))())()(())", "(((())(()))())()()()", "(((())(())))(((())))", "(((())(())))((()()))", "(((())(())))((())())", "(((())(())))((()))()", "(((())(())))(()(()))", "(((())(())))(()()())", "(((())(())))(()())()", "(((())(())))(())(())", "(((())(())))(())()()", "(((())(())))()((()))", "(((())(())))()(()())", "(((())(())))()(())()", "(((())(())))()()(())", "(((())(())))()()()()", "(((())()((((()))))))", "(((())()(((()())))))", "(((())()(((())()))))", "(((())()(((()))())))", "(((())()(((())))()))", "(((())()(((()))))())", "(((())()(((())))))()", "(((())()((()(())))))", "(((())()((()()()))))", "(((())()((()())())))", "(((())()((()()))()))", "(((())()((()())))())", "(((())()((()()))))()", "(((())()((())(()))))", "(((())()((())()())))", "(((())()((())())()))", "(((())()((())()))())", "(((())()((())())))()", "(((())()((()))(())))", "(((())()((()))()()))", "(((())()((()))())())", "(((())()((()))()))()", "(((())()((())))(()))", "(((())()((())))()())", "(((())()((())))())()", "(((())()((()))))(())", "(((())()((()))))()()", "(((())()(()((())))))", "(((())()(()(()()))))", "(((())()(()(())())))", "(((())()(()(()))()))", "(((())()(()(())))())", "(((())()(()(()))))()", "(((())()(()()(()))))", "(((())()(()()()())))", "(((())()(()()())()))", "(((())()(()()()))())", "(((())()(()()())))()", "(((())()(()())(())))", "(((())()(()())()()))", "(((())()(()())())())", "(((())()(()())()))()", "(((())()(()()))(()))", "(((())()(()()))()())", "(((())()(()()))())()", "(((())()(()())))(())", "(((())()(()())))()()", "(((())()(())((()))))", "(((())()(())(()())))", "(((())()(())(())()))", "(((())()(())(()))())", "(((())()(())(())))()", "(((())()(())()(())))", "(((())()(())()()()))", "(((())()(())()())())", "(((())()(())()()))()", "(((())()(())())(()))", "(((())()(())())()())", "(((())()(())())())()", "(((())()(())()))(())", "(((())()(())()))()()", "(((())()(()))((())))", "(((())()(()))(()()))", "(((())()(()))(())())", "(((())()(()))(()))()", "(((())()(()))()(()))", "(((())()(()))()()())", "(((())()(()))()())()", "(((())()(()))())(())", "(((())()(()))())()()", "(((())()(())))((()))", "(((())()(())))(()())", "(((())()(())))(())()", "(((())()(())))()(())", "(((())()(())))()()()", "(((())()()(((())))))", "(((())()()((()()))))", "(((())()()((())())))", "(((())()()((()))()))", "(((())()()((())))())", "(((())()()((()))))()", "(((())()()(()(()))))", "(((())()()(()()())))", "(((())()()(()())()))", "(((())()()(()()))())", "(((())()()(()())))()", "(((())()()(())(())))", "(((())()()(())()()))", "(((())()()(())())())", "(((())()()(())()))()", "(((())()()(()))(()))", "(((())()()(()))()())", "(((())()()(()))())()", "(((())()()(())))(())", "(((())()()(())))()()", "(((())()()()((()))))", "(((())()()()(()())))", "(((())()()()(())()))", "(((())()()()(()))())", "(((())()()()(())))()", "(((())()()()()(())))", "(((())()()()()()()))", "(((())()()()()())())", "(((())()()()()()))()", "(((())()()()())(()))", "(((())()()()())()())", "(((())()()()())())()", "(((())()()()()))(())", "(((())()()()()))()()", "(((())()()())((())))", "(((())()()())(()()))", "(((())()()())(())())", "(((())()()())(()))()", "(((())()()())()(()))", "(((())()()())()()())", "(((())()()())()())()", "(((())()()())())(())", "(((())()()())())()()", "(((())()()()))((()))", "(((())()()()))(()())", "(((())()()()))(())()", "(((())()()()))()(())", "(((())()()()))()()()", "(((())()())(((()))))", "(((())()())((()())))", "(((())()())((())()))", "(((())()())((()))())", "(((())()())((())))()", "(((())()())(()(())))", "(((())()())(()()()))", "(((())()())(()())())", "(((())()())(()()))()", "(((())()())(())(()))", "(((())()())(())()())", "(((())()())(())())()", "(((())()())(()))(())", "(((())()())(()))()()", "(((())()())()((())))", "(((())()())()(()()))", "(((())()())()(())())", "(((())()())()(()))()", "(((())()())()()(()))", "(((())()())()()()())", "(((())()())()()())()", "(((())()())()())(())", "(((())()())()())()()", "(((())()())())((()))", "(((())()())())(()())", "(((())()())())(())()", "(((())()())())()(())", "(((())()())())()()()", "(((())()()))(((())))", "(((())()()))((()()))", "(((())()()))((())())", "(((())()()))((()))()", "(((())()()))(()(()))", "(((())()()))(()()())", "(((())()()))(()())()", "(((())()()))(())(())", "(((())()()))(())()()", "(((())()()))()((()))", "(((())()()))()(()())", "(((())()()))()(())()", "(((())()()))()()(())", "(((())()()))()()()()", "(((())())((((())))))", "(((())())(((()()))))", "(((())())(((())())))", "(((())())(((()))()))", "(((())())(((())))())", "(((())())(((()))))()", "(((())())((()(()))))", "(((())())((()()())))", "(((())())((()())()))", "(((())())((()()))())", "(((())())((()())))()", "(((())())((())(())))", "(((())())((())()()))", "(((())())((())())())", "(((())())((())()))()", "(((())())((()))(()))", "(((())())((()))()())", "(((())())((()))())()", "(((())())((())))(())", "(((())())((())))()()", "(((())())(()((()))))", "(((())())(()(()())))", "(((())())(()(())()))", "(((())())(()(()))())", "(((())())(()(())))()", "(((())())(()()(())))", "(((())())(()()()()))", "(((())())(()()())())", "(((())())(()()()))()", "(((())())(()())(()))", "(((())())(()())()())", "(((())())(()())())()", "(((())())(()()))(())", "(((())())(()()))()()", "(((())())(())((())))", "(((())())(())(()()))", "(((())())(())(())())", "(((())())(())(()))()", "(((())())(())()(()))", "(((())())(())()()())", "(((())())(())()())()", "(((())())(())())(())", "(((())())(())())()()", "(((())())(()))((()))", "(((())())(()))(()())", "(((())())(()))(())()", "(((())())(()))()(())", "(((())())(()))()()()", "(((())())()(((()))))", "(((())())()((()())))", "(((())())()((())()))", "(((())())()((()))())", "(((())())()((())))()", "(((())())()(()(())))", "(((())())()(()()()))", "(((())())()(()())())", "(((())())()(()()))()", "(((())())()(())(()))", "(((())())()(())()())", "(((())())()(())())()", "(((())())()(()))(())", "(((())())()(()))()()", "(((())())()()((())))", "(((())())()()(()()))", "(((())())()()(())())", "(((())())()()(()))()", "(((())())()()()(()))", "(((())())()()()()())", "(((())())()()()())()", "(((())())()()())(())", "(((())())()()())()()", "(((())())()())((()))", "(((())())()())(()())", "(((())())()())(())()", "(((())())()())()(())", "(((())())()())()()()", "(((())())())(((())))", "(((())())())((()()))", "(((())())())((())())", "(((())())())((()))()", "(((())())())(()(()))", "(((())())())(()()())", "(((())())())(()())()", "(((())())())(())(())", "(((())())())(())()()", "(((())())())()((()))", "(((())())())()(()())", "(((())())())()(())()", "(((())())())()()(())", "(((())())())()()()()", "(((())()))((((()))))", "(((())()))(((()())))", "(((())()))(((())()))", "(((())()))(((()))())", "(((())()))(((())))()", "(((())()))((()(())))", "(((())()))((()()()))", "(((())()))((()())())", "(((())()))((()()))()", "(((())()))((())(()))", "(((())()))((())()())", "(((())()))((())())()", "(((())()))((()))(())", "(((())()))((()))()()", "(((())()))(()((())))", "(((())()))(()(()()))", "(((())()))(()(())())", "(((())()))(()(()))()", "(((())()))(()()(()))", "(((())()))(()()()())", "(((())()))(()()())()", "(((())()))(()())(())", "(((())()))(()())()()", "(((())()))(())((()))", "(((())()))(())(()())", "(((())()))(())(())()", "(((())()))(())()(())", "(((())()))(())()()()", "(((())()))()(((())))", "(((())()))()((()()))", "(((())()))()((())())", "(((())()))()((()))()", "(((())()))()(()(()))", "(((())()))()(()()())", "(((())()))()(()())()", "(((())()))()(())(())", "(((())()))()(())()()", "(((())()))()()((()))", "(((())()))()()(()())", "(((())()))()()(())()", "(((())()))()()()(())", "(((())()))()()()()()", "(((()))(((((()))))))", "(((()))((((()())))))", "(((()))((((())()))))", "(((()))((((()))())))", "(((()))((((())))()))", "(((()))((((()))))())", "(((()))((((())))))()", "(((()))(((()(())))))", "(((()))(((()()()))))", "(((()))(((()())())))", "(((()))(((()()))()))", "(((()))(((()())))())", "(((()))(((()()))))()", "(((()))(((())(()))))", "(((()))(((())()())))", "(((()))(((())())()))", "(((()))(((())()))())", "(((()))(((())())))()", "(((()))(((()))(())))", "(((()))(((()))()()))", "(((()))(((()))())())", "(((()))(((()))()))()", "(((()))(((())))(()))", "(((()))(((())))()())", "(((()))(((())))())()", "(((()))(((()))))(())", "(((()))(((()))))()()", "(((()))((()((())))))", "(((()))((()(()()))))", "(((()))((()(())())))", "(((()))((()(()))()))", "(((()))((()(())))())", "(((()))((()(()))))()", "(((()))((()()(()))))", "(((()))((()()()())))", "(((()))((()()())()))", "(((()))((()()()))())", "(((()))((()()())))()", "(((()))((()())(())))", "(((()))((()())()()))", "(((()))((()())())())", "(((()))((()())()))()", "(((()))((()()))(()))", "(((()))((()()))()())", "(((()))((()()))())()", "(((()))((()())))(())", "(((()))((()())))()()", "(((()))((())((()))))", "(((()))((())(()())))", "(((()))((())(())()))", "(((()))((())(()))())", "(((()))((())(())))()", "(((()))((())()(())))", "(((()))((())()()()))", "(((()))((())()())())", "(((()))((())()()))()", "(((()))((())())(()))", "(((()))((())())()())", "(((()))((())())())()", "(((()))((())()))(())", "(((()))((())()))()()", "(((()))((()))((())))", "(((()))((()))(()()))", "(((()))((()))(())())", "(((()))((()))(()))()", "(((()))((()))()(()))", "(((()))((()))()()())", "(((()))((()))()())()", "(((()))((()))())(())", "(((()))((()))())()()", "(((()))((())))((()))", "(((()))((())))(()())", "(((()))((())))(())()", "(((()))((())))()(())", "(((()))((())))()()()", "(((()))(()(((())))))", "(((()))(()((()()))))", "(((()))(()((())())))", "(((()))(()((()))()))", "(((()))(()((())))())", "(((()))(()((()))))()", "(((()))(()(()(()))))", "(((()))(()(()()())))", "(((()))(()(()())()))", "(((()))(()(()()))())", "(((()))(()(()())))()", "(((()))(()(())(())))", "(((()))(()(())()()))", "(((()))(()(())())())", "(((()))(()(())()))()", "(((()))(()(()))(()))", "(((()))(()(()))()())", "(((()))(()(()))())()", "(((()))(()(())))(())", "(((()))(()(())))()()", "(((()))(()()((()))))", "(((()))(()()(()())))", "(((()))(()()(())()))", "(((()))(()()(()))())", "(((()))(()()(())))()", "(((()))(()()()(())))", "(((()))(()()()()()))", "(((()))(()()()())())", "(((()))(()()()()))()", "(((()))(()()())(()))", "(((()))(()()())()())", "(((()))(()()())())()", "(((()))(()()()))(())", "(((()))(()()()))()()", "(((()))(()())((())))", "(((()))(()())(()()))", "(((()))(()())(())())", "(((()))(()())(()))()", "(((()))(()())()(()))", "(((()))(()())()()())", "(((()))(()())()())()", "(((()))(()())())(())", "(((()))(()())())()()", "(((()))(()()))((()))", "(((()))(()()))(()())", "(((()))(()()))(())()", "(((()))(()()))()(())", "(((()))(()()))()()()", "(((()))(())(((()))))", "(((()))(())((()())))", "(((()))(())((())()))", "(((()))(())((()))())", "(((()))(())((())))()", "(((()))(())(()(())))", "(((()))(())(()()()))", "(((()))(())(()())())", "(((()))(())(()()))()", "(((()))(())(())(()))", "(((()))(())(())()())", "(((()))(())(())())()", "(((()))(())(()))(())", "(((()))(())(()))()()", "(((()))(())()((())))", "(((()))(())()(()()))", "(((()))(())()(())())", "(((()))(())()(()))()", "(((()))(())()()(()))", "(((()))(())()()()())", "(((()))(())()()())()", "(((()))(())()())(())", "(((()))(())()())()()", "(((()))(())())((()))", "(((()))(())())(()())", "(((()))(())())(())()", "(((()))(())())()(())", "(((()))(())())()()()", "(((()))(()))(((())))", "(((()))(()))((()()))", "(((()))(()))((())())", "(((()))(()))((()))()", "(((()))(()))(()(()))", "(((()))(()))(()()())", "(((()))(()))(()())()", "(((()))(()))(())(())", "(((()))(()))(())()()", "(((()))(()))()((()))", "(((()))(()))()(()())", "(((()))(()))()(())()", "(((()))(()))()()(())", "(((()))(()))()()()()", "(((()))()((((())))))", "(((()))()(((()()))))", "(((()))()(((())())))", "(((()))()(((()))()))", "(((()))()(((())))())", "(((()))()(((()))))()", "(((()))()((()(()))))", "(((()))()((()()())))", "(((()))()((()())()))", "(((()))()((()()))())", "(((()))()((()())))()", "(((()))()((())(())))", "(((()))()((())()()))", "(((()))()((())())())", "(((()))()((())()))()", "(((()))()((()))(()))", "(((()))()((()))()())", "(((()))()((()))())()", "(((()))()((())))(())", "(((()))()((())))()()", "(((()))()(()((()))))", "(((()))()(()(()())))", "(((()))()(()(())()))", "(((()))()(()(()))())", "(((()))()(()(())))()", "(((()))()(()()(())))", "(((()))()(()()()()))", "(((()))()(()()())())", "(((()))()(()()()))()", "(((()))()(()())(()))", "(((()))()(()())()())", "(((()))()(()())())()", "(((()))()(()()))(())", "(((()))()(()()))()()", "(((()))()(())((())))", "(((()))()(())(()()))", "(((()))()(())(())())", "(((()))()(())(()))()", "(((()))()(())()(()))", "(((()))()(())()()())", "(((()))()(())()())()", "(((()))()(())())(())", "(((()))()(())())()()", "(((()))()(()))((()))", "(((()))()(()))(()())", "(((()))()(()))(())()", "(((()))()(()))()(())", "(((()))()(()))()()()", "(((()))()()(((()))))", "(((()))()()((()())))", "(((()))()()((())()))", "(((()))()()((()))())", "(((()))()()((())))()", "(((()))()()(()(())))", "(((()))()()(()()()))", "(((()))()()(()())())", "(((()))()()(()()))()", "(((()))()()(())(()))", "(((()))()()(())()())", "(((()))()()(())())()", "(((()))()()(()))(())", "(((()))()()(()))()()", "(((()))()()()((())))", "(((()))()()()(()()))", "(((()))()()()(())())", "(((()))()()()(()))()", "(((()))()()()()(()))", "(((()))()()()()()())", "(((()))()()()()())()", "(((()))()()()())(())", "(((()))()()()())()()", "(((()))()()())((()))", "(((()))()()())(()())", "(((()))()()())(())()", "(((()))()()())()(())", "(((()))()()())()()()", "(((()))()())(((())))", "(((()))()())((()()))", "(((()))()())((())())", "(((()))()())((()))()", "(((()))()())(()(()))", "(((()))()())(()()())", "(((()))()())(()())()", "(((()))()())(())(())", "(((()))()())(())()()", "(((()))()())()((()))", "(((()))()())()(()())", "(((()))()())()(())()", "(((()))()())()()(())", "(((()))()())()()()()", "(((()))())((((()))))", "(((()))())(((()())))", "(((()))())(((())()))", "(((()))())(((()))())", "(((()))())(((())))()", "(((()))())((()(())))", "(((()))())((()()()))", "(((()))())((()())())", "(((()))())((()()))()", "(((()))())((())(()))", "(((()))())((())()())", "(((()))())((())())()", "(((()))())((()))(())", "(((()))())((()))()()", "(((()))())(()((())))", "(((()))())(()(()()))", "(((()))())(()(())())", "(((()))())(()(()))()", "(((()))())(()()(()))", "(((()))())(()()()())", "(((()))())(()()())()", "(((()))())(()())(())", "(((()))())(()())()()", "(((()))())(())((()))", "(((()))())(())(()())", "(((()))())(())(())()", "(((()))())(())()(())", "(((()))())(())()()()", "(((()))())()(((())))", "(((()))())()((()()))", "(((()))())()((())())", "(((()))())()((()))()", "(((()))())()(()(()))", "(((()))())()(()()())", "(((()))())()(()())()", "(((()))())()(())(())", "(((()))())()(())()()", "(((()))())()()((()))", "(((()))())()()(()())", "(((()))())()()(())()", "(((()))())()()()(())", "(((()))())()()()()()", "(((())))(((((())))))", "(((())))((((()()))))", "(((())))((((())())))", "(((())))((((()))()))", "(((())))((((())))())", "(((())))((((()))))()", "(((())))(((()(()))))", "(((())))(((()()())))", "(((())))(((()())()))", "(((())))(((()()))())", "(((())))(((()())))()", "(((())))(((())(())))", "(((())))(((())()()))", "(((())))(((())())())", "(((())))(((())()))()", "(((())))(((()))(()))", "(((())))(((()))()())", "(((())))(((()))())()", "(((())))(((())))(())", "(((())))(((())))()()", "(((())))((()((()))))", "(((())))((()(()())))", "(((())))((()(())()))", "(((())))((()(()))())", "(((())))((()(())))()", "(((())))((()()(())))", "(((())))((()()()()))", "(((())))((()()())())", "(((())))((()()()))()", "(((())))((()())(()))", "(((())))((()())()())", "(((())))((()())())()", "(((())))((()()))(())", "(((())))((()()))()()", "(((())))((())((())))", "(((())))((())(()()))", "(((())))((())(())())", "(((())))((())(()))()", "(((())))((())()(()))", "(((())))((())()()())", "(((())))((())()())()", "(((())))((())())(())", "(((())))((())())()()", "(((())))((()))((()))", "(((())))((()))(()())", "(((())))((()))(())()", "(((())))((()))()(())", "(((())))((()))()()()", "(((())))(()(((()))))", "(((())))(()((()())))", "(((())))(()((())()))", "(((())))(()((()))())", "(((())))(()((())))()", "(((())))(()(()(())))", "(((())))(()(()()()))", "(((())))(()(()())())", "(((())))(()(()()))()", "(((())))(()(())(()))", "(((())))(()(())()())", "(((())))(()(())())()", "(((())))(()(()))(())", "(((())))(()(()))()()", "(((())))(()()((())))", "(((())))(()()(()()))", "(((())))(()()(())())", "(((())))(()()(()))()", "(((())))(()()()(()))", "(((())))(()()()()())", "(((())))(()()()())()", "(((())))(()()())(())", "(((())))(()()())()()", "(((())))(()())((()))", "(((())))(()())(()())", "(((())))(()())(())()", "(((())))(()())()(())", "(((())))(()())()()()", "(((())))(())(((())))", "(((())))(())((()()))", "(((())))(())((())())", "(((())))(())((()))()", "(((())))(())(()(()))", "(((())))(())(()()())", "(((())))(())(()())()", "(((())))(())(())(())", "(((())))(())(())()()", "(((())))(())()((()))", "(((())))(())()(()())", "(((())))(())()(())()", "(((())))(())()()(())", "(((())))(())()()()()", "(((())))()((((()))))", "(((())))()(((()())))", "(((())))()(((())()))", "(((())))()(((()))())", "(((())))()(((())))()", "(((())))()((()(())))", "(((())))()((()()()))", "(((())))()((()())())", "(((())))()((()()))()", "(((())))()((())(()))", "(((())))()((())()())", "(((())))()((())())()", "(((())))()((()))(())", "(((())))()((()))()()", "(((())))()(()((())))", "(((())))()(()(()()))", "(((())))()(()(())())", "(((())))()(()(()))()", "(((())))()(()()(()))", "(((())))()(()()()())", "(((())))()(()()())()", "(((())))()(()())(())", "(((())))()(()())()()", "(((())))()(())((()))", "(((())))()(())(()())", "(((())))()(())(())()", "(((())))()(())()(())", "(((())))()(())()()()", "(((())))()()(((())))", "(((())))()()((()()))", "(((())))()()((())())", "(((())))()()((()))()", "(((())))()()(()(()))", "(((())))()()(()()())", "(((())))()()(()())()", "(((())))()()(())(())", "(((())))()()(())()()", "(((())))()()()((()))", "(((())))()()()(()())", "(((())))()()()(())()", "(((())))()()()()(())", "(((())))()()()()()()", "((()((((((()))))))))", "((()(((((()())))))))", "((()(((((())()))))))", "((()(((((()))())))))", "((()(((((())))()))))", "((()(((((()))))())))", "((()(((((())))))()))", "((()(((((()))))))())", "((()(((((())))))))()", "((()((((()(())))))))", "((()((((()()()))))))", "((()((((()())())))))", "((()((((()()))()))))", "((()((((()())))())))", "((()((((()()))))()))", "((()((((()())))))())", "((()((((()()))))))()", "((()((((())(()))))))", "((()((((())()())))))", "((()((((())())()))))", "((()((((())()))())))", "((()((((())())))()))", "((()((((())()))))())", "((()((((())())))))()", "((()((((()))(())))))", "((()((((()))()()))))", "((()((((()))())())))", "((()((((()))()))()))", "((()((((()))())))())", "((()((((()))()))))()", "((()((((())))(()))))", "((()((((())))()())))", "((()((((())))())()))", "((()((((())))()))())", "((()((((())))())))()", "((()((((()))))(())))", "((()((((()))))()()))", "((()((((()))))())())", "((()((((()))))()))()", "((()((((())))))(()))", "((()((((())))))()())", "((()((((())))))())()", "((()((((()))))))(())", "((()((((()))))))()()", "((()(((()((())))))))", "((()(((()(()()))))))", "((()(((()(())())))))", "((()(((()(()))()))))", "((()(((()(())))())))", "((()(((()(()))))()))", "((()(((()(())))))())", "((()(((()(()))))))()", "((()(((()()(()))))))", "((()(((()()()())))))", "((()(((()()())()))))", "((()(((()()()))())))", "((()(((()()())))()))", "((()(((()()()))))())", "((()(((()()())))))()", "((()(((()())(())))))", "((()(((()())()()))))", "((()(((()())())())))", "((()(((()())()))()))", "((()(((()())())))())", "((()(((()())()))))()", "((()(((()()))(()))))", "((()(((()()))()())))", "((()(((()()))())()))", "((()(((()()))()))())", "((()(((()()))())))()", "((()(((()())))(())))", "((()(((()())))()()))", "((()(((()())))())())", "((()(((()())))()))()", "((()(((()()))))(()))", "((()(((()()))))()())", "((()(((()()))))())()", "((()(((()())))))(())", "((()(((()())))))()()", "((()(((())((()))))))", "((()(((())(()())))))", "((()(((())(())()))))", "((()(((())(()))())))", "((()(((())(())))()))", "((()(((())(()))))())", "((()(((())(())))))()", "((()(((())()(())))))", "((()(((())()()()))))", "((()(((())()())())))", "((()(((())()()))()))", "((()(((())()())))())", "((()(((())()()))))()", "((()(((())())(()))))", "((()(((())())()())))", "((()(((())())())()))", "((()(((())())()))())", "((()(((())())())))()", "((()(((())()))(())))", "((()(((())()))()()))", "((()(((())()))())())", "((()(((())()))()))()", "((()(((())())))(()))", "((()(((())())))()())", "((()(((())())))())()", "((()(((())()))))(())", "((()(((())()))))()()", "((()(((()))((())))))", "((()(((()))(()()))))", "((()(((()))(())())))", "((()(((()))(()))()))", "((()(((()))(())))())", "((()(((()))(()))))()", "((()(((()))()(()))))", "((()(((()))()()())))", "((()(((()))()())()))", "((()(((()))()()))())", "((()(((()))()())))()", "((()(((()))())(())))", "((()(((()))())()()))", "((()(((()))())())())", "((()(((()))())()))()", "((()(((()))()))(()))", "((()(((()))()))()())", "((()(((()))()))())()", "((()(((()))())))(())", "((()(((()))())))()()", "((()(((())))((()))))", "((()(((())))(()())))", "((()(((())))(())()))", "((()(((())))(()))())", "((()(((())))(())))()", "((()(((())))()(())))", "((()(((())))()()()))", "((()(((())))()())())", "((()(((())))()()))()", "((()(((())))())(()))", "((()(((())))())()())", "((()(((())))())())()", "((()(((())))()))(())", "((()(((())))()))()()", "((()(((()))))((())))", "((()(((()))))(()()))", "((()(((()))))(())())", "((()(((()))))(()))()", "((()(((()))))()(()))", "((()(((()))))()()())", "((()(((()))))()())()", "((()(((()))))())(())", "((()(((()))))())()()", "((()(((())))))((()))", "((()(((())))))(()())", "((()(((())))))(())()", "((()(((())))))()(())", "((()(((())))))()()()", "((()((()(((())))))))", "((()((()((()()))))))", "((()((()((())())))))", "((()((()((()))()))))", "((()((()((())))())))", "((()((()((()))))()))", "((()((()((())))))())", "((()((()((()))))))()", "((()((()(()(()))))))", "((()((()(()()())))))", "((()((()(()())()))))", "((()((()(()()))())))", "((()((()(()())))()))", "((()((()(()()))))())", "((()((()(()())))))()", "((()((()(())(())))))", "((()((()(())()()))))", "((()((()(())())())))", "((()((()(())()))()))", "((()((()(())())))())", "((()((()(())()))))()", "((()((()(()))(()))))", "((()((()(()))()())))", "((()((()(()))())()))", "((()((()(()))()))())", "((()((()(()))())))()", "((()((()(())))(())))", "((()((()(())))()()))", "((()((()(())))())())", "((()((()(())))()))()", "((()((()(()))))(()))", "((()((()(()))))()())", "((()((()(()))))())()", "((()((()(())))))(())", "((()((()(())))))()()", "((()((()()((()))))))", "((()((()()(()())))))", "((()((()()(())()))))", "((()((()()(()))())))", "((()((()()(())))()))", "((()((()()(()))))())", "((()((()()(())))))()", "((()((()()()(())))))", "((()((()()()()()))))", "((()((()()()())())))", "((()((()()()()))()))", "((()((()()()())))())", "((()((()()()()))))()", "((()((()()())(()))))", "((()((()()())()())))", "((()((()()())())()))", "((()((()()())()))())", "((()((()()())())))()", "((()((()()()))(())))", "((()((()()()))()()))", "((()((()()()))())())", "((()((()()()))()))()", "((()((()()())))(()))", "((()((()()())))()())", "((()((()()())))())()", "((()((()()()))))(())", "((()((()()()))))()()", "((()((()())((())))))", "((()((()())(()()))))", "((()((()())(())())))", "((()((()())(()))()))", "((()((()())(())))())", "((()((()())(()))))()", "((()((()())()(()))))", "((()((()())()()())))", "((()((()())()())()))", "((()((()())()()))())", "((()((()())()())))()", "((()((()())())(())))", "((()((()())())()()))", "((()((()())())())())", "((()((()())())()))()", "((()((()())()))(()))", "((()((()())()))()())", "((()((()())()))())()", "((()((()())())))(())", "((()((()())())))()()", "((()((()()))((()))))", "((()((()()))(()())))", "((()((()()))(())()))", "((()((()()))(()))())", "((()((()()))(())))()", "((()((()()))()(())))", "((()((()()))()()()))", "((()((()()))()())())", "((()((()()))()()))()", "((()((()()))())(()))", "((()((()()))())()())", "((()((()()))())())()", "((()((()()))()))(())", "((()((()()))()))()()", "((()((()())))((())))", "((()((()())))(()()))", "((()((()())))(())())", "((()((()())))(()))()", "((()((()())))()(()))", "((()((()())))()()())", "((()((()())))()())()", "((()((()())))())(())", "((()((()())))())()()", "((()((()()))))((()))", "((()((()()))))(()())", "((()((()()))))(())()", "((()((()()))))()(())", "((()((()()))))()()()", "((()((())(((()))))))", "((()((())((()())))))", "((()((())((())()))))", "((()((())((()))())))", "((()((())((())))()))", "((()((())((()))))())", "((()((())((())))))()", "((()((())(()(())))))", "((()((())(()()()))))", "((()((())(()())())))", "((()((())(()()))()))", "((()((())(()())))())", "((()((())(()()))))()", "((()((())(())(()))))", "((()((())(())()())))", "((()((())(())())()))", "((()((())(())()))())", "((()((())(())())))()", "((()((())(()))(())))", "((()((())(()))()()))", "((()((())(()))())())", "((()((())(()))()))()", "((()((())(())))(()))", "((()((())(())))()())", "((()((())(())))())()", "((()((())(()))))(())", "((()((())(()))))()()", "((()((())()((())))))", "((()((())()(()()))))", "((()((())()(())())))", "((()((())()(()))()))", "((()((())()(())))())", "((()((())()(()))))()", "((()((())()()(()))))", "((()((())()()()())))", "((()((())()()())()))", "((()((())()()()))())", "((()((())()()())))()", "((()((())()())(())))", "((()((())()())()()))", "((()((())()())())())", "((()((())()())()))()", "((()((())()()))(()))", "((()((())()()))()())", "((()((())()()))())()", "((()((())()())))(())", "((()((())()())))()()", "((()((())())((()))))", "((()((())())(()())))", "((()((())())(())()))", "((()((())())(()))())", "((()((())())(())))()", "((()((())())()(())))", "((()((())())()()()))", "((()((())())()())())", "((()((())())()()))()", "((()((())())())(()))", "((()((())())())()())", "((()((())())())())()", "((()((())())()))(())", "((()((())())()))()()", "((()((())()))((())))", "((()((())()))(()()))", "((()((())()))(())())", "((()((())()))(()))()", "((()((())()))()(()))", "((()((())()))()()())", "((()((())()))()())()", "((()((())()))())(())", "((()((())()))())()()", "((()((())())))((()))", "((()((())())))(()())", "((()((())())))(())()", "((()((())())))()(())", "((()((())())))()()()", "((()((()))(((())))))", "((()((()))((()()))))", "((()((()))((())())))", "((()((()))((()))()))", "((()((()))((())))())", "((()((()))((()))))()", "((()((()))(()(()))))", "((()((()))(()()())))", "((()((()))(()())()))", "((()((()))(()()))())", "((()((()))(()())))()", "((()((()))(())(())))", "((()((()))(())()()))", "((()((()))(())())())", "((()((()))(())()))()", "((()((()))(()))(()))", "((()((()))(()))()())", "((()((()))(()))())()", "((()((()))(())))(())", "((()((()))(())))()()", "((()((()))()((()))))", "((()((()))()(()())))", "((()((()))()(())()))", "((()((()))()(()))())", "((()((()))()(())))()", "((()((()))()()(())))", "((()((()))()()()()))", "((()((()))()()())())", "((()((()))()()()))()", "((()((()))()())(()))", "((()((()))()())()())", "((()((()))()())())()", "((()((()))()()))(())", "((()((()))()()))()()", "((()((()))())((())))", "((()((()))())(()()))", "((()((()))())(())())", "((()((()))())(()))()", "((()((()))())()(()))", "((()((()))())()()())", "((()((()))())()())()", "((()((()))())())(())", "((()((()))())())()()", "((()((()))()))((()))", "((()((()))()))(()())", "((()((()))()))(())()", "((()((()))()))()(())", "((()((()))()))()()()", "((()((())))(((()))))", "((()((())))((()())))", "((()((())))((())()))", "((()((())))((()))())", "((()((())))((())))()", "((()((())))(()(())))", "((()((())))(()()()))", "((()((())))(()())())", "((()((())))(()()))()", "((()((())))(())(()))", "((()((())))(())()())", "((()((())))(())())()", "((()((())))(()))(())", "((()((())))(()))()()", "((()((())))()((())))", "((()((())))()(()()))", "((()((())))()(())())", "((()((())))()(()))()", "((()((())))()()(()))", "((()((())))()()()())", "((()((())))()()())()", "((()((())))()())(())", "((()((())))()())()()", "((()((())))())((()))", "((()((())))())(()())", "((()((())))())(())()", "((()((())))())()(())", "((()((())))())()()()", "((()((()))))(((())))", "((()((()))))((()()))", "((()((()))))((())())", "((()((()))))((()))()", "((()((()))))(()(()))", "((()((()))))(()()())", "((()((()))))(()())()", "((()((()))))(())(())", "((()((()))))(())()()", "((()((()))))()((()))", "((()((()))))()(()())", "((()((()))))()(())()", "((()((()))))()()(())", "((()((()))))()()()()", "((()(()((((())))))))", "((()(()(((()()))))))", "((()(()(((())())))))", "((()(()(((()))()))))", "((()(()(((())))())))", "((()(()(((()))))()))", "((()(()(((())))))())", "((()(()(((()))))))()", "((()(()((()(()))))))", "((()(()((()()())))))", "((()(()((()())()))))", "((()(()((()()))())))", "((()(()((()())))()))", "((()(()((()()))))())", "((()(()((()())))))()", "((()(()((())(())))))", "((()(()((())()()))))", "((()(()((())())())))", "((()(()((())()))()))", "((()(()((())())))())", "((()(()((())()))))()", "((()(()((()))(()))))", "((()(()((()))()())))", "((()(()((()))())()))", "((()(()((()))()))())", "((()(()((()))())))()", "((()(()((())))(())))", "((()(()((())))()()))", "((()(()((())))())())", "((()(()((())))()))()", "((()(()((()))))(()))", "((()(()((()))))()())", "((()(()((()))))())()", "((()(()((())))))(())", "((()(()((())))))()()", "((()(()(()((()))))))", "((()(()(()(()())))))", "((()(()(()(())()))))", "((()(()(()(()))())))", "((()(()(()(())))()))", "((()(()(()(()))))())", "((()(()(()(())))))()", "((()(()(()()(())))))", "((()(()(()()()()))))", "((()(()(()()())())))", "((()(()(()()()))()))", "((()(()(()()())))())", "((()(()(()()()))))()", "((()(()(()())(()))))", "((()(()(()())()())))", "((()(()(()())())()))", "((()(()(()())()))())", "((()(()(()())())))()", "((()(()(()()))(())))", "((()(()(()()))()()))", "((()(()(()()))())())", "((()(()(()()))()))()", "((()(()(()())))(()))", "((()(()(()())))()())", "((()(()(()())))())()", "((()(()(()()))))(())", "((()(()(()()))))()()", "((()(()(())((())))))", "((()(()(())(()()))))", "((()(()(())(())())))", "((()(()(())(()))()))", "((()(()(())(())))())", "((()(()(())(()))))()", "((()(()(())()(()))))", "((()(()(())()()())))", "((()(()(())()())()))", "((()(()(())()()))())", "((()(()(())()())))()", "((()(()(())())(())))", "((()(()(())())()()))", "((()(()(())())())())", "((()(()(())())()))()", "((()(()(())()))(()))", "((()(()(())()))()())", "((()(()(())()))())()", "((()(()(())())))(())", "((()(()(())())))()()", "((()(()(()))((()))))", "((()(()(()))(()())))", "((()(()(()))(())()))", "((()(()(()))(()))())", "((()(()(()))(())))()", "((()(()(()))()(())))", "((()(()(()))()()()))", "((()(()(()))()())())", "((()(()(()))()()))()", "((()(()(()))())(()))", "((()(()(()))())()())", "((()(()(()))())())()", "((()(()(()))()))(())", "((()(()(()))()))()()", "((()(()(())))((())))", "((()(()(())))(()()))", "((()(()(())))(())())", "((()(()(())))(()))()", "((()(()(())))()(()))", "((()(()(())))()()())", "((()(()(())))()())()", "((()(()(())))())(())", "((()(()(())))())()()", "((()(()(()))))((()))", "((()(()(()))))(()())", "((()(()(()))))(())()", "((()(()(()))))()(())", "((()(()(()))))()()()", "((()(()()(((()))))))", "((()(()()((()())))))", "((()(()()((())()))))", "((()(()()((()))())))", "((()(()()((())))()))", "((()(()()((()))))())", "((()(()()((())))))()", "((()(()()(()(())))))", "((()(()()(()()()))))", "((()(()()(()())())))", "((()(()()(()()))()))", "((()(()()(()())))())", "((()(()()(()()))))()", "((()(()()(())(()))))", "((()(()()(())()())))", "((()(()()(())())()))", "((()(()()(())()))())", "((()(()()(())())))()", "((()(()()(()))(())))", "((()(()()(()))()()))", "((()(()()(()))())())", "((()(()()(()))()))()", "((()(()()(())))(()))", "((()(()()(())))()())", "((()(()()(())))())()", "((()(()()(()))))(())", "((()(()()(()))))()()", "((()(()()()((())))))", "((()(()()()(()()))))", "((()(()()()(())())))", "((()(()()()(()))()))", "((()(()()()(())))())", "((()(()()()(()))))()", "((()(()()()()(()))))", "((()(()()()()()())))", "((()(()()()()())()))", "((()(()()()()()))())", "((()(()()()()())))()", "((()(()()()())(())))", "((()(()()()())()()))", "((()(()()()())())())", "((()(()()()())()))()", "((()(()()()()))(()))", "((()(()()()()))()())", "((()(()()()()))())()", "((()(()()()())))(())", "((()(()()()())))()()", "((()(()()())((()))))", "((()(()()())(()())))", "((()(()()())(())()))", "((()(()()())(()))())", "((()(()()())(())))()", "((()(()()())()(())))", "((()(()()())()()()))", "((()(()()())()())())", "((()(()()())()()))()", "((()(()()())())(()))", "((()(()()())())()())", "((()(()()())())())()", "((()(()()())()))(())", "((()(()()())()))()()", "((()(()()()))((())))", "((()(()()()))(()()))", "((()(()()()))(())())", "((()(()()()))(()))()", "((()(()()()))()(()))", "((()(()()()))()()())", "((()(()()()))()())()", "((()(()()()))())(())", "((()(()()()))())()()", "((()(()()())))((()))", "((()(()()())))(()())", "((()(()()())))(())()", "((()(()()())))()(())", "((()(()()())))()()()", "((()(()())(((())))))", "((()(()())((()()))))", "((()(()())((())())))", "((()(()())((()))()))", "((()(()())((())))())", "((()(()())((()))))()", "((()(()())(()(()))))", "((()(()())(()()())))", "((()(()())(()())()))", "((()(()())(()()))())", "((()(()())(()())))()", "((()(()())(())(())))", "((()(()())(())()()))", "((()(()())(())())())", "((()(()())(())()))()", "((()(()())(()))(()))", "((()(()())(()))()())", "((()(()())(()))())()", "((()(()())(())))(())", "((()(()())(())))()()", "((()(()())()((()))))", "((()(()())()(()())))", "((()(()())()(())()))", "((()(()())()(()))())", "((()(()())()(())))()", "((()(()())()()(())))", "((()(()())()()()()))", "((()(()())()()())())", "((()(()())()()()))()", "((()(()())()())(()))", "((()(()())()())()())", "((()(()())()())())()", "((()(()())()()))(())", "((()(()())()()))()()", "((()(()())())((())))", "((()(()())())(()()))", "((()(()())())(())())", "((()(()())())(()))()", "((()(()())())()(()))", "((()(()())())()()())", "((()(()())())()())()", "((()(()())())())(())", "((()(()())())())()()", "((()(()())()))((()))", "((()(()())()))(()())", "((()(()())()))(())()", "((()(()())()))()(())", "((()(()())()))()()()", "((()(()()))(((()))))", "((()(()()))((()())))", "((()(()()))((())()))", "((()(()()))((()))())", "((()(()()))((())))()", "((()(()()))(()(())))", "((()(()()))(()()()))", "((()(()()))(()())())", "((()(()()))(()()))()", "((()(()()))(())(()))", "((()(()()))(())()())", "((()(()()))(())())()", "((()(()()))(()))(())", "((()(()()))(()))()()", "((()(()()))()((())))", "((()(()()))()(()()))", "((()(()()))()(())())", "((()(()()))()(()))()", "((()(()()))()()(()))", "((()(()()))()()()())", "((()(()()))()()())()", "((()(()()))()())(())", "((()(()()))()())()()", "((()(()()))())((()))", "((()(()()))())(()())", "((()(()()))())(())()", "((()(()()))())()(())", "((()(()()))())()()()", "((()(()())))(((())))", "((()(()())))((()()))", "((()(()())))((())())", "((()(()())))((()))()", "((()(()())))(()(()))", "((()(()())))(()()())", "((()(()())))(()())()", "((()(()())))(())(())", "((()(()())))(())()()", "((()(()())))()((()))", "((()(()())))()(()())", "((()(()())))()(())()", "((()(()())))()()(())", "((()(()())))()()()()", "((()(())((((()))))))", "((()(())(((()())))))", "((()(())(((())()))))", "((()(())(((()))())))", "((()(())(((())))()))", "((()(())(((()))))())", "((()(())(((())))))()", "((()(())((()(())))))", "((()(())((()()()))))", "((()(())((()())())))", "((()(())((()()))()))", "((()(())((()())))())", "((()(())((()()))))()", "((()(())((())(()))))", "((()(())((())()())))", "((()(())((())())()))", "((()(())((())()))())", "((()(())((())())))()", "((()(())((()))(())))", "((()(())((()))()()))", "((()(())((()))())())", "((()(())((()))()))()", "((()(())((())))(()))", "((()(())((())))()())", "((()(())((())))())()", "((()(())((()))))(())", "((()(())((()))))()()", "((()(())(()((())))))", "((()(())(()(()()))))", "((()(())(()(())())))", "((()(())(()(()))()))", "((()(())(()(())))())", "((()(())(()(()))))()", "((()(())(()()(()))))", "((()(())(()()()())))", "((()(())(()()())()))", "((()(())(()()()))())", "((()(())(()()())))()", "((()(())(()())(())))", "((()(())(()())()()))", "((()(())(()())())())", "((()(())(()())()))()", "((()(())(()()))(()))", "((()(())(()()))()())", "((()(())(()()))())()", "((()(())(()())))(())", "((()(())(()())))()()", "((()(())(())((()))))", "((()(())(())(()())))", "((()(())(())(())()))", "((()(())(())(()))())", "((()(())(())(())))()", "((()(())(())()(())))", "((()(())(())()()()))", "((()(())(())()())())", "((()(())(())()()))()", "((()(())(())())(()))", "((()(())(())())()())", "((()(())(())())())()", "((()(())(())()))(())", "((()(())(())()))()()", "((()(())(()))((())))", "((()(())(()))(()()))", "((()(())(()))(())())", "((()(())(()))(()))()", "((()(())(()))()(()))", "((()(())(()))()()())", "((()(())(()))()())()", "((()(())(()))())(())", "((()(())(()))())()()", "((()(())(())))((()))", "((()(())(())))(()())", "((()(())(())))(())()", "((()(())(())))()(())", "((()(())(())))()()()", "((()(())()(((())))))", "((()(())()((()()))))", "((()(())()((())())))", "((()(())()((()))()))", "((()(())()((())))())", "((()(())()((()))))()", "((()(())()(()(()))))", "((()(())()(()()())))", "((()(())()(()())()))", "((()(())()(()()))())", "((()(())()(()())))()", "((()(())()(())(())))", "((()(())()(())()()))", "((()(())()(())())())", "((()(())()(())()))()", "((()(())()(()))(()))", "((()(())()(()))()())", "((()(())()(()))())()", "((()(())()(())))(())", "((()(())()(())))()()", "((()(())()()((()))))", "((()(())()()(()())))", "((()(())()()(())()))", "((()(())()()(()))())", "((()(())()()(())))()", "((()(())()()()(())))", "((()(())()()()()()))", "((()(())()()()())())", "((()(())()()()()))()", "((()(())()()())(()))", "((()(())()()())()())", "((()(())()()())())()", "((()(())()()()))(())", "((()(())()()()))()()", "((()(())()())((())))", "((()(())()())(()()))", "((()(())()())(())())", "((()(())()())(()))()", "((()(())()())()(()))", "((()(())()())()()())", "((()(())()())()())()", "((()(())()())())(())", "((()(())()())())()()", "((()(())()()))((()))", "((()(())()()))(()())", "((()(())()()))(())()", "((()(())()()))()(())", "((()(())()()))()()()", "((()(())())(((()))))", "((()(())())((()())))", "((()(())())((())()))", "((()(())())((()))())", "((()(())())((())))()", "((()(())())(()(())))", "((()(())())(()()()))", "((()(())())(()())())", "((()(())())(()()))()", "((()(())())(())(()))", "((()(())())(())()())", "((()(())())(())())()", "((()(())())(()))(())", "((()(())())(()))()()", "((()(())())()((())))", "((()(())())()(()()))", "((()(())())()(())())", "((()(())())()(()))()", "((()(())())()()(()))", "((()(())())()()()())", "((()(())())()()())()", "((()(())())()())(())", "((()(())())()())()()", "((()(())())())((()))", "((()(())())())(()())", "((()(())())())(())()", "((()(())())())()(())", "((()(())())())()()()", "((()(())()))(((())))", "((()(())()))((()()))", "((()(())()))((())())", "((()(())()))((()))()", "((()(())()))(()(()))", "((()(())()))(()()())", "((()(())()))(()())()", "((()(())()))(())(())", "((()(())()))(())()()", "((()(())()))()((()))", "((()(())()))()(()())", "((()(())()))()(())()", "((()(())()))()()(())", "((()(())()))()()()()", "((()(()))((((())))))", "((()(()))(((()()))))", "((()(()))(((())())))", "((()(()))(((()))()))", "((()(()))(((())))())", "((()(()))(((()))))()", "((()(()))((()(()))))", "((()(()))((()()())))", "((()(()))((()())()))", "((()(()))((()()))())", "((()(()))((()())))()", "((()(()))((())(())))", "((()(()))((())()()))", "((()(()))((())())())", "((()(()))((())()))()", "((()(()))((()))(()))", "((()(()))((()))()())", "((()(()))((()))())()", "((()(()))((())))(())", "((()(()))((())))()()", "((()(()))(()((()))))", "((()(()))(()(()())))", "((()(()))(()(())()))", "((()(()))(()(()))())", "((()(()))(()(())))()", "((()(()))(()()(())))", "((()(()))(()()()()))", "((()(()))(()()())())", "((()(()))(()()()))()", "((()(()))(()())(()))", "((()(()))(()())()())", "((()(()))(()())())()", "((()(()))(()()))(())", "((()(()))(()()))()()", "((()(()))(())((())))", "((()(()))(())(()()))", "((()(()))(())(())())", "((()(()))(())(()))()", "((()(()))(())()(()))", "((()(()))(())()()())", "((()(()))(())()())()", "((()(()))(())())(())", "((()(()))(())())()()", "((()(()))(()))((()))", "((()(()))(()))(()())", "((()(()))(()))(())()", "((()(()))(()))()(())", "((()(()))(()))()()()", "((()(()))()(((()))))", "((()(()))()((()())))", "((()(()))()((())()))", "((()(()))()((()))())", "((()(()))()((())))()", "((()(()))()(()(())))", "((()(()))()(()()()))", "((()(()))()(()())())", "((()(()))()(()()))()", "((()(()))()(())(()))", "((()(()))()(())()())", "((()(()))()(())())()", "((()(()))()(()))(())", "((()(()))()(()))()()", "((()(()))()()((())))", "((()(()))()()(()()))", "((()(()))()()(())())", "((()(()))()()(()))()", "((()(()))()()()(()))", "((()(()))()()()()())", "((()(()))()()()())()", "((()(()))()()())(())", "((()(()))()()())()()", "((()(()))()())((()))", "((()(()))()())(()())", "((()(()))()())(())()", "((()(()))()())()(())", "((()(()))()())()()()", "((()(()))())(((())))", "((()(()))())((()()))", "((()(()))())((())())", "((()(()))())((()))()", "((()(()))())(()(()))", "((()(()))())(()()())", "((()(()))())(()())()", "((()(()))())(())(())", "((()(()))())(())()()", "((()(()))())()((()))", "((()(()))())()(()())", "((()(()))())()(())()", "((()(()))())()()(())", "((()(()))())()()()()", "((()(())))((((()))))", "((()(())))(((()())))", "((()(())))(((())()))", "((()(())))(((()))())", "((()(())))(((())))()", "((()(())))((()(())))", "((()(())))((()()()))", "((()(())))((()())())", "((()(())))((()()))()", "((()(())))((())(()))", "((()(())))((())()())", "((()(())))((())())()", "((()(())))((()))(())", "((()(())))((()))()()", "((()(())))(()((())))", "((()(())))(()(()()))", "((()(())))(()(())())", "((()(())))(()(()))()", "((()(())))(()()(()))", "((()(())))(()()()())", "((()(())))(()()())()", "((()(())))(()())(())", "((()(())))(()())()()", "((()(())))(())((()))", "((()(())))(())(()())", "((()(())))(())(())()", "((()(())))(())()(())", "((()(())))(())()()()", "((()(())))()(((())))", "((()(())))()((()()))", "((()(())))()((())())", "((()(())))()((()))()", "((()(())))()(()(()))", "((()(())))()(()()())", "((()(())))()(()())()", "((()(())))()(())(())", "((()(())))()(())()()", "((()(())))()()((()))", "((()(())))()()(()())", "((()(())))()()(())()", "((()(())))()()()(())", "((()(())))()()()()()", "((()()(((((())))))))", "((()()((((()()))))))", "((()()((((())())))))", "((()()((((()))()))))", "((()()((((())))())))", "((()()((((()))))()))", "((()()((((())))))())", "((()()((((()))))))()", "((()()(((()(()))))))", "((()()(((()()())))))", "((()()(((()())()))))", "((()()(((()()))())))", "((()()(((()())))()))", "((()()(((()()))))())", "((()()(((()())))))()", "((()()(((())(())))))", "((()()(((())()()))))", "((()()(((())())())))", "((()()(((())()))()))", "((()()(((())())))())", "((()()(((())()))))()", "((()()(((()))(()))))", "((()()(((()))()())))", "((()()(((()))())()))", "((()()(((()))()))())", "((()()(((()))())))()", "((()()(((())))(())))", "((()()(((())))()()))", "((()()(((())))())())", "((()()(((())))()))()", "((()()(((()))))(()))", "((()()(((()))))()())", "((()()(((()))))())()", "((()()(((())))))(())", "((()()(((())))))()()", "((()()((()((()))))))", "((()()((()(()())))))", "((()()((()(())()))))", "((()()((()(()))())))", "((()()((()(())))()))", "((()()((()(()))))())", "((()()((()(())))))()", "((()()((()()(())))))", "((()()((()()()()))))", "((()()((()()())())))", "((()()((()()()))()))", "((()()((()()())))())", "((()()((()()()))))()", "((()()((()())(()))))", "((()()((()())()())))", "((()()((()())())()))", "((()()((()())()))())", "((()()((()())())))()", "((()()((()()))(())))", "((()()((()()))()()))", "((()()((()()))())())", "((()()((()()))()))()", "((()()((()())))(()))", "((()()((()())))()())", "((()()((()())))())()", "((()()((()()))))(())", "((()()((()()))))()()", "((()()((())((())))))", "((()()((())(()()))))", "((()()((())(())())))", "((()()((())(()))()))", "((()()((())(())))())", "((()()((())(()))))()", "((()()((())()(()))))", "((()()((())()()())))", "((()()((())()())()))", "((()()((())()()))())", "((()()((())()())))()", "((()()((())())(())))", "((()()((())())()()))", "((()()((())())())())", "((()()((())())()))()", "((()()((())()))(()))", "((()()((())()))()())", "((()()((())()))())()", "((()()((())())))(())", "((()()((())())))()()", "((()()((()))((()))))", "((()()((()))(()())))", "((()()((()))(())()))", "((()()((()))(()))())", "((()()((()))(())))()", "((()()((()))()(())))", "((()()((()))()()()))", "((()()((()))()())())", "((()()((()))()()))()", "((()()((()))())(()))", "((()()((()))())()())", "((()()((()))())())()", "((()()((()))()))(())", "((()()((()))()))()()", "((()()((())))((())))", "((()()((())))(()()))", "((()()((())))(())())", "((()()((())))(()))()", "((()()((())))()(()))", "((()()((())))()()())", "((()()((())))()())()", "((()()((())))())(())", "((()()((())))())()()", "((()()((()))))((()))", "((()()((()))))(()())", "((()()((()))))(())()", "((()()((()))))()(())", "((()()((()))))()()()", "((()()(()(((()))))))", "((()()(()((()())))))", "((()()(()((())()))))", "((()()(()((()))())))", "((()()(()((())))()))", "((()()(()((()))))())", "((()()(()((())))))()", "((()()(()(()(())))))", "((()()(()(()()()))))", "((()()(()(()())())))", "((()()(()(()()))()))", "((()()(()(()())))())", "((()()(()(()()))))()", "((()()(()(())(()))))", "((()()(()(())()())))", "((()()(()(())())()))", "((()()(()(())()))())", "((()()(()(())())))()", "((()()(()(()))(())))", "((()()(()(()))()()))", "((()()(()(()))())())", "((()()(()(()))()))()", "((()()(()(())))(()))", "((()()(()(())))()())", "((()()(()(())))())()", "((()()(()(()))))(())", "((()()(()(()))))()()", "((()()(()()((())))))", "((()()(()()(()()))))", "((()()(()()(())())))", "((()()(()()(()))()))", "((()()(()()(())))())", "((()()(()()(()))))()", "((()()(()()()(()))))", "((()()(()()()()())))", "((()()(()()()())()))", "((()()(()()()()))())", "((()()(()()()())))()", "((()()(()()())(())))", "((()()(()()())()()))", "((()()(()()())())())", "((()()(()()())()))()", "((()()(()()()))(()))", "((()()(()()()))()())", "((()()(()()()))())()", "((()()(()()())))(())", "((()()(()()())))()()", "((()()(()())((()))))", "((()()(()())(()())))", "((()()(()())(())()))", "((()()(()())(()))())", "((()()(()())(())))()", "((()()(()())()(())))", "((()()(()())()()()))", "((()()(()())()())())", "((()()(()())()()))()", "((()()(()())())(()))", "((()()(()())())()())", "((()()(()())())())()", "((()()(()())()))(())", "((()()(()())()))()()", "((()()(()()))((())))", "((()()(()()))(()()))", "((()()(()()))(())())", "((()()(()()))(()))()", "((()()(()()))()(()))", "((()()(()()))()()())", "((()()(()()))()())()", "((()()(()()))())(())", "((()()(()()))())()()", "((()()(()())))((()))", "((()()(()())))(()())", "((()()(()())))(())()", "((()()(()())))()(())", "((()()(()())))()()()", "((()()(())(((())))))", "((()()(())((()()))))", "((()()(())((())())))", "((()()(())((()))()))", "((()()(())((())))())", "((()()(())((()))))()", "((()()(())(()(()))))", "((()()(())(()()())))", "((()()(())(()())()))", "((()()(())(()()))())", "((()()(())(()())))()", "((()()(())(())(())))", "((()()(())(())()()))", "((()()(())(())())())", "((()()(())(())()))()", "((()()(())(()))(()))", "((()()(())(()))()())", "((()()(())(()))())()", "((()()(())(())))(())", "((()()(())(())))()()", "((()()(())()((()))))", "((()()(())()(()())))", "((()()(())()(())()))", "((()()(())()(()))())", "((()()(())()(())))()", "((()()(())()()(())))", "((()()(())()()()()))", "((()()(())()()())())", "((()()(())()()()))()", "((()()(())()())(()))", "((()()(())()())()())", "((()()(())()())())()", "((()()(())()()))(())", "((()()(())()()))()()", "((()()(())())((())))", "((()()(())())(()()))", "((()()(())())(())())", "((()()(())())(()))()", "((()()(())())()(()))", "((()()(())())()()())", "((()()(())())()())()", "((()()(())())())(())", "((()()(())())())()()", "((()()(())()))((()))", "((()()(())()))(()())", "((()()(())()))(())()", "((()()(())()))()(())", "((()()(())()))()()()", "((()()(()))(((()))))", "((()()(()))((()())))", "((()()(()))((())()))", "((()()(()))((()))())", "((()()(()))((())))()", "((()()(()))(()(())))", "((()()(()))(()()()))", "((()()(()))(()())())", "((()()(()))(()()))()", "((()()(()))(())(()))", "((()()(()))(())()())", "((()()(()))(())())()", "((()()(()))(()))(())", "((()()(()))(()))()()", "((()()(()))()((())))", "((()()(()))()(()()))", "((()()(()))()(())())", "((()()(()))()(()))()", "((()()(()))()()(()))", "((()()(()))()()()())", "((()()(()))()()())()", "((()()(()))()())(())", "((()()(()))()())()()", "((()()(()))())((()))", "((()()(()))())(()())", "((()()(()))())(())()", "((()()(()))())()(())", "((()()(()))())()()()", "((()()(())))(((())))", "((()()(())))((()()))", "((()()(())))((())())", "((()()(())))((()))()", "((()()(())))(()(()))", "((()()(())))(()()())", "((()()(())))(()())()", "((()()(())))(())(())", "((()()(())))(())()()", "((()()(())))()((()))", "((()()(())))()(()())", "((()()(())))()(())()", "((()()(())))()()(())", "((()()(())))()()()()", "((()()()((((()))))))", "((()()()(((()())))))", "((()()()(((())()))))", "((()()()(((()))())))", "((()()()(((())))()))", "((()()()(((()))))())", "((()()()(((())))))()", "((()()()((()(())))))", "((()()()((()()()))))", "((()()()((()())())))", "((()()()((()()))()))", "((()()()((()())))())", "((()()()((()()))))()", "((()()()((())(()))))", "((()()()((())()())))", "((()()()((())())()))", "((()()()((())()))())", "((()()()((())())))()", "((()()()((()))(())))", "((()()()((()))()()))", "((()()()((()))())())", "((()()()((()))()))()", "((()()()((())))(()))", "((()()()((())))()())", "((()()()((())))())()", "((()()()((()))))(())", "((()()()((()))))()()", "((()()()(()((())))))", "((()()()(()(()()))))", "((()()()(()(())())))", "((()()()(()(()))()))", "((()()()(()(())))())", "((()()()(()(()))))()", "((()()()(()()(()))))", "((()()()(()()()())))", "((()()()(()()())()))", "((()()()(()()()))())", "((()()()(()()())))()", "((()()()(()())(())))", "((()()()(()())()()))", "((()()()(()())())())", "((()()()(()())()))()", "((()()()(()()))(()))", "((()()()(()()))()())", "((()()()(()()))())()", "((()()()(()())))(())", "((()()()(()())))()()", "((()()()(())((()))))", "((()()()(())(()())))", "((()()()(())(())()))", "((()()()(())(()))())", "((()()()(())(())))()", "((()()()(())()(())))", "((()()()(())()()()))", "((()()()(())()())())", "((()()()(())()()))()", "((()()()(())())(()))", "((()()()(())())()())", "((()()()(())())())()", "((()()()(())()))(())", "((()()()(())()))()()", "((()()()(()))((())))", "((()()()(()))(()()))", "((()()()(()))(())())", "((()()()(()))(()))()", "((()()()(()))()(()))", "((()()()(()))()()())", "((()()()(()))()())()", "((()()()(()))())(())", "((()()()(()))())()()", "((()()()(())))((()))", "((()()()(())))(()())", "((()()()(())))(())()", "((()()()(())))()(())", "((()()()(())))()()()", "((()()()()(((())))))", "((()()()()((()()))))", "((()()()()((())())))", "((()()()()((()))()))", "((()()()()((())))())", "((()()()()((()))))()", "((()()()()(()(()))))", "((()()()()(()()())))", "((()()()()(()())()))", "((()()()()(()()))())", "((()()()()(()())))()", "((()()()()(())(())))", "((()()()()(())()()))", "((()()()()(())())())", "((()()()()(())()))()", "((()()()()(()))(()))", "((()()()()(()))()())", "((()()()()(()))())()", "((()()()()(())))(())", "((()()()()(())))()()", "((()()()()()((()))))", "((()()()()()(()())))", "((()()()()()(())()))", "((()()()()()(()))())", "((()()()()()(())))()", "((()()()()()()(())))", "((()()()()()()()()))", "((()()()()()()())())", "((()()()()()()()))()", "((()()()()()())(()))", "((()()()()()())()())", "((()()()()()())())()", "((()()()()()()))(())", "((()()()()()()))()()", "((()()()()())((())))", "((()()()()())(()()))", "((()()()()())(())())", "((()()()()())(()))()", "((()()()()())()(()))", "((()()()()())()()())", "((()()()()())()())()", "((()()()()())())(())", "((()()()()())())()()", "((()()()()()))((()))", "((()()()()()))(()())", "((()()()()()))(())()", "((()()()()()))()(())", "((()()()()()))()()()", "((()()()())(((()))))", "((()()()())((()())))", "((()()()())((())()))", "((()()()())((()))())", "((()()()())((())))()", "((()()()())(()(())))", "((()()()())(()()()))", "((()()()())(()())())", "((()()()())(()()))()", "((()()()())(())(()))", "((()()()())(())()())", "((()()()())(())())()", "((()()()())(()))(())", "((()()()())(()))()()", "((()()()())()((())))", "((()()()())()(()()))", "((()()()())()(())())", "((()()()())()(()))()", "((()()()())()()(()))", "((()()()())()()()())", "((()()()())()()())()", "((()()()())()())(())", "((()()()())()())()()", "((()()()())())((()))", "((()()()())())(()())", "((()()()())())(())()", "((()()()())())()(())", "((()()()())())()()()", "((()()()()))(((())))", "((()()()()))((()()))", "((()()()()))((())())", "((()()()()))((()))()", "((()()()()))(()(()))", "((()()()()))(()()())", "((()()()()))(()())()", "((()()()()))(())(())", "((()()()()))(())()()", "((()()()()))()((()))", "((()()()()))()(()())", "((()()()()))()(())()", "((()()()()))()()(())", "((()()()()))()()()()", "((()()())((((())))))", "((()()())(((()()))))", "((()()())(((())())))", "((()()())(((()))()))", "((()()())(((())))())", "((()()())(((()))))()", "((()()())((()(()))))", "((()()())((()()())))", "((()()())((()())()))", "((()()())((()()))())", "((()()())((()())))()", "((()()())((())(())))", "((()()())((())()()))", "((()()())((())())())", "((()()())((())()))()", "((()()())((()))(()))", "((()()())((()))()())", "((()()())((()))())()", "((()()())((())))(())", "((()()())((())))()()", "((()()())(()((()))))", "((()()())(()(()())))", "((()()())(()(())()))", "((()()())(()(()))())", "((()()())(()(())))()", "((()()())(()()(())))", "((()()())(()()()()))", "((()()())(()()())())", "((()()())(()()()))()", "((()()())(()())(()))", "((()()())(()())()())", "((()()())(()())())()", "((()()())(()()))(())", "((()()())(()()))()()", "((()()())(())((())))", "((()()())(())(()()))", "((()()())(())(())())", "((()()())(())(()))()", "((()()())(())()(()))", "((()()())(())()()())", "((()()())(())()())()", "((()()())(())())(())", "((()()())(())())()()", "((()()())(()))((()))", "((()()())(()))(()())", "((()()())(()))(())()", "((()()())(()))()(())", "((()()())(()))()()()", "((()()())()(((()))))", "((()()())()((()())))", "((()()())()((())()))", "((()()())()((()))())", "((()()())()((())))()", "((()()())()(()(())))", "((()()())()(()()()))", "((()()())()(()())())", "((()()())()(()()))()", "((()()())()(())(()))", "((()()())()(())()())", "((()()())()(())())()", "((()()())()(()))(())", "((()()())()(()))()()", "((()()())()()((())))", "((()()())()()(()()))", "((()()())()()(())())", "((()()())()()(()))()", "((()()())()()()(()))", "((()()())()()()()())", "((()()())()()()())()", "((()()())()()())(())", "((()()())()()())()()", "((()()())()())((()))", "((()()())()())(()())", "((()()())()())(())()", "((()()())()())()(())", "((()()())()())()()()", "((()()())())(((())))", "((()()())())((()()))", "((()()())())((())())", "((()()())())((()))()", "((()()())())(()(()))", "((()()())())(()()())", "((()()())())(()())()", "((()()())())(())(())", "((()()())())(())()()", "((()()())())()((()))", "((()()())())()(()())", "((()()())())()(())()", "((()()())())()()(())", "((()()())())()()()()", "((()()()))((((()))))", "((()()()))(((()())))", "((()()()))(((())()))", "((()()()))(((()))())", "((()()()))(((())))()", "((()()()))((()(())))", "((()()()))((()()()))", "((()()()))((()())())", "((()()()))((()()))()", "((()()()))((())(()))", "((()()()))((())()())", "((()()()))((())())()", "((()()()))((()))(())", "((()()()))((()))()()", "((()()()))(()((())))", "((()()()))(()(()()))", "((()()()))(()(())())", "((()()()))(()(()))()", "((()()()))(()()(()))", "((()()()))(()()()())", "((()()()))(()()())()", "((()()()))(()())(())", "((()()()))(()())()()", "((()()()))(())((()))", "((()()()))(())(()())", "((()()()))(())(())()", "((()()()))(())()(())", "((()()()))(())()()()", "((()()()))()(((())))", "((()()()))()((()()))", "((()()()))()((())())", "((()()()))()((()))()", "((()()()))()(()(()))", "((()()()))()(()()())", "((()()()))()(()())()", "((()()()))()(())(())", "((()()()))()(())()()", "((()()()))()()((()))", "((()()()))()()(()())", "((()()()))()()(())()", "((()()()))()()()(())", "((()()()))()()()()()", "((()())(((((()))))))", "((()())((((()())))))", "((()())((((())()))))", "((()())((((()))())))", "((()())((((())))()))", "((()())((((()))))())", "((()())((((())))))()", "((()())(((()(())))))", "((()())(((()()()))))", "((()())(((()())())))", "((()())(((()()))()))", "((()())(((()())))())", "((()())(((()()))))()", "((()())(((())(()))))", "((()())(((())()())))", "((()())(((())())()))", "((()())(((())()))())", "((()())(((())())))()", "((()())(((()))(())))", "((()())(((()))()()))", "((()())(((()))())())", "((()())(((()))()))()", "((()())(((())))(()))", "((()())(((())))()())", "((()())(((())))())()", "((()())(((()))))(())", "((()())(((()))))()()", "((()())((()((())))))", "((()())((()(()()))))", "((()())((()(())())))", "((()())((()(()))()))", "((()())((()(())))())", "((()())((()(()))))()", "((()())((()()(()))))", "((()())((()()()())))", "((()())((()()())()))", "((()())((()()()))())", "((()())((()()())))()", "((()())((()())(())))", "((()())((()())()()))", "((()())((()())())())", "((()())((()())()))()", "((()())((()()))(()))", "((()())((()()))()())", "((()())((()()))())()", "((()())((()())))(())", "((()())((()())))()()", "((()())((())((()))))", "((()())((())(()())))", "((()())((())(())()))", "((()())((())(()))())", "((()())((())(())))()", "((()())((())()(())))", "((()())((())()()()))", "((()())((())()())())", "((()())((())()()))()", "((()())((())())(()))", "((()())((())())()())", "((()())((())())())()", "((()())((())()))(())", "((()())((())()))()()", "((()())((()))((())))", "((()())((()))(()()))", "((()())((()))(())())", "((()())((()))(()))()", "((()())((()))()(()))", "((()())((()))()()())", "((()())((()))()())()", "((()())((()))())(())", "((()())((()))())()()", "((()())((())))((()))", "((()())((())))(()())", "((()())((())))(())()", "((()())((())))()(())", "((()())((())))()()()", "((()())(()(((())))))", "((()())(()((()()))))", "((()())(()((())())))", "((()())(()((()))()))", "((()())(()((())))())", "((()())(()((()))))()", "((()())(()(()(()))))", "((()())(()(()()())))", "((()())(()(()())()))", "((()())(()(()()))())", "((()())(()(()())))()", "((()())(()(())(())))", "((()())(()(())()()))", "((()())(()(())())())", "((()())(()(())()))()", "((()())(()(()))(()))", "((()())(()(()))()())", "((()())(()(()))())()", "((()())(()(())))(())", "((()())(()(())))()()", "((()())(()()((()))))", "((()())(()()(()())))", "((()())(()()(())()))", "((()())(()()(()))())", "((()())(()()(())))()", "((()())(()()()(())))", "((()())(()()()()()))", "((()())(()()()())())", "((()())(()()()()))()", "((()())(()()())(()))", "((()())(()()())()())", "((()())(()()())())()", "((()())(()()()))(())", "((()())(()()()))()()", "((()())(()())((())))", "((()())(()())(()()))", "((()())(()())(())())", "((()())(()())(()))()", "((()())(()())()(()))", "((()())(()())()()())", "((()())(()())()())()", "((()())(()())())(())", "((()())(()())())()()", "((()())(()()))((()))", "((()())(()()))(()())", "((()())(()()))(())()", "((()())(()()))()(())", "((()())(()()))()()()", "((()())(())(((()))))", "((()())(())((()())))", "((()())(())((())()))", "((()())(())((()))())", "((()())(())((())))()", "((()())(())(()(())))", "((()())(())(()()()))", "((()())(())(()())())", "((()())(())(()()))()", "((()())(())(())(()))", "((()())(())(())()())", "((()())(())(())())()", "((()())(())(()))(())", "((()())(())(()))()()", "((()())(())()((())))", "((()())(())()(()()))", "((()())(())()(())())", "((()())(())()(()))()", "((()())(())()()(()))", "((()())(())()()()())", "((()())(())()()())()", "((()())(())()())(())", "((()())(())()())()()", "((()())(())())((()))", "((()())(())())(()())", "((()())(())())(())()", "((()())(())())()(())", "((()())(())())()()()", "((()())(()))(((())))", "((()())(()))((()()))", "((()())(()))((())())", "((()())(()))((()))()", "((()())(()))(()(()))", "((()())(()))(()()())", "((()())(()))(()())()", "((()())(()))(())(())", "((()())(()))(())()()", "((()())(()))()((()))", "((()())(()))()(()())", "((()())(()))()(())()", "((()())(()))()()(())", "((()())(()))()()()()", "((()())()((((())))))", "((()())()(((()()))))", "((()())()(((())())))", "((()())()(((()))()))", "((()())()(((())))())", "((()())()(((()))))()", "((()())()((()(()))))", "((()())()((()()())))", "((()())()((()())()))", "((()())()((()()))())", "((()())()((()())))()", "((()())()((())(())))", "((()())()((())()()))", "((()())()((())())())", "((()())()((())()))()", "((()())()((()))(()))", "((()())()((()))()())", "((()())()((()))())()", "((()())()((())))(())", "((()())()((())))()()", "((()())()(()((()))))", "((()())()(()(()())))", "((()())()(()(())()))", "((()())()(()(()))())", "((()())()(()(())))()", "((()())()(()()(())))", "((()())()(()()()()))", "((()())()(()()())())", "((()())()(()()()))()", "((()())()(()())(()))", "((()())()(()())()())", "((()())()(()())())()", "((()())()(()()))(())", "((()())()(()()))()()", "((()())()(())((())))", "((()())()(())(()()))", "((()())()(())(())())", "((()())()(())(()))()", "((()())()(())()(()))", "((()())()(())()()())", "((()())()(())()())()", "((()())()(())())(())", "((()())()(())())()()", "((()())()(()))((()))", "((()())()(()))(()())", "((()())()(()))(())()", "((()())()(()))()(())", "((()())()(()))()()()", "((()())()()(((()))))", "((()())()()((()())))", "((()())()()((())()))", "((()())()()((()))())", "((()())()()((())))()", "((()())()()(()(())))", "((()())()()(()()()))", "((()())()()(()())())", "((()())()()(()()))()", "((()())()()(())(()))", "((()())()()(())()())", "((()())()()(())())()", "((()())()()(()))(())", "((()())()()(()))()()", "((()())()()()((())))", "((()())()()()(()()))", "((()())()()()(())())", "((()())()()()(()))()", "((()())()()()()(()))", "((()())()()()()()())", "((()())()()()()())()", "((()())()()()())(())", "((()())()()()())()()", "((()())()()())((()))", "((()())()()())(()())", "((()())()()())(())()", "((()())()()())()(())", "((()())()()())()()()", "((()())()())(((())))", "((()())()())((()()))", "((()())()())((())())", "((()())()())((()))()", "((()())()())(()(()))", "((()())()())(()()())", "((()())()())(()())()", "((()())()())(())(())", "((()())()())(())()()", "((()())()())()((()))", "((()())()())()(()())", "((()())()())()(())()", "((()())()())()()(())", "((()())()())()()()()", "((()())())((((()))))", "((()())())(((()())))", "((()())())(((())()))", "((()())())(((()))())", "((()())())(((())))()", "((()())())((()(())))", "((()())())((()()()))", "((()())())((()())())", "((()())())((()()))()", "((()())())((())(()))", "((()())())((())()())", "((()())())((())())()", "((()())())((()))(())", "((()())())((()))()()", "((()())())(()((())))", "((()())())(()(()()))", "((()())())(()(())())", "((()())())(()(()))()", "((()())())(()()(()))", "((()())())(()()()())", "((()())())(()()())()", "((()())())(()())(())", "((()())())(()())()()", "((()())())(())((()))", "((()())())(())(()())", "((()())())(())(())()", "((()())())(())()(())", "((()())())(())()()()", "((()())())()(((())))", "((()())())()((()()))", "((()())())()((())())", "((()())())()((()))()", "((()())())()(()(()))", "((()())())()(()()())", "((()())())()(()())()", "((()())())()(())(())", "((()())())()(())()()", "((()())())()()((()))", "((()())())()()(()())", "((()())())()()(())()", "((()())())()()()(())", "((()())())()()()()()", "((()()))(((((())))))", "((()()))((((()()))))", "((()()))((((())())))", "((()()))((((()))()))", "((()()))((((())))())", "((()()))((((()))))()", "((()()))(((()(()))))", "((()()))(((()()())))", "((()()))(((()())()))", "((()()))(((()()))())", "((()()))(((()())))()", "((()()))(((())(())))", "((()()))(((())()()))", "((()()))(((())())())", "((()()))(((())()))()", "((()()))(((()))(()))", "((()()))(((()))()())", "((()()))(((()))())()", "((()()))(((())))(())", "((()()))(((())))()()", "((()()))((()((()))))", "((()()))((()(()())))", "((()()))((()(())()))", "((()()))((()(()))())", "((()()))((()(())))()", "((()()))((()()(())))", "((()()))((()()()()))", "((()()))((()()())())", "((()()))((()()()))()", "((()()))((()())(()))", "((()()))((()())()())", "((()()))((()())())()", "((()()))((()()))(())", "((()()))((()()))()()", "((()()))((())((())))", "((()()))((())(()()))", "((()()))((())(())())", "((()()))((())(()))()", "((()()))((())()(()))", "((()()))((())()()())", "((()()))((())()())()", "((()()))((())())(())", "((()()))((())())()()", "((()()))((()))((()))", "((()()))((()))(()())", "((()()))((()))(())()", "((()()))((()))()(())", "((()()))((()))()()()", "((()()))(()(((()))))", "((()()))(()((()())))", "((()()))(()((())()))", "((()()))(()((()))())", "((()()))(()((())))()", "((()()))(()(()(())))", "((()()))(()(()()()))", "((()()))(()(()())())", "((()()))(()(()()))()", "((()()))(()(())(()))", "((()()))(()(())()())", "((()()))(()(())())()", "((()()))(()(()))(())", "((()()))(()(()))()()", "((()()))(()()((())))", "((()()))(()()(()()))", "((()()))(()()(())())", "((()()))(()()(()))()", "((()()))(()()()(()))", "((()()))(()()()()())", "((()()))(()()()())()", "((()()))(()()())(())", "((()()))(()()())()()", "((()()))(()())((()))", "((()()))(()())(()())", "((()()))(()())(())()", "((()()))(()())()(())", "((()()))(()())()()()", "((()()))(())(((())))", "((()()))(())((()()))", "((()()))(())((())())", "((()()))(())((()))()", "((()()))(())(()(()))", "((()()))(())(()()())", "((()()))(())(()())()", "((()()))(())(())(())", "((()()))(())(())()()", "((()()))(())()((()))", "((()()))(())()(()())", "((()()))(())()(())()", "((()()))(())()()(())", "((()()))(())()()()()", "((()()))()((((()))))", "((()()))()(((()())))", "((()()))()(((())()))", "((()()))()(((()))())", "((()()))()(((())))()", "((()()))()((()(())))", "((()()))()((()()()))", "((()()))()((()())())", "((()()))()((()()))()", "((()()))()((())(()))", "((()()))()((())()())", "((()()))()((())())()", "((()()))()((()))(())", "((()()))()((()))()()", "((()()))()(()((())))", "((()()))()(()(()()))", "((()()))()(()(())())", "((()()))()(()(()))()", "((()()))()(()()(()))", "((()()))()(()()()())", "((()()))()(()()())()", "((()()))()(()())(())", "((()()))()(()())()()", "((()()))()(())((()))", "((()()))()(())(()())", "((()()))()(())(())()", "((()()))()(())()(())", "((()()))()(())()()()", "((()()))()()(((())))", "((()()))()()((()()))", "((()()))()()((())())", "((()()))()()((()))()", "((()()))()()(()(()))", "((()()))()()(()()())", "((()()))()()(()())()", "((()()))()()(())(())", "((()()))()()(())()()", "((()()))()()()((()))", "((()()))()()()(()())", "((()()))()()()(())()", "((()()))()()()()(())", "((()()))()()()()()()", "((())((((((())))))))", "((())(((((()()))))))", "((())(((((())())))))", "((())(((((()))()))))", "((())(((((())))())))", "((())(((((()))))()))", "((())(((((())))))())", "((())(((((()))))))()", "((())((((()(()))))))", "((())((((()()())))))", "((())((((()())()))))", "((())((((()()))())))", "((())((((()())))()))", "((())((((()()))))())", "((())((((()())))))()", "((())((((())(())))))", "((())((((())()()))))", "((())((((())())())))", "((())((((())()))()))", "((())((((())())))())", "((())((((())()))))()", "((())((((()))(()))))", "((())((((()))()())))", "((())((((()))())()))", "((())((((()))()))())", "((())((((()))())))()", "((())((((())))(())))", "((())((((())))()()))", "((())((((())))())())", "((())((((())))()))()", "((())((((()))))(()))", "((())((((()))))()())", "((())((((()))))())()", "((())((((())))))(())", "((())((((())))))()()", "((())(((()((()))))))", "((())(((()(()())))))", "((())(((()(())()))))", "((())(((()(()))())))", "((())(((()(())))()))", "((())(((()(()))))())", "((())(((()(())))))()", "((())(((()()(())))))", "((())(((()()()()))))", "((())(((()()())())))", "((())(((()()()))()))", "((())(((()()())))())", "((())(((()()()))))()", "((())(((()())(()))))", "((())(((()())()())))", "((())(((()())())()))", "((())(((()())()))())", "((())(((()())())))()", "((())(((()()))(())))", "((())(((()()))()()))", "((())(((()()))())())", "((())(((()()))()))()", "((())(((()())))(()))", "((())(((()())))()())", "((())(((()())))())()", "((())(((()()))))(())", "((())(((()()))))()()", "((())(((())((())))))", "((())(((())(()()))))", "((())(((())(())())))", "((())(((())(()))()))", "((())(((())(())))())", "((())(((())(()))))()", "((())(((())()(()))))", "((())(((())()()())))", "((())(((())()())()))", "((())(((())()()))())", "((())(((())()())))()", "((())(((())())(())))", "((())(((())())()()))", "((())(((())())())())", "((())(((())())()))()", "((())(((())()))(()))", "((())(((())()))()())", "((())(((())()))())()", "((())(((())())))(())", "((())(((())())))()()", "((())(((()))((()))))", "((())(((()))(()())))", "((())(((()))(())()))", "((())(((()))(()))())", "((())(((()))(())))()", "((())(((()))()(())))", "((())(((()))()()()))", "((())(((()))()())())", "((())(((()))()()))()", "((())(((()))())(()))", "((())(((()))())()())", "((())(((()))())())()", "((())(((()))()))(())", "((())(((()))()))()()", "((())(((())))((())))", "((())(((())))(()()))", "((())(((())))(())())", "((())(((())))(()))()", "((())(((())))()(()))", "((())(((())))()()())", "((())(((())))()())()", "((())(((())))())(())", "((())(((())))())()()", "((())(((()))))((()))", "((())(((()))))(()())", "((())(((()))))(())()", "((())(((()))))()(())", "((())(((()))))()()()", "((())((()(((()))))))", "((())((()((()())))))", "((())((()((())()))))", "((())((()((()))())))", "((())((()((())))()))", "((())((()((()))))())", "((())((()((())))))()", "((())((()(()(())))))", "((())((()(()()()))))", "((())((()(()())())))", "((())((()(()()))()))", "((())((()(()())))())", "((())((()(()()))))()", "((())((()(())(()))))", "((())((()(())()())))", "((())((()(())())()))", "((())((()(())()))())", "((())((()(())())))()", "((())((()(()))(())))", "((())((()(()))()()))", "((())((()(()))())())", "((())((()(()))()))()", "((())((()(())))(()))", "((())((()(())))()())", "((())((()(())))())()", "((())((()(()))))(())", "((())((()(()))))()()", "((())((()()((())))))", "((())((()()(()()))))", "((())((()()(())())))", "((())((()()(()))()))", "((())((()()(())))())", "((())((()()(()))))()", "((())((()()()(()))))", "((())((()()()()())))", "((())((()()()())()))", "((())((()()()()))())", "((())((()()()())))()", "((())((()()())(())))", "((())((()()())()()))", "((())((()()())())())", "((())((()()())()))()", "((())((()()()))(()))", "((())((()()()))()())", "((())((()()()))())()", "((())((()()())))(())", "((())((()()())))()()", "((())((()())((()))))", "((())((()())(()())))", "((())((()())(())()))", "((())((()())(()))())", "((())((()())(())))()", "((())((()())()(())))", "((())((()())()()()))", "((())((()())()())())", "((())((()())()()))()", "((())((()())())(()))", "((())((()())())()())", "((())((()())())())()", "((())((()())()))(())", "((())((()())()))()()", "((())((()()))((())))", "((())((()()))(()()))", "((())((()()))(())())", "((())((()()))(()))()", "((())((()()))()(()))", "((())((()()))()()())", "((())((()()))()())()", "((())((()()))())(())", "((())((()()))())()()", "((())((()())))((()))", "((())((()())))(()())", "((())((()())))(())()", "((())((()())))()(())", "((())((()())))()()()", "((())((())(((())))))", "((())((())((()()))))", "((())((())((())())))", "((())((())((()))()))", "((())((())((())))())", "((())((())((()))))()", "((())((())(()(()))))", "((())((())(()()())))", "((())((())(()())()))", "((())((())(()()))())", "((())((())(()())))()", "((())((())(())(())))", "((())((())(())()()))", "((())((())(())())())", "((())((())(())()))()", "((())((())(()))(()))", "((())((())(()))()())", "((())((())(()))())()", "((())((())(())))(())", "((())((())(())))()()", "((())((())()((()))))", "((())((())()(()())))", "((())((())()(())()))", "((())((())()(()))())", "((())((())()(())))()", "((())((())()()(())))", "((())((())()()()()))", "((())((())()()())())", "((())((())()()()))()", "((())((())()())(()))", "((())((())()())()())", "((())((())()())())()", "((())((())()()))(())", "((())((())()()))()()", "((())((())())((())))", "((())((())())(()()))", "((())((())())(())())", "((())((())())(()))()", "((())((())())()(()))", "((())((())())()()())", "((())((())())()())()", "((())((())())())(())", "((())((())())())()()", "((())((())()))((()))", "((())((())()))(()())", "((())((())()))(())()", "((())((())()))()(())", "((())((())()))()()()", "((())((()))(((()))))", "((())((()))((()())))", "((())((()))((())()))", "((())((()))((()))())", "((())((()))((())))()", "((())((()))(()(())))", "((())((()))(()()()))", "((())((()))(()())())", "((())((()))(()()))()", "((())((()))(())(()))", "((())((()))(())()())", "((())((()))(())())()", "((())((()))(()))(())", "((())((()))(()))()()", "((())((()))()((())))", "((())((()))()(()()))", "((())((()))()(())())", "((())((()))()(()))()", "((())((()))()()(()))", "((())((()))()()()())", "((())((()))()()())()", "((())((()))()())(())", "((())((()))()())()()", "((())((()))())((()))", "((())((()))())(()())", "((())((()))())(())()", "((())((()))())()(())", "((())((()))())()()()", "((())((())))(((())))", "((())((())))((()()))", "((())((())))((())())", "((())((())))((()))()", "((())((())))(()(()))", "((())((())))(()()())", "((())((())))(()())()", "((())((())))(())(())", "((())((())))(())()()", "((())((())))()((()))", "((())((())))()(()())", "((())((())))()(())()", "((())((())))()()(())", "((())((())))()()()()", "((())(()((((()))))))", "((())(()(((()())))))", "((())(()(((())()))))", "((())(()(((()))())))", "((())(()(((())))()))", "((())(()(((()))))())", "((())(()(((())))))()", "((())(()((()(())))))", "((())(()((()()()))))", "((())(()((()())())))", "((())(()((()()))()))", "((())(()((()())))())", "((())(()((()()))))()", "((())(()((())(()))))", "((())(()((())()())))", "((())(()((())())()))", "((())(()((())()))())", "((())(()((())())))()", "((())(()((()))(())))", "((())(()((()))()()))", "((())(()((()))())())", "((())(()((()))()))()", "((())(()((())))(()))", "((())(()((())))()())", "((())(()((())))())()", "((())(()((()))))(())", "((())(()((()))))()()", "((())(()(()((())))))", "((())(()(()(()()))))", "((())(()(()(())())))", "((())(()(()(()))()))", "((())(()(()(())))())", "((())(()(()(()))))()", "((())(()(()()(()))))", "((())(()(()()()())))", "((())(()(()()())()))", "((())(()(()()()))())", "((())(()(()()())))()", "((())(()(()())(())))", "((())(()(()())()()))", "((())(()(()())())())", "((())(()(()())()))()", "((())(()(()()))(()))", "((())(()(()()))()())", "((())(()(()()))())()", "((())(()(()())))(())", "((())(()(()())))()()", "((())(()(())((()))))", "((())(()(())(()())))", "((())(()(())(())()))", "((())(()(())(()))())", "((())(()(())(())))()", "((())(()(())()(())))", "((())(()(())()()()))", "((())(()(())()())())", "((())(()(())()()))()", "((())(()(())())(()))", "((())(()(())())()())", "((())(()(())())())()", "((())(()(())()))(())", "((())(()(())()))()()", "((())(()(()))((())))", "((())(()(()))(()()))", "((())(()(()))(())())", "((())(()(()))(()))()", "((())(()(()))()(()))", "((())(()(()))()()())", "((())(()(()))()())()", "((())(()(()))())(())", "((())(()(()))())()()", "((())(()(())))((()))", "((())(()(())))(()())", "((())(()(())))(())()", "((())(()(())))()(())", "((())(()(())))()()()", "((())(()()(((())))))", "((())(()()((()()))))", "((())(()()((())())))", "((())(()()((()))()))", "((())(()()((())))())", "((())(()()((()))))()", "((())(()()(()(()))))", "((())(()()(()()())))", "((())(()()(()())()))", "((())(()()(()()))())", "((())(()()(()())))()", "((())(()()(())(())))", "((())(()()(())()()))", "((())(()()(())())())", "((())(()()(())()))()", "((())(()()(()))(()))", "((())(()()(()))()())", "((())(()()(()))())()", "((())(()()(())))(())", "((())(()()(())))()()", "((())(()()()((()))))", "((())(()()()(()())))", "((())(()()()(())()))", "((())(()()()(()))())", "((())(()()()(())))()", "((())(()()()()(())))", "((())(()()()()()()))", "((())(()()()()())())", "((())(()()()()()))()", "((())(()()()())(()))", "((())(()()()())()())", "((())(()()()())())()", "((())(()()()()))(())", "((())(()()()()))()()", "((())(()()())((())))", "((())(()()())(()()))", "((())(()()())(())())", "((())(()()())(()))()", "((())(()()())()(()))", "((())(()()())()()())", "((())(()()())()())()", "((())(()()())())(())", "((())(()()())())()()", "((())(()()()))((()))", "((())(()()()))(()())", "((())(()()()))(())()", "((())(()()()))()(())", "((())(()()()))()()()", "((())(()())(((()))))", "((())(()())((()())))", "((())(()())((())()))", "((())(()())((()))())", "((())(()())((())))()", "((())(()())(()(())))", "((())(()())(()()()))", "((())(()())(()())())", "((())(()())(()()))()", "((())(()())(())(()))", "((())(()())(())()())", "((())(()())(())())()", "((())(()())(()))(())", "((())(()())(()))()()", "((())(()())()((())))", "((())(()())()(()()))", "((())(()())()(())())", "((())(()())()(()))()", "((())(()())()()(()))", "((())(()())()()()())", "((())(()())()()())()", "((())(()())()())(())", "((())(()())()())()()", "((())(()())())((()))", "((())(()())())(()())", "((())(()())())(())()", "((())(()())())()(())", "((())(()())())()()()", "((())(()()))(((())))", "((())(()()))((()()))", "((())(()()))((())())", "((())(()()))((()))()", "((())(()()))(()(()))", "((())(()()))(()()())", "((())(()()))(()())()", "((())(()()))(())(())", "((())(()()))(())()()", "((())(()()))()((()))", "((())(()()))()(()())", "((())(()()))()(())()", "((())(()()))()()(())", "((())(()()))()()()()", "((())(())((((())))))", "((())(())(((()()))))", "((())(())(((())())))", "((())(())(((()))()))", "((())(())(((())))())", "((())(())(((()))))()", "((())(())((()(()))))", "((())(())((()()())))", "((())(())((()())()))", "((())(())((()()))())", "((())(())((()())))()", "((())(())((())(())))", "((())(())((())()()))", "((())(())((())())())", "((())(())((())()))()", "((())(())((()))(()))", "((())(())((()))()())", "((())(())((()))())()", "((())(())((())))(())", "((())(())((())))()()", "((())(())(()((()))))", "((())(())(()(()())))", "((())(())(()(())()))", "((())(())(()(()))())", "((())(())(()(())))()", "((())(())(()()(())))", "((())(())(()()()()))", "((())(())(()()())())", "((())(())(()()()))()", "((())(())(()())(()))", "((())(())(()())()())", "((())(())(()())())()", "((())(())(()()))(())", "((())(())(()()))()()", "((())(())(())((())))", "((())(())(())(()()))", "((())(())(())(())())", "((())(())(())(()))()", "((())(())(())()(()))", "((())(())(())()()())", "((())(())(())()())()", "((())(())(())())(())", "((())(())(())())()()", "((())(())(()))((()))", "((())(())(()))(()())", "((())(())(()))(())()", "((())(())(()))()(())", "((())(())(()))()()()", "((())(())()(((()))))", "((())(())()((()())))", "((())(())()((())()))", "((())(())()((()))())", "((())(())()((())))()", "((())(())()(()(())))", "((())(())()(()()()))", "((())(())()(()())())", "((())(())()(()()))()", "((())(())()(())(()))", "((())(())()(())()())", "((())(())()(())())()", "((())(())()(()))(())", "((())(())()(()))()()", "((())(())()()((())))", "((())(())()()(()()))", "((())(())()()(())())", "((())(())()()(()))()", "((())(())()()()(()))", "((())(())()()()()())", "((())(())()()()())()", "((())(())()()())(())", "((())(())()()())()()", "((())(())()())((()))", "((())(())()())(()())", "((())(())()())(())()", "((())(())()())()(())", "((())(())()())()()()", "((())(())())(((())))", "((())(())())((()()))", "((())(())())((())())", "((())(())())((()))()", "((())(())())(()(()))", "((())(())())(()()())", "((())(())())(()())()", "((())(())())(())(())", "((())(())())(())()()", "((())(())())()((()))", "((())(())())()(()())", "((())(())())()(())()", "((())(())())()()(())", "((())(())())()()()()", "((())(()))((((()))))", "((())(()))(((()())))", "((())(()))(((())()))", "((())(()))(((()))())", "((())(()))(((())))()", "((())(()))((()(())))", "((())(()))((()()()))", "((())(()))((()())())", "((())(()))((()()))()", "((())(()))((())(()))", "((())(()))((())()())", "((())(()))((())())()", "((())(()))((()))(())", "((())(()))((()))()()", "((())(()))(()((())))", "((())(()))(()(()()))", "((())(()))(()(())())", "((())(()))(()(()))()", "((())(()))(()()(()))", "((())(()))(()()()())", "((())(()))(()()())()", "((())(()))(()())(())", "((())(()))(()())()()", "((())(()))(())((()))", "((())(()))(())(()())", "((())(()))(())(())()", "((())(()))(())()(())", "((())(()))(())()()()", "((())(()))()(((())))", "((())(()))()((()()))", "((())(()))()((())())", "((())(()))()((()))()", "((())(()))()(()(()))", "((())(()))()(()()())", "((())(()))()(()())()", "((())(()))()(())(())", "((())(()))()(())()()", "((())(()))()()((()))", "((())(()))()()(()())", "((())(()))()()(())()", "((())(()))()()()(())", "((())(()))()()()()()", "((())()(((((()))))))", "((())()((((()())))))", "((())()((((())()))))", "((())()((((()))())))", "((())()((((())))()))", "((())()((((()))))())", "((())()((((())))))()", "((())()(((()(())))))", "((())()(((()()()))))", "((())()(((()())())))", "((())()(((()()))()))", "((())()(((()())))())", "((())()(((()()))))()", "((())()(((())(()))))", "((())()(((())()())))", "((())()(((())())()))", "((())()(((())()))())", "((())()(((())())))()", "((())()(((()))(())))", "((())()(((()))()()))", "((())()(((()))())())", "((())()(((()))()))()", "((())()(((())))(()))", "((())()(((())))()())", "((())()(((())))())()", "((())()(((()))))(())", "((())()(((()))))()()", "((())()((()((())))))", "((())()((()(()()))))", "((())()((()(())())))", "((())()((()(()))()))", "((())()((()(())))())", "((())()((()(()))))()", "((())()((()()(()))))", "((())()((()()()())))", "((())()((()()())()))", "((())()((()()()))())", "((())()((()()())))()", "((())()((()())(())))", "((())()((()())()()))", "((())()((()())())())", "((())()((()())()))()", "((())()((()()))(()))", "((())()((()()))()())", "((())()((()()))())()", "((())()((()())))(())", "((())()((()())))()()", "((())()((())((()))))", "((())()((())(()())))", "((())()((())(())()))", "((())()((())(()))())", "((())()((())(())))()", "((())()((())()(())))", "((())()((())()()()))", "((())()((())()())())", "((())()((())()()))()", "((())()((())())(()))", "((())()((())())()())", "((())()((())())())()", "((())()((())()))(())", "((())()((())()))()()", "((())()((()))((())))", "((())()((()))(()()))", "((())()((()))(())())", "((())()((()))(()))()", "((())()((()))()(()))", "((())()((()))()()())", "((())()((()))()())()", "((())()((()))())(())", "((())()((()))())()()", "((())()((())))((()))", "((())()((())))(()())", "((())()((())))(())()", "((())()((())))()(())", "((())()((())))()()()", "((())()(()(((())))))", "((())()(()((()()))))", "((())()(()((())())))", "((())()(()((()))()))", "((())()(()((())))())", "((())()(()((()))))()", "((())()(()(()(()))))", "((())()(()(()()())))", "((())()(()(()())()))", "((())()(()(()()))())", "((())()(()(()())))()", "((())()(()(())(())))", "((())()(()(())()()))", "((())()(()(())())())", "((())()(()(())()))()", "((())()(()(()))(()))", "((())()(()(()))()())", "((())()(()(()))())()", "((())()(()(())))(())", "((())()(()(())))()()", "((())()(()()((()))))", "((())()(()()(()())))", "((())()(()()(())()))", "((())()(()()(()))())", "((())()(()()(())))()", "((())()(()()()(())))", "((())()(()()()()()))", "((())()(()()()())())", "((())()(()()()()))()", "((())()(()()())(()))", "((())()(()()())()())", "((())()(()()())())()", "((())()(()()()))(())", "((())()(()()()))()()", "((())()(()())((())))", "((())()(()())(()()))", "((())()(()())(())())", "((())()(()())(()))()", "((())()(()())()(()))", "((())()(()())()()())", "((())()(()())()())()", "((())()(()())())(())", "((())()(()())())()()", "((())()(()()))((()))", "((())()(()()))(()())", "((())()(()()))(())()", "((())()(()()))()(())", "((())()(()()))()()()", "((())()(())(((()))))", "((())()(())((()())))", "((())()(())((())()))", "((())()(())((()))())", "((())()(())((())))()", "((())()(())(()(())))", "((())()(())(()()()))", "((())()(())(()())())", "((())()(())(()()))()", "((())()(())(())(()))", "((())()(())(())()())", "((())()(())(())())()", "((())()(())(()))(())", "((())()(())(()))()()", "((())()(())()((())))", "((())()(())()(()()))", "((())()(())()(())())", "((())()(())()(()))()", "((())()(())()()(()))", "((())()(())()()()())", "((())()(())()()())()", "((())()(())()())(())", "((())()(())()())()()", "((())()(())())((()))", "((())()(())())(()())", "((())()(())())(())()", "((())()(())())()(())", "((())()(())())()()()", "((())()(()))(((())))", "((())()(()))((()()))", "((())()(()))((())())", "((())()(()))((()))()", "((())()(()))(()(()))", "((())()(()))(()()())", "((())()(()))(()())()", "((())()(()))(())(())", "((())()(()))(())()()", "((())()(()))()((()))", "((())()(()))()(()())", "((())()(()))()(())()", "((())()(()))()()(())", "((())()(()))()()()()", "((())()()((((())))))", "((())()()(((()()))))", "((())()()(((())())))", "((())()()(((()))()))", "((())()()(((())))())", "((())()()(((()))))()", "((())()()((()(()))))", "((())()()((()()())))", "((())()()((()())()))", "((())()()((()()))())", "((())()()((()())))()", "((())()()((())(())))", "((())()()((())()()))", "((())()()((())())())", "((())()()((())()))()", "((())()()((()))(()))", "((())()()((()))()())", "((())()()((()))())()", "((())()()((())))(())", "((())()()((())))()()", "((())()()(()((()))))", "((())()()(()(()())))", "((())()()(()(())()))", "((())()()(()(()))())", "((())()()(()(())))()", "((())()()(()()(())))", "((())()()(()()()()))", "((())()()(()()())())", "((())()()(()()()))()", "((())()()(()())(()))", "((())()()(()())()())", "((())()()(()())())()", "((())()()(()()))(())", "((())()()(()()))()()", "((())()()(())((())))", "((())()()(())(()()))", "((())()()(())(())())", "((())()()(())(()))()", "((())()()(())()(()))", "((())()()(())()()())", "((())()()(())()())()", "((())()()(())())(())", "((())()()(())())()()", "((())()()(()))((()))", "((())()()(()))(()())", "((())()()(()))(())()", "((())()()(()))()(())", "((())()()(()))()()()", "((())()()()(((()))))", "((())()()()((()())))", "((())()()()((())()))", "((())()()()((()))())", "((())()()()((())))()", "((())()()()(()(())))", "((())()()()(()()()))", "((())()()()(()())())", "((())()()()(()()))()", "((())()()()(())(()))", "((())()()()(())()())", "((())()()()(())())()", "((())()()()(()))(())", "((())()()()(()))()()", "((())()()()()((())))", "((())()()()()(()()))", "((())()()()()(())())", "((())()()()()(()))()", "((())()()()()()(()))", "((())()()()()()()())", "((())()()()()()())()", "((())()()()()())(())", "((())()()()()())()()", "((())()()()())((()))", "((())()()()())(()())", "((())()()()())(())()", "((())()()()())()(())", "((())()()()())()()()", "((())()()())(((())))", "((())()()())((()()))", "((())()()())((())())", "((())()()())((()))()", "((())()()())(()(()))", "((())()()())(()()())", "((())()()())(()())()", "((())()()())(())(())", "((())()()())(())()()", "((())()()())()((()))", "((())()()())()(()())", "((())()()())()(())()", "((())()()())()()(())", "((())()()())()()()()", "((())()())((((()))))", "((())()())(((()())))", "((())()())(((())()))", "((())()())(((()))())", "((())()())(((())))()", "((())()())((()(())))", "((())()())((()()()))", "((())()())((()())())", "((())()())((()()))()", "((())()())((())(()))", "((())()())((())()())", "((())()())((())())()", "((())()())((()))(())", "((())()())((()))()()", "((())()())(()((())))", "((())()())(()(()()))", "((())()())(()(())())", "((())()())(()(()))()", "((())()())(()()(()))", "((())()())(()()()())", "((())()())(()()())()", "((())()())(()())(())", "((())()())(()())()()", "((())()())(())((()))", "((())()())(())(()())", "((())()())(())(())()", "((())()())(())()(())", "((())()())(())()()()", "((())()())()(((())))", "((())()())()((()()))", "((())()())()((())())", "((())()())()((()))()", "((())()())()(()(()))", "((())()())()(()()())", "((())()())()(()())()", "((())()())()(())(())", "((())()())()(())()()", "((())()())()()((()))", "((())()())()()(()())", "((())()())()()(())()", "((())()())()()()(())", "((())()())()()()()()", "((())())(((((())))))", "((())())((((()()))))", "((())())((((())())))", "((())())((((()))()))", "((())())((((())))())", "((())())((((()))))()", "((())())(((()(()))))", "((())())(((()()())))", "((())())(((()())()))", "((())())(((()()))())", "((())())(((()())))()", "((())())(((())(())))", "((())())(((())()()))", "((())())(((())())())", "((())())(((())()))()", "((())())(((()))(()))", "((())())(((()))()())", "((())())(((()))())()", "((())())(((())))(())", "((())())(((())))()()", "((())())((()((()))))", "((())())((()(()())))", "((())())((()(())()))", "((())())((()(()))())", "((())())((()(())))()", "((())())((()()(())))", "((())())((()()()()))", "((())())((()()())())", "((())())((()()()))()", "((())())((()())(()))", "((())())((()())()())", "((())())((()())())()", "((())())((()()))(())", "((())())((()()))()()", "((())())((())((())))", "((())())((())(()()))", "((())())((())(())())", "((())())((())(()))()", "((())())((())()(()))", "((())())((())()()())", "((())())((())()())()", "((())())((())())(())", "((())())((())())()()", "((())())((()))((()))", "((())())((()))(()())", "((())())((()))(())()", "((())())((()))()(())", "((())())((()))()()()", "((())())(()(((()))))", "((())())(()((()())))", "((())())(()((())()))", "((())())(()((()))())", "((())())(()((())))()", "((())())(()(()(())))", "((())())(()(()()()))", "((())())(()(()())())", "((())())(()(()()))()", "((())())(()(())(()))", "((())())(()(())()())", "((())())(()(())())()", "((())())(()(()))(())", "((())())(()(()))()()", "((())())(()()((())))", "((())())(()()(()()))", "((())())(()()(())())", "((())())(()()(()))()", "((())())(()()()(()))", "((())())(()()()()())", "((())())(()()()())()", "((())())(()()())(())", "((())())(()()())()()", "((())())(()())((()))", "((())())(()())(()())", "((())())(()())(())()", "((())())(()())()(())", "((())())(()())()()()", "((())())(())(((())))", "((())())(())((()()))", "((())())(())((())())", "((())())(())((()))()", "((())())(())(()(()))", "((())())(())(()()())", "((())())(())(()())()", "((())())(())(())(())", "((())())(())(())()()", "((())())(())()((()))", "((())())(())()(()())", "((())())(())()(())()", "((())())(())()()(())", "((())())(())()()()()", "((())())()((((()))))", "((())())()(((()())))", "((())())()(((())()))", "((())())()(((()))())", "((())())()(((())))()", "((())())()((()(())))", "((())())()((()()()))", "((())())()((()())())", "((())())()((()()))()", "((())())()((())(()))", "((())())()((())()())", "((())())()((())())()", "((())())()((()))(())", "((())())()((()))()()", "((())())()(()((())))", "((())())()(()(()()))", "((())())()(()(())())", "((())())()(()(()))()", "((())())()(()()(()))", "((())())()(()()()())", "((())())()(()()())()", "((())())()(()())(())", "((())())()(()())()()", "((())())()(())((()))", "((())())()(())(()())", "((())())()(())(())()", "((())())()(())()(())", "((())())()(())()()()", "((())())()()(((())))", "((())())()()((()()))", "((())())()()((())())", "((())())()()((()))()", "((())())()()(()(()))", "((())())()()(()()())", "((())())()()(()())()", "((())())()()(())(())", "((())())()()(())()()", "((())())()()()((()))", "((())())()()()(()())", "((())())()()()(())()", "((())())()()()()(())", "((())())()()()()()()", "((()))((((((()))))))", "((()))(((((()())))))", "((()))(((((())()))))", "((()))(((((()))())))", "((()))(((((())))()))", "((()))(((((()))))())", "((()))(((((())))))()", "((()))((((()(())))))", "((()))((((()()()))))", "((()))((((()())())))", "((()))((((()()))()))", "((()))((((()())))())", "((()))((((()()))))()", "((()))((((())(()))))", "((()))((((())()())))", "((()))((((())())()))", "((()))((((())()))())", "((()))((((())())))()", "((()))((((()))(())))", "((()))((((()))()()))", "((()))((((()))())())", "((()))((((()))()))()", "((()))((((())))(()))", "((()))((((())))()())", "((()))((((())))())()", "((()))((((()))))(())", "((()))((((()))))()()", "((()))(((()((())))))", "((()))(((()(()()))))", "((()))(((()(())())))", "((()))(((()(()))()))", "((()))(((()(())))())", "((()))(((()(()))))()", "((()))(((()()(()))))", "((()))(((()()()())))", "((()))(((()()())()))", "((()))(((()()()))())", "((()))(((()()())))()", "((()))(((()())(())))", "((()))(((()())()()))", "((()))(((()())())())", "((()))(((()())()))()", "((()))(((()()))(()))", "((()))(((()()))()())", "((()))(((()()))())()", "((()))(((()())))(())", "((()))(((()())))()()", "((()))(((())((()))))", "((()))(((())(()())))", "((()))(((())(())()))", "((()))(((())(()))())", "((()))(((())(())))()", "((()))(((())()(())))", "((()))(((())()()()))", "((()))(((())()())())", "((()))(((())()()))()", "((()))(((())())(()))", "((()))(((())())()())", "((()))(((())())())()", "((()))(((())()))(())", "((()))(((())()))()()", "((()))(((()))((())))", "((()))(((()))(()()))", "((()))(((()))(())())", "((()))(((()))(()))()", "((()))(((()))()(()))", "((()))(((()))()()())", "((()))(((()))()())()", "((()))(((()))())(())", "((()))(((()))())()()", "((()))(((())))((()))", "((()))(((())))(()())", "((()))(((())))(())()", "((()))(((())))()(())", "((()))(((())))()()()", "((()))((()(((())))))", "((()))((()((()()))))", "((()))((()((())())))", "((()))((()((()))()))", "((()))((()((())))())", "((()))((()((()))))()", "((()))((()(()(()))))", "((()))((()(()()())))", "((()))((()(()())()))", "((()))((()(()()))())", "((()))((()(()())))()", "((()))((()(())(())))", "((()))((()(())()()))", "((()))((()(())())())", "((()))((()(())()))()", "((()))((()(()))(()))", "((()))((()(()))()())", "((()))((()(()))())()", "((()))((()(())))(())", "((()))((()(())))()()", "((()))((()()((()))))", "((()))((()()(()())))", "((()))((()()(())()))", "((()))((()()(()))())", "((()))((()()(())))()", "((()))((()()()(())))", "((()))((()()()()()))", "((()))((()()()())())", "((()))((()()()()))()", "((()))((()()())(()))", "((()))((()()())()())", "((()))((()()())())()", "((()))((()()()))(())", "((()))((()()()))()()", "((()))((()())((())))", "((()))((()())(()()))", "((()))((()())(())())", "((()))((()())(()))()", "((()))((()())()(()))", "((()))((()())()()())", "((()))((()())()())()", "((()))((()())())(())", "((()))((()())())()()", "((()))((()()))((()))", "((()))((()()))(()())", "((()))((()()))(())()", "((()))((()()))()(())", "((()))((()()))()()()", "((()))((())(((()))))", "((()))((())((()())))", "((()))((())((())()))", "((()))((())((()))())", "((()))((())((())))()", "((()))((())(()(())))", "((()))((())(()()()))", "((()))((())(()())())", "((()))((())(()()))()", "((()))((())(())(()))", "((()))((())(())()())", "((()))((())(())())()", "((()))((())(()))(())", "((()))((())(()))()()", "((()))((())()((())))", "((()))((())()(()()))", "((()))((())()(())())", "((()))((())()(()))()", "((()))((())()()(()))", "((()))((())()()()())", "((()))((())()()())()", "((()))((())()())(())", "((()))((())()())()()", "((()))((())())((()))", "((()))((())())(()())", "((()))((())())(())()", "((()))((())())()(())", "((()))((())())()()()", "((()))((()))(((())))", "((()))((()))((()()))", "((()))((()))((())())", "((()))((()))((()))()", "((()))((()))(()(()))", "((()))((()))(()()())", "((()))((()))(()())()", "((()))((()))(())(())", "((()))((()))(())()()", "((()))((()))()((()))", "((()))((()))()(()())", "((()))((()))()(())()", "((()))((()))()()(())", "((()))((()))()()()()", "((()))(()((((())))))", "((()))(()(((()()))))", "((()))(()(((())())))", "((()))(()(((()))()))", "((()))(()(((())))())", "((()))(()(((()))))()", "((()))(()((()(()))))", "((()))(()((()()())))", "((()))(()((()())()))", "((()))(()((()()))())", "((()))(()((()())))()", "((()))(()((())(())))", "((()))(()((())()()))", "((()))(()((())())())", "((()))(()((())()))()", "((()))(()((()))(()))", "((()))(()((()))()())", "((()))(()((()))())()", "((()))(()((())))(())", "((()))(()((())))()()", "((()))(()(()((()))))", "((()))(()(()(()())))", "((()))(()(()(())()))", "((()))(()(()(()))())", "((()))(()(()(())))()", "((()))(()(()()(())))", "((()))(()(()()()()))", "((()))(()(()()())())", "((()))(()(()()()))()", "((()))(()(()())(()))", "((()))(()(()())()())", "((()))(()(()())())()", "((()))(()(()()))(())", "((()))(()(()()))()()", "((()))(()(())((())))", "((()))(()(())(()()))", "((()))(()(())(())())", "((()))(()(())(()))()", "((()))(()(())()(()))", "((()))(()(())()()())", "((()))(()(())()())()", "((()))(()(())())(())", "((()))(()(())())()()", "((()))(()(()))((()))", "((()))(()(()))(()())", "((()))(()(()))(())()", "((()))(()(()))()(())", "((()))(()(()))()()()", "((()))(()()(((()))))", "((()))(()()((()())))", "((()))(()()((())()))", "((()))(()()((()))())", "((()))(()()((())))()", "((()))(()()(()(())))", "((()))(()()(()()()))", "((()))(()()(()())())", "((()))(()()(()()))()", "((()))(()()(())(()))", "((()))(()()(())()())", "((()))(()()(())())()", "((()))(()()(()))(())", "((()))(()()(()))()()", "((()))(()()()((())))", "((()))(()()()(()()))", "((()))(()()()(())())", "((()))(()()()(()))()", "((()))(()()()()(()))", "((()))(()()()()()())", "((()))(()()()()())()", "((()))(()()()())(())", "((()))(()()()())()()", "((()))(()()())((()))", "((()))(()()())(()())", "((()))(()()())(())()", "((()))(()()())()(())", "((()))(()()())()()()", "((()))(()())(((())))", "((()))(()())((()()))", "((()))(()())((())())", "((()))(()())((()))()", "((()))(()())(()(()))", "((()))(()())(()()())", "((()))(()())(()())()", "((()))(()())(())(())", "((()))(()())(())()()", "((()))(()())()((()))", "((()))(()())()(()())", "((()))(()())()(())()", "((()))(()())()()(())", "((()))(()())()()()()", "((()))(())((((()))))", "((()))(())(((()())))", "((()))(())(((())()))", "((()))(())(((()))())", "((()))(())(((())))()", "((()))(())((()(())))", "((()))(())((()()()))", "((()))(())((()())())", "((()))(())((()()))()", "((()))(())((())(()))", "((()))(())((())()())", "((()))(())((())())()", "((()))(())((()))(())", "((()))(())((()))()()", "((()))(())(()((())))", "((()))(())(()(()()))", "((()))(())(()(())())", "((()))(())(()(()))()", "((()))(())(()()(()))", "((()))(())(()()()())", "((()))(())(()()())()", "((()))(())(()())(())", "((()))(())(()())()()", "((()))(())(())((()))", "((()))(())(())(()())", "((()))(())(())(())()", "((()))(())(())()(())", "((()))(())(())()()()", "((()))(())()(((())))", "((()))(())()((()()))", "((()))(())()((())())", "((()))(())()((()))()", "((()))(())()(()(()))", "((()))(())()(()()())", "((()))(())()(()())()", "((()))(())()(())(())", "((()))(())()(())()()", "((()))(())()()((()))", "((()))(())()()(()())", "((()))(())()()(())()", "((()))(())()()()(())", "((()))(())()()()()()", "((()))()(((((())))))", "((()))()((((()()))))", "((()))()((((())())))", "((()))()((((()))()))", "((()))()((((())))())", "((()))()((((()))))()", "((()))()(((()(()))))", "((()))()(((()()())))", "((()))()(((()())()))", "((()))()(((()()))())", "((()))()(((()())))()", "((()))()(((())(())))", "((()))()(((())()()))", "((()))()(((())())())", "((()))()(((())()))()", "((()))()(((()))(()))", "((()))()(((()))()())", "((()))()(((()))())()", "((()))()(((())))(())", "((()))()(((())))()()", "((()))()((()((()))))", "((()))()((()(()())))", "((()))()((()(())()))", "((()))()((()(()))())", "((()))()((()(())))()", "((()))()((()()(())))", "((()))()((()()()()))", "((()))()((()()())())", "((()))()((()()()))()", "((()))()((()())(()))", "((()))()((()())()())", "((()))()((()())())()", "((()))()((()()))(())", "((()))()((()()))()()", "((()))()((())((())))", "((()))()((())(()()))", "((()))()((())(())())", "((()))()((())(()))()", "((()))()((())()(()))", "((()))()((())()()())", "((()))()((())()())()", "((()))()((())())(())", "((()))()((())())()()", "((()))()((()))((()))", "((()))()((()))(()())", "((()))()((()))(())()", "((()))()((()))()(())", "((()))()((()))()()()", "((()))()(()(((()))))", "((()))()(()((()())))", "((()))()(()((())()))", "((()))()(()((()))())", "((()))()(()((())))()", "((()))()(()(()(())))", "((()))()(()(()()()))", "((()))()(()(()())())", "((()))()(()(()()))()", "((()))()(()(())(()))", "((()))()(()(())()())", "((()))()(()(())())()", "((()))()(()(()))(())", "((()))()(()(()))()()", "((()))()(()()((())))", "((()))()(()()(()()))", "((()))()(()()(())())", "((()))()(()()(()))()", "((()))()(()()()(()))", "((()))()(()()()()())", "((()))()(()()()())()", "((()))()(()()())(())", "((()))()(()()())()()", "((()))()(()())((()))", "((()))()(()())(()())", "((()))()(()())(())()", "((()))()(()())()(())", "((()))()(()())()()()", "((()))()(())(((())))", "((()))()(())((()()))", "((()))()(())((())())", "((()))()(())((()))()", "((()))()(())(()(()))", "((()))()(())(()()())", "((()))()(())(()())()", "((()))()(())(())(())", "((()))()(())(())()()", "((()))()(())()((()))", "((()))()(())()(()())", "((()))()(())()(())()", "((()))()(())()()(())", "((()))()(())()()()()", "((()))()()((((()))))", "((()))()()(((()())))", "((()))()()(((())()))", "((()))()()(((()))())", "((()))()()(((())))()", "((()))()()((()(())))", "((()))()()((()()()))", "((()))()()((()())())", "((()))()()((()()))()", "((()))()()((())(()))", "((()))()()((())()())", "((()))()()((())())()", "((()))()()((()))(())", "((()))()()((()))()()", "((()))()()(()((())))", "((()))()()(()(()()))", "((()))()()(()(())())", "((()))()()(()(()))()", "((()))()()(()()(()))", "((()))()()(()()()())", "((()))()()(()()())()", "((()))()()(()())(())", "((()))()()(()())()()", "((()))()()(())((()))", "((()))()()(())(()())", "((()))()()(())(())()", "((()))()()(())()(())", "((()))()()(())()()()", "((()))()()()(((())))", "((()))()()()((()()))", "((()))()()()((())())", "((()))()()()((()))()", "((()))()()()(()(()))", "((()))()()()(()()())", "((()))()()()(()())()", "((()))()()()(())(())", "((()))()()()(())()()", "((()))()()()()((()))", "((()))()()()()(()())", "((()))()()()()(())()", "((()))()()()()()(())", "((()))()()()()()()()", "(()(((((((()))))))))", "(()((((((()())))))))", "(()((((((())()))))))", "(()((((((()))())))))", "(()((((((())))()))))", "(()((((((()))))())))", "(()((((((())))))()))", "(()((((((()))))))())", "(()((((((())))))))()", "(()(((((()(())))))))", "(()(((((()()()))))))", "(()(((((()())())))))", "(()(((((()()))()))))", "(()(((((()())))())))", "(()(((((()()))))()))", "(()(((((()())))))())", "(()(((((()()))))))()", "(()(((((())(()))))))", "(()(((((())()())))))", "(()(((((())())()))))", "(()(((((())()))())))", "(()(((((())())))()))", "(()(((((())()))))())", "(()(((((())())))))()", "(()(((((()))(())))))", "(()(((((()))()()))))", "(()(((((()))())())))", "(()(((((()))()))()))", "(()(((((()))())))())", "(()(((((()))()))))()", "(()(((((())))(()))))", "(()(((((())))()())))", "(()(((((())))())()))", "(()(((((())))()))())", "(()(((((())))())))()", "(()(((((()))))(())))", "(()(((((()))))()()))", "(()(((((()))))())())", "(()(((((()))))()))()", "(()(((((())))))(()))", "(()(((((())))))()())", "(()(((((())))))())()", "(()(((((()))))))(())", "(()(((((()))))))()()", "(()((((()((())))))))", "(()((((()(()()))))))", "(()((((()(())())))))", "(()((((()(()))()))))", "(()((((()(())))())))", "(()((((()(()))))()))", "(()((((()(())))))())", "(()((((()(()))))))()", "(()((((()()(()))))))", "(()((((()()()())))))", "(()((((()()())()))))", "(()((((()()()))())))", "(()((((()()())))()))", "(()((((()()()))))())", "(()((((()()())))))()", "(()((((()())(())))))", "(()((((()())()()))))", "(()((((()())())())))", "(()((((()())()))()))", "(()((((()())())))())", "(()((((()())()))))()", "(()((((()()))(()))))", "(()((((()()))()())))", "(()((((()()))())()))", "(()((((()()))()))())", "(()((((()()))())))()", "(()((((()())))(())))", "(()((((()())))()()))", "(()((((()())))())())", "(()((((()())))()))()", "(()((((()()))))(()))", "(()((((()()))))()())", "(()((((()()))))())()", "(()((((()())))))(())", "(()((((()())))))()()", "(()((((())((()))))))", "(()((((())(()())))))", "(()((((())(())()))))", "(()((((())(()))())))", "(()((((())(())))()))", "(()((((())(()))))())", "(()((((())(())))))()", "(()((((())()(())))))", "(()((((())()()()))))", "(()((((())()())())))", "(()((((())()()))()))", "(()((((())()())))())", "(()((((())()()))))()", "(()((((())())(()))))", "(()((((())())()())))", "(()((((())())())()))", "(()((((())())()))())", "(()((((())())())))()", "(()((((())()))(())))", "(()((((())()))()()))", "(()((((())()))())())", "(()((((())()))()))()", "(()((((())())))(()))", "(()((((())())))()())", "(()((((())())))())()", "(()((((())()))))(())", "(()((((())()))))()()", "(()((((()))((())))))", "(()((((()))(()()))))", "(()((((()))(())())))", "(()((((()))(()))()))", "(()((((()))(())))())", "(()((((()))(()))))()", "(()((((()))()(()))))", "(()((((()))()()())))", "(()((((()))()())()))", "(()((((()))()()))())", "(()((((()))()())))()", "(()((((()))())(())))", "(()((((()))())()()))", "(()((((()))())())())", "(()((((()))())()))()", "(()((((()))()))(()))", "(()((((()))()))()())", "(()((((()))()))())()", "(()((((()))())))(())", "(()((((()))())))()()", "(()((((())))((()))))", "(()((((())))(()())))", "(()((((())))(())()))", "(()((((())))(()))())", "(()((((())))(())))()", "(()((((())))()(())))", "(()((((())))()()()))", "(()((((())))()())())", "(()((((())))()()))()", "(()((((())))())(()))", "(()((((())))())()())", "(()((((())))())())()", "(()((((())))()))(())", "(()((((())))()))()()", "(()((((()))))((())))", "(()((((()))))(()()))", "(()((((()))))(())())", "(()((((()))))(()))()", "(()((((()))))()(()))", "(()((((()))))()()())", "(()((((()))))()())()", "(()((((()))))())(())", "(()((((()))))())()()", "(()((((())))))((()))", "(()((((())))))(()())", "(()((((())))))(())()", "(()((((())))))()(())", "(()((((())))))()()()", "(()(((()(((())))))))", "(()(((()((()()))))))", "(()(((()((())())))))", "(()(((()((()))()))))", "(()(((()((())))())))", "(()(((()((()))))()))", "(()(((()((())))))())", "(()(((()((()))))))()", "(()(((()(()(()))))))", "(()(((()(()()())))))", "(()(((()(()())()))))", "(()(((()(()()))())))", "(()(((()(()())))()))", "(()(((()(()()))))())", "(()(((()(()())))))()", "(()(((()(())(())))))", "(()(((()(())()()))))", "(()(((()(())())())))", "(()(((()(())()))()))", "(()(((()(())())))())", "(()(((()(())()))))()", "(()(((()(()))(()))))", "(()(((()(()))()())))", "(()(((()(()))())()))", "(()(((()(()))()))())", "(()(((()(()))())))()", "(()(((()(())))(())))", "(()(((()(())))()()))", "(()(((()(())))())())", "(()(((()(())))()))()", "(()(((()(()))))(()))", "(()(((()(()))))()())", "(()(((()(()))))())()", "(()(((()(())))))(())", "(()(((()(())))))()()", "(()(((()()((()))))))", "(()(((()()(()())))))", "(()(((()()(())()))))", "(()(((()()(()))())))", "(()(((()()(())))()))", "(()(((()()(()))))())", "(()(((()()(())))))()", "(()(((()()()(())))))", "(()(((()()()()()))))", "(()(((()()()())())))", "(()(((()()()()))()))", "(()(((()()()())))())", "(()(((()()()()))))()", "(()(((()()())(()))))", "(()(((()()())()())))", "(()(((()()())())()))", "(()(((()()())()))())", "(()(((()()())())))()", "(()(((()()()))(())))", "(()(((()()()))()()))", "(()(((()()()))())())", "(()(((()()()))()))()", "(()(((()()())))(()))", "(()(((()()())))()())", "(()(((()()())))())()", "(()(((()()()))))(())", "(()(((()()()))))()()", "(()(((()())((())))))", "(()(((()())(()()))))", "(()(((()())(())())))", "(()(((()())(()))()))", "(()(((()())(())))())", "(()(((()())(()))))()", "(()(((()())()(()))))", "(()(((()())()()())))", "(()(((()())()())()))", "(()(((()())()()))())", "(()(((()())()())))()", "(()(((()())())(())))", "(()(((()())())()()))", "(()(((()())())())())", "(()(((()())())()))()", "(()(((()())()))(()))", "(()(((()())()))()())", "(()(((()())()))())()", "(()(((()())())))(())", "(()(((()())())))()()", "(()(((()()))((()))))", "(()(((()()))(()())))", "(()(((()()))(())()))", "(()(((()()))(()))())", "(()(((()()))(())))()", "(()(((()()))()(())))", "(()(((()()))()()()))", "(()(((()()))()())())", "(()(((()()))()()))()", "(()(((()()))())(()))", "(()(((()()))())()())", "(()(((()()))())())()", "(()(((()()))()))(())", "(()(((()()))()))()()", "(()(((()())))((())))", "(()(((()())))(()()))", "(()(((()())))(())())", "(()(((()())))(()))()", "(()(((()())))()(()))", "(()(((()())))()()())", "(()(((()())))()())()", "(()(((()())))())(())", "(()(((()())))())()()", "(()(((()()))))((()))", "(()(((()()))))(()())", "(()(((()()))))(())()", "(()(((()()))))()(())", "(()(((()()))))()()()", "(()(((())(((()))))))", "(()(((())((()())))))", "(()(((())((())()))))", "(()(((())((()))())))", "(()(((())((())))()))", "(()(((())((()))))())", "(()(((())((())))))()", "(()(((())(()(())))))", "(()(((())(()()()))))", "(()(((())(()())())))", "(()(((())(()()))()))", "(()(((())(()())))())", "(()(((())(()()))))()", "(()(((())(())(()))))", "(()(((())(())()())))", "(()(((())(())())()))", "(()(((())(())()))())", "(()(((())(())())))()", "(()(((())(()))(())))", "(()(((())(()))()()))", "(()(((())(()))())())", "(()(((())(()))()))()", "(()(((())(())))(()))", "(()(((())(())))()())", "(()(((())(())))())()", "(()(((())(()))))(())", "(()(((())(()))))()()", "(()(((())()((())))))", "(()(((())()(()()))))", "(()(((())()(())())))", "(()(((())()(()))()))", "(()(((())()(())))())", "(()(((())()(()))))()", "(()(((())()()(()))))", "(()(((())()()()())))", "(()(((())()()())()))", "(()(((())()()()))())", "(()(((())()()())))()", "(()(((())()())(())))", "(()(((())()())()()))", "(()(((())()())())())", "(()(((())()())()))()", "(()(((())()()))(()))", "(()(((())()()))()())", "(()(((())()()))())()", "(()(((())()())))(())", "(()(((())()())))()()", "(()(((())())((()))))", "(()(((())())(()())))", "(()(((())())(())()))", "(()(((())())(()))())", "(()(((())())(())))()", "(()(((())())()(())))", "(()(((())())()()()))", "(()(((())())()())())", "(()(((())())()()))()", "(()(((())())())(()))", "(()(((())())())()())", "(()(((())())())())()", "(()(((())())()))(())", "(()(((())())()))()()", "(()(((())()))((())))", "(()(((())()))(()()))", "(()(((())()))(())())", "(()(((())()))(()))()", "(()(((())()))()(()))", "(()(((())()))()()())", "(()(((())()))()())()", "(()(((())()))())(())", "(()(((())()))())()()", "(()(((())())))((()))", "(()(((())())))(()())", "(()(((())())))(())()", "(()(((())())))()(())", "(()(((())())))()()()", "(()(((()))(((())))))", "(()(((()))((()()))))", "(()(((()))((())())))", "(()(((()))((()))()))", "(()(((()))((())))())", "(()(((()))((()))))()", "(()(((()))(()(()))))", "(()(((()))(()()())))", "(()(((()))(()())()))", "(()(((()))(()()))())", "(()(((()))(()())))()", "(()(((()))(())(())))", "(()(((()))(())()()))", "(()(((()))(())())())", "(()(((()))(())()))()", "(()(((()))(()))(()))", "(()(((()))(()))()())", "(()(((()))(()))())()", "(()(((()))(())))(())", "(()(((()))(())))()()", "(()(((()))()((()))))", "(()(((()))()(()())))", "(()(((()))()(())()))", "(()(((()))()(()))())", "(()(((()))()(())))()", "(()(((()))()()(())))", "(()(((()))()()()()))", "(()(((()))()()())())", "(()(((()))()()()))()", "(()(((()))()())(()))", "(()(((()))()())()())", "(()(((()))()())())()", "(()(((()))()()))(())", "(()(((()))()()))()()", "(()(((()))())((())))", "(()(((()))())(()()))", "(()(((()))())(())())", "(()(((()))())(()))()", "(()(((()))())()(()))", "(()(((()))())()()())", "(()(((()))())()())()", "(()(((()))())())(())", "(()(((()))())())()()", "(()(((()))()))((()))", "(()(((()))()))(()())", "(()(((()))()))(())()", "(()(((()))()))()(())", "(()(((()))()))()()()", "(()(((())))(((()))))", "(()(((())))((()())))", "(()(((())))((())()))", "(()(((())))((()))())", "(()(((())))((())))()", "(()(((())))(()(())))", "(()(((())))(()()()))", "(()(((())))(()())())", "(()(((())))(()()))()", "(()(((())))(())(()))", "(()(((())))(())()())", "(()(((())))(())())()", "(()(((())))(()))(())", "(()(((())))(()))()()", "(()(((())))()((())))", "(()(((())))()(()()))", "(()(((())))()(())())", "(()(((())))()(()))()", "(()(((())))()()(()))", "(()(((())))()()()())", "(()(((())))()()())()", "(()(((())))()())(())", "(()(((())))()())()()", "(()(((())))())((()))", "(()(((())))())(()())", "(()(((())))())(())()", "(()(((())))())()(())", "(()(((())))())()()()", "(()(((()))))(((())))", "(()(((()))))((()()))", "(()(((()))))((())())", "(()(((()))))((()))()", "(()(((()))))(()(()))", "(()(((()))))(()()())", "(()(((()))))(()())()", "(()(((()))))(())(())", "(()(((()))))(())()()", "(()(((()))))()((()))", "(()(((()))))()(()())", "(()(((()))))()(())()", "(()(((()))))()()(())", "(()(((()))))()()()()", "(()((()((((())))))))", "(()((()(((()()))))))", "(()((()(((())())))))", "(()((()(((()))()))))", "(()((()(((())))())))", "(()((()(((()))))()))", "(()((()(((())))))())", "(()((()(((()))))))()", "(()((()((()(()))))))", "(()((()((()()())))))", "(()((()((()())()))))", "(()((()((()()))())))", "(()((()((()())))()))", "(()((()((()()))))())", "(()((()((()())))))()", "(()((()((())(())))))", "(()((()((())()()))))", "(()((()((())())())))", "(()((()((())()))()))", "(()((()((())())))())", "(()((()((())()))))()", "(()((()((()))(()))))", "(()((()((()))()())))", "(()((()((()))())()))", "(()((()((()))()))())", "(()((()((()))())))()", "(()((()((())))(())))", "(()((()((())))()()))", "(()((()((())))())())", "(()((()((())))()))()", "(()((()((()))))(()))", "(()((()((()))))()())", "(()((()((()))))())()", "(()((()((())))))(())", "(()((()((())))))()()", "(()((()(()((()))))))", "(()((()(()(()())))))", "(()((()(()(())()))))", "(()((()(()(()))())))", "(()((()(()(())))()))", "(()((()(()(()))))())", "(()((()(()(())))))()", "(()((()(()()(())))))", "(()((()(()()()()))))", "(()((()(()()())())))", "(()((()(()()()))()))", "(()((()(()()())))())", "(()((()(()()()))))()", "(()((()(()())(()))))", "(()((()(()())()())))", "(()((()(()())())()))", "(()((()(()())()))())", "(()((()(()())())))()", "(()((()(()()))(())))", "(()((()(()()))()()))", "(()((()(()()))())())", "(()((()(()()))()))()", "(()((()(()())))(()))", "(()((()(()())))()())", "(()((()(()())))())()", "(()((()(()()))))(())", "(()((()(()()))))()()", "(()((()(())((())))))", "(()((()(())(()()))))", "(()((()(())(())())))", "(()((()(())(()))()))", "(()((()(())(())))())", "(()((()(())(()))))()", "(()((()(())()(()))))", "(()((()(())()()())))", "(()((()(())()())()))", "(()((()(())()()))())", "(()((()(())()())))()", "(()((()(())())(())))", "(()((()(())())()()))", "(()((()(())())())())", "(()((()(())())()))()", "(()((()(())()))(()))", "(()((()(())()))()())", "(()((()(())()))())()", "(()((()(())())))(())", "(()((()(())())))()()", "(()((()(()))((()))))", "(()((()(()))(()())))", "(()((()(()))(())()))", "(()((()(()))(()))())", "(()((()(()))(())))()", "(()((()(()))()(())))", "(()((()(()))()()()))", "(()((()(()))()())())", "(()((()(()))()()))()", "(()((()(()))())(()))", "(()((()(()))())()())", "(()((()(()))())())()", "(()((()(()))()))(())", "(()((()(()))()))()()", "(()((()(())))((())))", "(()((()(())))(()()))", "(()((()(())))(())())", "(()((()(())))(()))()", "(()((()(())))()(()))", "(()((()(())))()()())", "(()((()(())))()())()", "(()((()(())))())(())", "(()((()(())))())()()", "(()((()(()))))((()))", "(()((()(()))))(()())", "(()((()(()))))(())()", "(()((()(()))))()(())", "(()((()(()))))()()()", "(()((()()(((()))))))", "(()((()()((()())))))", "(()((()()((())()))))", "(()((()()((()))())))", "(()((()()((())))()))", "(()((()()((()))))())", "(()((()()((())))))()", "(()((()()(()(())))))", "(()((()()(()()()))))", "(()((()()(()())())))", "(()((()()(()()))()))", "(()((()()(()())))())", "(()((()()(()()))))()", "(()((()()(())(()))))", "(()((()()(())()())))", "(()((()()(())())()))", "(()((()()(())()))())", "(()((()()(())())))()", "(()((()()(()))(())))", "(()((()()(()))()()))", "(()((()()(()))())())", "(()((()()(()))()))()", "(()((()()(())))(()))", "(()((()()(())))()())", "(()((()()(())))())()", "(()((()()(()))))(())", "(()((()()(()))))()()", "(()((()()()((())))))", "(()((()()()(()()))))", "(()((()()()(())())))", "(()((()()()(()))()))", "(()((()()()(())))())", "(()((()()()(()))))()", "(()((()()()()(()))))", "(()((()()()()()())))", "(()((()()()()())()))", "(()((()()()()()))())", "(()((()()()()())))()", "(()((()()()())(())))", "(()((()()()())()()))", "(()((()()()())())())", "(()((()()()())()))()", "(()((()()()()))(()))", "(()((()()()()))()())", "(()((()()()()))())()", "(()((()()()())))(())", "(()((()()()())))()()", "(()((()()())((()))))", "(()((()()())(()())))", "(()((()()())(())()))", "(()((()()())(()))())", "(()((()()())(())))()", "(()((()()())()(())))", "(()((()()())()()()))", "(()((()()())()())())", "(()((()()())()()))()", "(()((()()())())(()))", "(()((()()())())()())", "(()((()()())())())()", "(()((()()())()))(())", "(()((()()())()))()()", "(()((()()()))((())))", "(()((()()()))(()()))", "(()((()()()))(())())", "(()((()()()))(()))()", "(()((()()()))()(()))", "(()((()()()))()()())", "(()((()()()))()())()", "(()((()()()))())(())", "(()((()()()))())()()", "(()((()()())))((()))", "(()((()()())))(()())", "(()((()()())))(())()", "(()((()()())))()(())", "(()((()()())))()()()", "(()((()())(((())))))", "(()((()())((()()))))", "(()((()())((())())))", "(()((()())((()))()))", "(()((()())((())))())", "(()((()())((()))))()", "(()((()())(()(()))))", "(()((()())(()()())))", "(()((()())(()())()))", "(()((()())(()()))())", "(()((()())(()())))()", "(()((()())(())(())))", "(()((()())(())()()))", "(()((()())(())())())", "(()((()())(())()))()", "(()((()())(()))(()))", "(()((()())(()))()())", "(()((()())(()))())()", "(()((()())(())))(())", "(()((()())(())))()()", "(()((()())()((()))))", "(()((()())()(()())))", "(()((()())()(())()))", "(()((()())()(()))())", "(()((()())()(())))()", "(()((()())()()(())))", "(()((()())()()()()))", "(()((()())()()())())", "(()((()())()()()))()", "(()((()())()())(()))", "(()((()())()())()())", "(()((()())()())())()", "(()((()())()()))(())", "(()((()())()()))()()", "(()((()())())((())))", "(()((()())())(()()))", "(()((()())())(())())", "(()((()())())(()))()", "(()((()())())()(()))", "(()((()())())()()())", "(()((()())())()())()", "(()((()())())())(())", "(()((()())())())()()", "(()((()())()))((()))", "(()((()())()))(()())", "(()((()())()))(())()", "(()((()())()))()(())", "(()((()())()))()()()", "(()((()()))(((()))))", "(()((()()))((()())))", "(()((()()))((())()))", "(()((()()))((()))())", "(()((()()))((())))()", "(()((()()))(()(())))", "(()((()()))(()()()))", "(()((()()))(()())())", "(()((()()))(()()))()", "(()((()()))(())(()))", "(()((()()))(())()())", "(()((()()))(())())()", "(()((()()))(()))(())", "(()((()()))(()))()()", "(()((()()))()((())))", "(()((()()))()(()()))", "(()((()()))()(())())", "(()((()()))()(()))()", "(()((()()))()()(()))", "(()((()()))()()()())", "(()((()()))()()())()", "(()((()()))()())(())", "(()((()()))()())()()", "(()((()()))())((()))", "(()((()()))())(()())", "(()((()()))())(())()", "(()((()()))())()(())", "(()((()()))())()()()", "(()((()())))(((())))", "(()((()())))((()()))", "(()((()())))((())())", "(()((()())))((()))()", "(()((()())))(()(()))", "(()((()())))(()()())", "(()((()())))(()())()", "(()((()())))(())(())", "(()((()())))(())()()", "(()((()())))()((()))", "(()((()())))()(()())", "(()((()())))()(())()", "(()((()())))()()(())", "(()((()())))()()()()", "(()((())((((()))))))", "(()((())(((()())))))", "(()((())(((())()))))", "(()((())(((()))())))", "(()((())(((())))()))", "(()((())(((()))))())", "(()((())(((())))))()", "(()((())((()(())))))", "(()((())((()()()))))", "(()((())((()())())))", "(()((())((()()))()))", "(()((())((()())))())", "(()((())((()()))))()", "(()((())((())(()))))", "(()((())((())()())))", "(()((())((())())()))", "(()((())((())()))())", "(()((())((())())))()", "(()((())((()))(())))", "(()((())((()))()()))", "(()((())((()))())())", "(()((())((()))()))()", "(()((())((())))(()))", "(()((())((())))()())", "(()((())((())))())()", "(()((())((()))))(())", "(()((())((()))))()()", "(()((())(()((())))))", "(()((())(()(()()))))", "(()((())(()(())())))", "(()((())(()(()))()))", "(()((())(()(())))())", "(()((())(()(()))))()", "(()((())(()()(()))))", "(()((())(()()()())))", "(()((())(()()())()))", "(()((())(()()()))())", "(()((())(()()())))()", "(()((())(()())(())))", "(()((())(()())()()))", "(()((())(()())())())", "(()((())(()())()))()", "(()((())(()()))(()))", "(()((())(()()))()())", "(()((())(()()))())()", "(()((())(()())))(())", "(()((())(()())))()()", "(()((())(())((()))))", "(()((())(())(()())))", "(()((())(())(())()))", "(()((())(())(()))())", "(()((())(())(())))()", "(()((())(())()(())))", "(()((())(())()()()))", "(()((())(())()())())", "(()((())(())()()))()", "(()((())(())())(()))", "(()((())(())())()())", "(()((())(())())())()", "(()((())(())()))(())", "(()((())(())()))()()", "(()((())(()))((())))", "(()((())(()))(()()))", "(()((())(()))(())())", "(()((())(()))(()))()", "(()((())(()))()(()))", "(()((())(()))()()())", "(()((())(()))()())()", "(()((())(()))())(())", "(()((())(()))())()()", "(()((())(())))((()))", "(()((())(())))(()())", "(()((())(())))(())()", "(()((())(())))()(())", "(()((())(())))()()()", "(()((())()(((())))))", "(()((())()((()()))))", "(()((())()((())())))", "(()((())()((()))()))", "(()((())()((())))())", "(()((())()((()))))()", "(()((())()(()(()))))", "(()((())()(()()())))", "(()((())()(()())()))", "(()((())()(()()))())", "(()((())()(()())))()", "(()((())()(())(())))", "(()((())()(())()()))", "(()((())()(())())())", "(()((())()(())()))()", "(()((())()(()))(()))", "(()((())()(()))()())", "(()((())()(()))())()", "(()((())()(())))(())", "(()((())()(())))()()", "(()((())()()((()))))", "(()((())()()(()())))", "(()((())()()(())()))", "(()((())()()(()))())", "(()((())()()(())))()", "(()((())()()()(())))", "(()((())()()()()()))", "(()((())()()()())())", "(()((())()()()()))()", "(()((())()()())(()))", "(()((())()()())()())", "(()((())()()())())()", "(()((())()()()))(())", "(()((())()()()))()()", "(()((())()())((())))", "(()((())()())(()()))", "(()((())()())(())())", "(()((())()())(()))()", "(()((())()())()(()))", "(()((())()())()()())", "(()((())()())()())()", "(()((())()())())(())", "(()((())()())())()()", "(()((())()()))((()))", "(()((())()()))(()())", "(()((())()()))(())()", "(()((())()()))()(())", "(()((())()()))()()()", "(()((())())(((()))))", "(()((())())((()())))", "(()((())())((())()))", "(()((())())((()))())", "(()((())())((())))()", "(()((())())(()(())))", "(()((())())(()()()))", "(()((())())(()())())", "(()((())())(()()))()", "(()((())())(())(()))", "(()((())())(())()())", "(()((())())(())())()", "(()((())())(()))(())", "(()((())())(()))()()", "(()((())())()((())))", "(()((())())()(()()))", "(()((())())()(())())", "(()((())())()(()))()", "(()((())())()()(()))", "(()((())())()()()())", "(()((())())()()())()", "(()((())())()())(())", "(()((())())()())()()", "(()((())())())((()))", "(()((())())())(()())", "(()((())())())(())()", "(()((())())())()(())", "(()((())())())()()()", "(()((())()))(((())))", "(()((())()))((()()))", "(()((())()))((())())", "(()((())()))((()))()", "(()((())()))(()(()))", "(()((())()))(()()())", "(()((())()))(()())()", "(()((())()))(())(())", "(()((())()))(())()()", "(()((())()))()((()))", "(()((())()))()(()())", "(()((())()))()(())()", "(()((())()))()()(())", "(()((())()))()()()()", "(()((()))((((())))))", "(()((()))(((()()))))", "(()((()))(((())())))", "(()((()))(((()))()))", "(()((()))(((())))())", "(()((()))(((()))))()", "(()((()))((()(()))))", "(()((()))((()()())))", "(()((()))((()())()))", "(()((()))((()()))())", "(()((()))((()())))()", "(()((()))((())(())))", "(()((()))((())()()))", "(()((()))((())())())", "(()((()))((())()))()", "(()((()))((()))(()))", "(()((()))((()))()())", "(()((()))((()))())()", "(()((()))((())))(())", "(()((()))((())))()()", "(()((()))(()((()))))", "(()((()))(()(()())))", "(()((()))(()(())()))", "(()((()))(()(()))())", "(()((()))(()(())))()", "(()((()))(()()(())))", "(()((()))(()()()()))", "(()((()))(()()())())", "(()((()))(()()()))()", "(()((()))(()())(()))", "(()((()))(()())()())", "(()((()))(()())())()", "(()((()))(()()))(())", "(()((()))(()()))()()", "(()((()))(())((())))", "(()((()))(())(()()))", "(()((()))(())(())())", "(()((()))(())(()))()", "(()((()))(())()(()))", "(()((()))(())()()())", "(()((()))(())()())()", "(()((()))(())())(())", "(()((()))(())())()()", "(()((()))(()))((()))", "(()((()))(()))(()())", "(()((()))(()))(())()", "(()((()))(()))()(())", "(()((()))(()))()()()", "(()((()))()(((()))))", "(()((()))()((()())))", "(()((()))()((())()))", "(()((()))()((()))())", "(()((()))()((())))()", "(()((()))()(()(())))", "(()((()))()(()()()))", "(()((()))()(()())())", "(()((()))()(()()))()", "(()((()))()(())(()))", "(()((()))()(())()())", "(()((()))()(())())()", "(()((()))()(()))(())", "(()((()))()(()))()()", "(()((()))()()((())))", "(()((()))()()(()()))", "(()((()))()()(())())", "(()((()))()()(()))()", "(()((()))()()()(()))", "(()((()))()()()()())", "(()((()))()()()())()", "(()((()))()()())(())", "(()((()))()()())()()", "(()((()))()())((()))", "(()((()))()())(()())", "(()((()))()())(())()", "(()((()))()())()(())", "(()((()))()())()()()", "(()((()))())(((())))", "(()((()))())((()()))", "(()((()))())((())())", "(()((()))())((()))()", "(()((()))())(()(()))", "(()((()))())(()()())", "(()((()))())(()())()", "(()((()))())(())(())", "(()((()))())(())()()", "(()((()))())()((()))", "(()((()))())()(()())", "(()((()))())()(())()", "(()((()))())()()(())", "(()((()))())()()()()", "(()((())))((((()))))", "(()((())))(((()())))", "(()((())))(((())()))", "(()((())))(((()))())", "(()((())))(((())))()", "(()((())))((()(())))", "(()((())))((()()()))", "(()((())))((()())())", "(()((())))((()()))()", "(()((())))((())(()))", "(()((())))((())()())", "(()((())))((())())()", "(()((())))((()))(())", "(()((())))((()))()()", "(()((())))(()((())))", "(()((())))(()(()()))", "(()((())))(()(())())", "(()((())))(()(()))()", "(()((())))(()()(()))", "(()((())))(()()()())", "(()((())))(()()())()", "(()((())))(()())(())", "(()((())))(()())()()", "(()((())))(())((()))", "(()((())))(())(()())", "(()((())))(())(())()", "(()((())))(())()(())", "(()((())))(())()()()", "(()((())))()(((())))", "(()((())))()((()()))", "(()((())))()((())())", "(()((())))()((()))()", "(()((())))()(()(()))", "(()((())))()(()()())", "(()((())))()(()())()", "(()((())))()(())(())", "(()((())))()(())()()", "(()((())))()()((()))", "(()((())))()()(()())", "(()((())))()()(())()", "(()((())))()()()(())", "(()((())))()()()()()", "(()(()(((((())))))))", "(()(()((((()()))))))", "(()(()((((())())))))", "(()(()((((()))()))))", "(()(()((((())))())))", "(()(()((((()))))()))", "(()(()((((())))))())", "(()(()((((()))))))()", "(()(()(((()(()))))))", "(()(()(((()()())))))", "(()(()(((()())()))))", "(()(()(((()()))())))", "(()(()(((()())))()))", "(()(()(((()()))))())", "(()(()(((()())))))()", "(()(()(((())(())))))", "(()(()(((())()()))))", "(()(()(((())())())))", "(()(()(((())()))()))", "(()(()(((())())))())", "(()(()(((())()))))()", "(()(()(((()))(()))))", "(()(()(((()))()())))", "(()(()(((()))())()))", "(()(()(((()))()))())", "(()(()(((()))())))()", "(()(()(((())))(())))", "(()(()(((())))()()))", "(()(()(((())))())())", "(()(()(((())))()))()", "(()(()(((()))))(()))", "(()(()(((()))))()())", "(()(()(((()))))())()", "(()(()(((())))))(())", "(()(()(((())))))()()", "(()(()((()((()))))))", "(()(()((()(()())))))", "(()(()((()(())()))))", "(()(()((()(()))())))", "(()(()((()(())))()))", "(()(()((()(()))))())", "(()(()((()(())))))()", "(()(()((()()(())))))", "(()(()((()()()()))))", "(()(()((()()())())))", "(()(()((()()()))()))", "(()(()((()()())))())", "(()(()((()()()))))()", "(()(()((()())(()))))", "(()(()((()())()())))", "(()(()((()())())()))", "(()(()((()())()))())", "(()(()((()())())))()", "(()(()((()()))(())))", "(()(()((()()))()()))", "(()(()((()()))())())", "(()(()((()()))()))()", "(()(()((()())))(()))", "(()(()((()())))()())", "(()(()((()())))())()", "(()(()((()()))))(())", "(()(()((()()))))()()", "(()(()((())((())))))", "(()(()((())(()()))))", "(()(()((())(())())))", "(()(()((())(()))()))", "(()(()((())(())))())", "(()(()((())(()))))()", "(()(()((())()(()))))", "(()(()((())()()())))", "(()(()((())()())()))", "(()(()((())()()))())", "(()(()((())()())))()", "(()(()((())())(())))", "(()(()((())())()()))", "(()(()((())())())())", "(()(()((())())()))()", "(()(()((())()))(()))", "(()(()((())()))()())", "(()(()((())()))())()", "(()(()((())())))(())", "(()(()((())())))()()", "(()(()((()))((()))))", "(()(()((()))(()())))", "(()(()((()))(())()))", "(()(()((()))(()))())", "(()(()((()))(())))()", "(()(()((()))()(())))", "(()(()((()))()()()))", "(()(()((()))()())())", "(()(()((()))()()))()", "(()(()((()))())(()))", "(()(()((()))())()())", "(()(()((()))())())()", "(()(()((()))()))(())", "(()(()((()))()))()()", "(()(()((())))((())))", "(()(()((())))(()()))", "(()(()((())))(())())", "(()(()((())))(()))()", "(()(()((())))()(()))", "(()(()((())))()()())", "(()(()((())))()())()", "(()(()((())))())(())", "(()(()((())))())()()", "(()(()((()))))((()))", "(()(()((()))))(()())", "(()(()((()))))(())()", "(()(()((()))))()(())", "(()(()((()))))()()()", "(()(()(()(((()))))))", "(()(()(()((()())))))", "(()(()(()((())()))))", "(()(()(()((()))())))", "(()(()(()((())))()))", "(()(()(()((()))))())", "(()(()(()((())))))()", "(()(()(()(()(())))))", "(()(()(()(()()()))))", "(()(()(()(()())())))", "(()(()(()(()()))()))", "(()(()(()(()())))())", "(()(()(()(()()))))()", "(()(()(()(())(()))))", "(()(()(()(())()())))", "(()(()(()(())())()))", "(()(()(()(())()))())", "(()(()(()(())())))()", "(()(()(()(()))(())))", "(()(()(()(()))()()))", "(()(()(()(()))())())", "(()(()(()(()))()))()", "(()(()(()(())))(()))", "(()(()(()(())))()())", "(()(()(()(())))())()", "(()(()(()(()))))(())", "(()(()(()(()))))()()", "(()(()(()()((())))))", "(()(()(()()(()()))))", "(()(()(()()(())())))", "(()(()(()()(()))()))", "(()(()(()()(())))())", "(()(()(()()(()))))()", "(()(()(()()()(()))))", "(()(()(()()()()())))", "(()(()(()()()())()))", "(()(()(()()()()))())", "(()(()(()()()())))()", "(()(()(()()())(())))", "(()(()(()()())()()))", "(()(()(()()())())())", "(()(()(()()())()))()", "(()(()(()()()))(()))", "(()(()(()()()))()())", "(()(()(()()()))())()", "(()(()(()()())))(())", "(()(()(()()())))()()", "(()(()(()())((()))))", "(()(()(()())(()())))", "(()(()(()())(())()))", "(()(()(()())(()))())", "(()(()(()())(())))()", "(()(()(()())()(())))", "(()(()(()())()()()))", "(()(()(()())()())())", "(()(()(()())()()))()", "(()(()(()())())(()))", "(()(()(()())())()())", "(()(()(()())())())()", "(()(()(()())()))(())", "(()(()(()())()))()()", "(()(()(()()))((())))", "(()(()(()()))(()()))", "(()(()(()()))(())())", "(()(()(()()))(()))()", "(()(()(()()))()(()))", "(()(()(()()))()()())", "(()(()(()()))()())()", "(()(()(()()))())(())", "(()(()(()()))())()()", "(()(()(()())))((()))", "(()(()(()())))(()())", "(()(()(()())))(())()", "(()(()(()())))()(())", "(()(()(()())))()()()", "(()(()(())(((())))))", "(()(()(())((()()))))", "(()(()(())((())())))", "(()(()(())((()))()))", "(()(()(())((())))())", "(()(()(())((()))))()", "(()(()(())(()(()))))", "(()(()(())(()()())))", "(()(()(())(()())()))", "(()(()(())(()()))())", "(()(()(())(()())))()", "(()(()(())(())(())))", "(()(()(())(())()()))", "(()(()(())(())())())", "(()(()(())(())()))()", "(()(()(())(()))(()))", "(()(()(())(()))()())", "(()(()(())(()))())()", "(()(()(())(())))(())", "(()(()(())(())))()()", "(()(()(())()((()))))", "(()(()(())()(()())))", "(()(()(())()(())()))", "(()(()(())()(()))())", "(()(()(())()(())))()", "(()(()(())()()(())))", "(()(()(())()()()()))", "(()(()(())()()())())", "(()(()(())()()()))()", "(()(()(())()())(()))", "(()(()(())()())()())", "(()(()(())()())())()", "(()(()(())()()))(())", "(()(()(())()()))()()", "(()(()(())())((())))", "(()(()(())())(()()))", "(()(()(())())(())())", "(()(()(())())(()))()", "(()(()(())())()(()))", "(()(()(())())()()())", "(()(()(())())()())()", "(()(()(())())())(())", "(()(()(())())())()()", "(()(()(())()))((()))", "(()(()(())()))(()())", "(()(()(())()))(())()", "(()(()(())()))()(())", "(()(()(())()))()()()", "(()(()(()))(((()))))", "(()(()(()))((()())))", "(()(()(()))((())()))", "(()(()(()))((()))())", "(()(()(()))((())))()", "(()(()(()))(()(())))", "(()(()(()))(()()()))", "(()(()(()))(()())())", "(()(()(()))(()()))()", "(()(()(()))(())(()))", "(()(()(()))(())()())", "(()(()(()))(())())()", "(()(()(()))(()))(())", "(()(()(()))(()))()()", "(()(()(()))()((())))", "(()(()(()))()(()()))", "(()(()(()))()(())())", "(()(()(()))()(()))()", "(()(()(()))()()(()))", "(()(()(()))()()()())", "(()(()(()))()()())()", "(()(()(()))()())(())", "(()(()(()))()())()()", "(()(()(()))())((()))", "(()(()(()))())(()())", "(()(()(()))())(())()", "(()(()(()))())()(())", "(()(()(()))())()()()", "(()(()(())))(((())))", "(()(()(())))((()()))", "(()(()(())))((())())", "(()(()(())))((()))()", "(()(()(())))(()(()))", "(()(()(())))(()()())", "(()(()(())))(()())()", "(()(()(())))(())(())", "(()(()(())))(())()()", "(()(()(())))()((()))", "(()(()(())))()(()())", "(()(()(())))()(())()", "(()(()(())))()()(())", "(()(()(())))()()()()", "(()(()()((((()))))))", "(()(()()(((()())))))", "(()(()()(((())()))))", "(()(()()(((()))())))", "(()(()()(((())))()))", "(()(()()(((()))))())", "(()(()()(((())))))()", "(()(()()((()(())))))", "(()(()()((()()()))))", "(()(()()((()())())))", "(()(()()((()()))()))", "(()(()()((()())))())", "(()(()()((()()))))()", "(()(()()((())(()))))", "(()(()()((())()())))", "(()(()()((())())()))", "(()(()()((())()))())", "(()(()()((())())))()", "(()(()()((()))(())))", "(()(()()((()))()()))", "(()(()()((()))())())", "(()(()()((()))()))()", "(()(()()((())))(()))", "(()(()()((())))()())", "(()(()()((())))())()", "(()(()()((()))))(())", "(()(()()((()))))()()", "(()(()()(()((())))))", "(()(()()(()(()()))))", "(()(()()(()(())())))", "(()(()()(()(()))()))", "(()(()()(()(())))())", "(()(()()(()(()))))()", "(()(()()(()()(()))))", "(()(()()(()()()())))", "(()(()()(()()())()))", "(()(()()(()()()))())", "(()(()()(()()())))()", "(()(()()(()())(())))", "(()(()()(()())()()))", "(()(()()(()())())())", "(()(()()(()())()))()", "(()(()()(()()))(()))", "(()(()()(()()))()())", "(()(()()(()()))())()", "(()(()()(()())))(())", "(()(()()(()())))()()", "(()(()()(())((()))))", "(()(()()(())(()())))", "(()(()()(())(())()))", "(()(()()(())(()))())", "(()(()()(())(())))()", "(()(()()(())()(())))", "(()(()()(())()()()))", "(()(()()(())()())())", "(()(()()(())()()))()", "(()(()()(())())(()))", "(()(()()(())())()())", "(()(()()(())())())()", "(()(()()(())()))(())", "(()(()()(())()))()()", "(()(()()(()))((())))", "(()(()()(()))(()()))", "(()(()()(()))(())())", "(()(()()(()))(()))()", "(()(()()(()))()(()))", "(()(()()(()))()()())", "(()(()()(()))()())()", "(()(()()(()))())(())", "(()(()()(()))())()()", "(()(()()(())))((()))", "(()(()()(())))(()())", "(()(()()(())))(())()", "(()(()()(())))()(())", "(()(()()(())))()()()", "(()(()()()(((())))))", "(()(()()()((()()))))", "(()(()()()((())())))", "(()(()()()((()))()))", "(()(()()()((())))())", "(()(()()()((()))))()", "(()(()()()(()(()))))", "(()(()()()(()()())))", "(()(()()()(()())()))", "(()(()()()(()()))())", "(()(()()()(()())))()", "(()(()()()(())(())))", "(()(()()()(())()()))", "(()(()()()(())())())", "(()(()()()(())()))()", "(()(()()()(()))(()))", "(()(()()()(()))()())", "(()(()()()(()))())()", "(()(()()()(())))(())", "(()(()()()(())))()()", "(()(()()()()((()))))", "(()(()()()()(()())))", "(()(()()()()(())()))", "(()(()()()()(()))())", "(()(()()()()(())))()", "(()(()()()()()(())))", "(()(()()()()()()()))", "(()(()()()()()())())", "(()(()()()()()()))()", "(()(()()()()())(()))", "(()(()()()()())()())", "(()(()()()()())())()", "(()(()()()()()))(())", "(()(()()()()()))()()", "(()(()()()())((())))", "(()(()()()())(()()))", "(()(()()()())(())())", "(()(()()()())(()))()", "(()(()()()())()(()))", "(()(()()()())()()())", "(()(()()()())()())()", "(()(()()()())())(())", "(()(()()()())())()()", "(()(()()()()))((()))", "(()(()()()()))(()())", "(()(()()()()))(())()", "(()(()()()()))()(())", "(()(()()()()))()()()", "(()(()()())(((()))))", "(()(()()())((()())))", "(()(()()())((())()))", "(()(()()())((()))())", "(()(()()())((())))()", "(()(()()())(()(())))", "(()(()()())(()()()))", "(()(()()())(()())())", "(()(()()())(()()))()", "(()(()()())(())(()))", "(()(()()())(())()())", "(()(()()())(())())()", "(()(()()())(()))(())", "(()(()()())(()))()()", "(()(()()())()((())))", "(()(()()())()(()()))", "(()(()()())()(())())", "(()(()()())()(()))()", "(()(()()())()()(()))", "(()(()()())()()()())", "(()(()()())()()())()", "(()(()()())()())(())", "(()(()()())()())()()", "(()(()()())())((()))", "(()(()()())())(()())", "(()(()()())())(())()", "(()(()()())())()(())", "(()(()()())())()()()", "(()(()()()))(((())))", "(()(()()()))((()()))", "(()(()()()))((())())", "(()(()()()))((()))()", "(()(()()()))(()(()))", "(()(()()()))(()()())", "(()(()()()))(()())()", "(()(()()()))(())(())", "(()(()()()))(())()()", "(()(()()()))()((()))", "(()(()()()))()(()())", "(()(()()()))()(())()", "(()(()()()))()()(())", "(()(()()()))()()()()", "(()(()())((((())))))", "(()(()())(((()()))))", "(()(()())(((())())))", "(()(()())(((()))()))", "(()(()())(((())))())", "(()(()())(((()))))()", "(()(()())((()(()))))", "(()(()())((()()())))", "(()(()())((()())()))", "(()(()())((()()))())", "(()(()())((()())))()", "(()(()())((())(())))", "(()(()())((())()()))", "(()(()())((())())())", "(()(()())((())()))()", "(()(()())((()))(()))", "(()(()())((()))()())", "(()(()())((()))())()", "(()(()())((())))(())", "(()(()())((())))()()", "(()(()())(()((()))))", "(()(()())(()(()())))", "(()(()())(()(())()))", "(()(()())(()(()))())", "(()(()())(()(())))()", "(()(()())(()()(())))", "(()(()())(()()()()))", "(()(()())(()()())())", "(()(()())(()()()))()", "(()(()())(()())(()))", "(()(()())(()())()())", "(()(()())(()())())()", "(()(()())(()()))(())", "(()(()())(()()))()()", "(()(()())(())((())))", "(()(()())(())(()()))", "(()(()())(())(())())", "(()(()())(())(()))()", "(()(()())(())()(()))", "(()(()())(())()()())", "(()(()())(())()())()", "(()(()())(())())(())", "(()(()())(())())()()", "(()(()())(()))((()))", "(()(()())(()))(()())", "(()(()())(()))(())()", "(()(()())(()))()(())", "(()(()())(()))()()()", "(()(()())()(((()))))", "(()(()())()((()())))", "(()(()())()((())()))", "(()(()())()((()))())", "(()(()())()((())))()", "(()(()())()(()(())))", "(()(()())()(()()()))", "(()(()())()(()())())", "(()(()())()(()()))()", "(()(()())()(())(()))", "(()(()())()(())()())", "(()(()())()(())())()", "(()(()())()(()))(())", "(()(()())()(()))()()", "(()(()())()()((())))", "(()(()())()()(()()))", "(()(()())()()(())())", "(()(()())()()(()))()", "(()(()())()()()(()))", "(()(()())()()()()())", "(()(()())()()()())()", "(()(()())()()())(())", "(()(()())()()())()()", "(()(()())()())((()))", "(()(()())()())(()())", "(()(()())()())(())()", "(()(()())()())()(())", "(()(()())()())()()()", "(()(()())())(((())))", "(()(()())())((()()))", "(()(()())())((())())", "(()(()())())((()))()", "(()(()())())(()(()))", "(()(()())())(()()())", "(()(()())())(()())()", "(()(()())())(())(())", "(()(()())())(())()()", "(()(()())())()((()))", "(()(()())())()(()())", "(()(()())())()(())()", "(()(()())())()()(())", "(()(()())())()()()()", "(()(()()))((((()))))", "(()(()()))(((()())))", "(()(()()))(((())()))", "(()(()()))(((()))())", "(()(()()))(((())))()", "(()(()()))((()(())))", "(()(()()))((()()()))", "(()(()()))((()())())", "(()(()()))((()()))()", "(()(()()))((())(()))", "(()(()()))((())()())", "(()(()()))((())())()", "(()(()()))((()))(())", "(()(()()))((()))()()", "(()(()()))(()((())))", "(()(()()))(()(()()))", "(()(()()))(()(())())", "(()(()()))(()(()))()", "(()(()()))(()()(()))", "(()(()()))(()()()())", "(()(()()))(()()())()", "(()(()()))(()())(())", "(()(()()))(()())()()", "(()(()()))(())((()))", "(()(()()))(())(()())", "(()(()()))(())(())()", "(()(()()))(())()(())", "(()(()()))(())()()()", "(()(()()))()(((())))", "(()(()()))()((()()))", "(()(()()))()((())())", "(()(()()))()((()))()", "(()(()()))()(()(()))", "(()(()()))()(()()())", "(()(()()))()(()())()", "(()(()()))()(())(())", "(()(()()))()(())()()", "(()(()()))()()((()))", "(()(()()))()()(()())", "(()(()()))()()(())()", "(()(()()))()()()(())", "(()(()()))()()()()()", "(()(())(((((()))))))", "(()(())((((()())))))", "(()(())((((())()))))", "(()(())((((()))())))", "(()(())((((())))()))", "(()(())((((()))))())", "(()(())((((())))))()", "(()(())(((()(())))))", "(()(())(((()()()))))", "(()(())(((()())())))", "(()(())(((()()))()))", "(()(())(((()())))())", "(()(())(((()()))))()", "(()(())(((())(()))))", "(()(())(((())()())))", "(()(())(((())())()))", "(()(())(((())()))())", "(()(())(((())())))()", "(()(())(((()))(())))", "(()(())(((()))()()))", "(()(())(((()))())())", "(()(())(((()))()))()", "(()(())(((())))(()))", "(()(())(((())))()())", "(()(())(((())))())()", "(()(())(((()))))(())", "(()(())(((()))))()()", "(()(())((()((())))))", "(()(())((()(()()))))", "(()(())((()(())())))", "(()(())((()(()))()))", "(()(())((()(())))())", "(()(())((()(()))))()", "(()(())((()()(()))))", "(()(())((()()()())))", "(()(())((()()())()))", "(()(())((()()()))())", "(()(())((()()())))()", "(()(())((()())(())))", "(()(())((()())()()))", "(()(())((()())())())", "(()(())((()())()))()", "(()(())((()()))(()))", "(()(())((()()))()())", "(()(())((()()))())()", "(()(())((()())))(())", "(()(())((()())))()()", "(()(())((())((()))))", "(()(())((())(()())))", "(()(())((())(())()))", "(()(())((())(()))())", "(()(())((())(())))()", "(()(())((())()(())))", "(()(())((())()()()))", "(()(())((())()())())", "(()(())((())()()))()", "(()(())((())())(()))", "(()(())((())())()())", "(()(())((())())())()", "(()(())((())()))(())", "(()(())((())()))()()", "(()(())((()))((())))", "(()(())((()))(()()))", "(()(())((()))(())())", "(()(())((()))(()))()", "(()(())((()))()(()))", "(()(())((()))()()())", "(()(())((()))()())()", "(()(())((()))())(())", "(()(())((()))())()()", "(()(())((())))((()))", "(()(())((())))(()())", "(()(())((())))(())()", "(()(())((())))()(())", "(()(())((())))()()()", "(()(())(()(((())))))", "(()(())(()((()()))))", "(()(())(()((())())))", "(()(())(()((()))()))", "(()(())(()((())))())", "(()(())(()((()))))()", "(()(())(()(()(()))))", "(()(())(()(()()())))", "(()(())(()(()())()))", "(()(())(()(()()))())", "(()(())(()(()())))()", "(()(())(()(())(())))", "(()(())(()(())()()))", "(()(())(()(())())())", "(()(())(()(())()))()", "(()(())(()(()))(()))", "(()(())(()(()))()())", "(()(())(()(()))())()", "(()(())(()(())))(())", "(()(())(()(())))()()", "(()(())(()()((()))))", "(()(())(()()(()())))", "(()(())(()()(())()))", "(()(())(()()(()))())", "(()(())(()()(())))()", "(()(())(()()()(())))", "(()(())(()()()()()))", "(()(())(()()()())())", "(()(())(()()()()))()", "(()(())(()()())(()))", "(()(())(()()())()())", "(()(())(()()())())()", "(()(())(()()()))(())", "(()(())(()()()))()()", "(()(())(()())((())))", "(()(())(()())(()()))", "(()(())(()())(())())", "(()(())(()())(()))()", "(()(())(()())()(()))", "(()(())(()())()()())", "(()(())(()())()())()", "(()(())(()())())(())", "(()(())(()())())()()", "(()(())(()()))((()))", "(()(())(()()))(()())", "(()(())(()()))(())()", "(()(())(()()))()(())", "(()(())(()()))()()()", "(()(())(())(((()))))", "(()(())(())((()())))", "(()(())(())((())()))", "(()(())(())((()))())", "(()(())(())((())))()", "(()(())(())(()(())))", "(()(())(())(()()()))", "(()(())(())(()())())", "(()(())(())(()()))()", "(()(())(())(())(()))", "(()(())(())(())()())", "(()(())(())(())())()", "(()(())(())(()))(())", "(()(())(())(()))()()", "(()(())(())()((())))", "(()(())(())()(()()))", "(()(())(())()(())())", "(()(())(())()(()))()", "(()(())(())()()(()))", "(()(())(())()()()())", "(()(())(())()()())()", "(()(())(())()())(())", "(()(())(())()())()()", "(()(())(())())((()))", "(()(())(())())(()())", "(()(())(())())(())()", "(()(())(())())()(())", "(()(())(())())()()()", "(()(())(()))(((())))", "(()(())(()))((()()))", "(()(())(()))((())())", "(()(())(()))((()))()", "(()(())(()))(()(()))", "(()(())(()))(()()())", "(()(())(()))(()())()", "(()(())(()))(())(())", "(()(())(()))(())()()", "(()(())(()))()((()))", "(()(())(()))()(()())", "(()(())(()))()(())()", "(()(())(()))()()(())", "(()(())(()))()()()()", "(()(())()((((())))))", "(()(())()(((()()))))", "(()(())()(((())())))", "(()(())()(((()))()))", "(()(())()(((())))())", "(()(())()(((()))))()", "(()(())()((()(()))))", "(()(())()((()()())))", "(()(())()((()())()))", "(()(())()((()()))())", "(()(())()((()())))()", "(()(())()((())(())))", "(()(())()((())()()))", "(()(())()((())())())", "(()(())()((())()))()", "(()(())()((()))(()))", "(()(())()((()))()())", "(()(())()((()))())()", "(()(())()((())))(())", "(()(())()((())))()()", "(()(())()(()((()))))", "(()(())()(()(()())))", "(()(())()(()(())()))", "(()(())()(()(()))())", "(()(())()(()(())))()", "(()(())()(()()(())))", "(()(())()(()()()()))", "(()(())()(()()())())", "(()(())()(()()()))()", "(()(())()(()())(()))", "(()(())()(()())()())", "(()(())()(()())())()", "(()(())()(()()))(())", "(()(())()(()()))()()", "(()(())()(())((())))", "(()(())()(())(()()))", "(()(())()(())(())())", "(()(())()(())(()))()", "(()(())()(())()(()))", "(()(())()(())()()())", "(()(())()(())()())()", "(()(())()(())())(())", "(()(())()(())())()()", "(()(())()(()))((()))", "(()(())()(()))(()())", "(()(())()(()))(())()", "(()(())()(()))()(())", "(()(())()(()))()()()", "(()(())()()(((()))))", "(()(())()()((()())))", "(()(())()()((())()))", "(()(())()()((()))())", "(()(())()()((())))()", "(()(())()()(()(())))", "(()(())()()(()()()))", "(()(())()()(()())())", "(()(())()()(()()))()", "(()(())()()(())(()))", "(()(())()()(())()())", "(()(())()()(())())()", "(()(())()()(()))(())", "(()(())()()(()))()()", "(()(())()()()((())))", "(()(())()()()(()()))", "(()(())()()()(())())", "(()(())()()()(()))()", "(()(())()()()()(()))", "(()(())()()()()()())", "(()(())()()()()())()", "(()(())()()()())(())", "(()(())()()()())()()", "(()(())()()())((()))", "(()(())()()())(()())", "(()(())()()())(())()", "(()(())()()())()(())", "(()(())()()())()()()", "(()(())()())(((())))", "(()(())()())((()()))", "(()(())()())((())())", "(()(())()())((()))()", "(()(())()())(()(()))", "(()(())()())(()()())", "(()(())()())(()())()", "(()(())()())(())(())", "(()(())()())(())()()", "(()(())()())()((()))", "(()(())()())()(()())", "(()(())()())()(())()", "(()(())()())()()(())", "(()(())()())()()()()", "(()(())())((((()))))", "(()(())())(((()())))", "(()(())())(((())()))", "(()(())())(((()))())", "(()(())())(((())))()", "(()(())())((()(())))", "(()(())())((()()()))", "(()(())())((()())())", "(()(())())((()()))()", "(()(())())((())(()))", "(()(())())((())()())", "(()(())())((())())()", "(()(())())((()))(())", "(()(())())((()))()()", "(()(())())(()((())))", "(()(())())(()(()()))", "(()(())())(()(())())", "(()(())())(()(()))()", "(()(())())(()()(()))", "(()(())())(()()()())", "(()(())())(()()())()", "(()(())())(()())(())", "(()(())())(()())()()", "(()(())())(())((()))", "(()(())())(())(()())", "(()(())())(())(())()", "(()(())())(())()(())", "(()(())())(())()()()", "(()(())())()(((())))", "(()(())())()((()()))", "(()(())())()((())())", "(()(())())()((()))()", "(()(())())()(()(()))", "(()(())())()(()()())", "(()(())())()(()())()", "(()(())())()(())(())", "(()(())())()(())()()", "(()(())())()()((()))", "(()(())())()()(()())", "(()(())())()()(())()", "(()(())())()()()(())", "(()(())())()()()()()", "(()(()))(((((())))))", "(()(()))((((()()))))", "(()(()))((((())())))", "(()(()))((((()))()))", "(()(()))((((())))())", "(()(()))((((()))))()", "(()(()))(((()(()))))", "(()(()))(((()()())))", "(()(()))(((()())()))", "(()(()))(((()()))())", "(()(()))(((()())))()", "(()(()))(((())(())))", "(()(()))(((())()()))", "(()(()))(((())())())", "(()(()))(((())()))()", "(()(()))(((()))(()))", "(()(()))(((()))()())", "(()(()))(((()))())()", "(()(()))(((())))(())", "(()(()))(((())))()()", "(()(()))((()((()))))", "(()(()))((()(()())))", "(()(()))((()(())()))", "(()(()))((()(()))())", "(()(()))((()(())))()", "(()(()))((()()(())))", "(()(()))((()()()()))", "(()(()))((()()())())", "(()(()))((()()()))()", "(()(()))((()())(()))", "(()(()))((()())()())", "(()(()))((()())())()", "(()(()))((()()))(())", "(()(()))((()()))()()", "(()(()))((())((())))", "(()(()))((())(()()))", "(()(()))((())(())())", "(()(()))((())(()))()", "(()(()))((())()(()))", "(()(()))((())()()())", "(()(()))((())()())()", "(()(()))((())())(())", "(()(()))((())())()()", "(()(()))((()))((()))", "(()(()))((()))(()())", "(()(()))((()))(())()", "(()(()))((()))()(())", "(()(()))((()))()()()", "(()(()))(()(((()))))", "(()(()))(()((()())))", "(()(()))(()((())()))", "(()(()))(()((()))())", "(()(()))(()((())))()", "(()(()))(()(()(())))", "(()(()))(()(()()()))", "(()(()))(()(()())())", "(()(()))(()(()()))()", "(()(()))(()(())(()))", "(()(()))(()(())()())", "(()(()))(()(())())()", "(()(()))(()(()))(())", "(()(()))(()(()))()()", "(()(()))(()()((())))", "(()(()))(()()(()()))", "(()(()))(()()(())())", "(()(()))(()()(()))()", "(()(()))(()()()(()))", "(()(()))(()()()()())", "(()(()))(()()()())()", "(()(()))(()()())(())", "(()(()))(()()())()()", "(()(()))(()())((()))", "(()(()))(()())(()())", "(()(()))(()())(())()", "(()(()))(()())()(())", "(()(()))(()())()()()", "(()(()))(())(((())))", "(()(()))(())((()()))", "(()(()))(())((())())", "(()(()))(())((()))()", "(()(()))(())(()(()))", "(()(()))(())(()()())", "(()(()))(())(()())()", "(()(()))(())(())(())", "(()(()))(())(())()()", "(()(()))(())()((()))", "(()(()))(())()(()())", "(()(()))(())()(())()", "(()(()))(())()()(())", "(()(()))(())()()()()", "(()(()))()((((()))))", "(()(()))()(((()())))", "(()(()))()(((())()))", "(()(()))()(((()))())", "(()(()))()(((())))()", "(()(()))()((()(())))", "(()(()))()((()()()))", "(()(()))()((()())())", "(()(()))()((()()))()", "(()(()))()((())(()))", "(()(()))()((())()())", "(()(()))()((())())()", "(()(()))()((()))(())", "(()(()))()((()))()()", "(()(()))()(()((())))", "(()(()))()(()(()()))", "(()(()))()(()(())())", "(()(()))()(()(()))()", "(()(()))()(()()(()))", "(()(()))()(()()()())", "(()(()))()(()()())()", "(()(()))()(()())(())", "(()(()))()(()())()()", "(()(()))()(())((()))", "(()(()))()(())(()())", "(()(()))()(())(())()", "(()(()))()(())()(())", "(()(()))()(())()()()", "(()(()))()()(((())))", "(()(()))()()((()()))", "(()(()))()()((())())", "(()(()))()()((()))()", "(()(()))()()(()(()))", "(()(()))()()(()()())", "(()(()))()()(()())()", "(()(()))()()(())(())", "(()(()))()()(())()()", "(()(()))()()()((()))", "(()(()))()()()(()())", "(()(()))()()()(())()", "(()(()))()()()()(())", "(()(()))()()()()()()", "(()()((((((())))))))", "(()()(((((()()))))))", "(()()(((((())())))))", "(()()(((((()))()))))", "(()()(((((())))())))", "(()()(((((()))))()))", "(()()(((((())))))())", "(()()(((((()))))))()", "(()()((((()(()))))))", "(()()((((()()())))))", "(()()((((()())()))))", "(()()((((()()))())))", "(()()((((()())))()))", "(()()((((()()))))())", "(()()((((()())))))()", "(()()((((())(())))))", "(()()((((())()()))))", "(()()((((())())())))", "(()()((((())()))()))", "(()()((((())())))())", "(()()((((())()))))()", "(()()((((()))(()))))", "(()()((((()))()())))", "(()()((((()))())()))", "(()()((((()))()))())", "(()()((((()))())))()", "(()()((((())))(())))", "(()()((((())))()()))", "(()()((((())))())())", "(()()((((())))()))()", "(()()((((()))))(()))", "(()()((((()))))()())", "(()()((((()))))())()", "(()()((((())))))(())", "(()()((((())))))()()", "(()()(((()((()))))))", "(()()(((()(()())))))", "(()()(((()(())()))))", "(()()(((()(()))())))", "(()()(((()(())))()))", "(()()(((()(()))))())", "(()()(((()(())))))()", "(()()(((()()(())))))", "(()()(((()()()()))))", "(()()(((()()())())))", "(()()(((()()()))()))", "(()()(((()()())))())", "(()()(((()()()))))()", "(()()(((()())(()))))", "(()()(((()())()())))", "(()()(((()())())()))", "(()()(((()())()))())", "(()()(((()())())))()", "(()()(((()()))(())))", "(()()(((()()))()()))", "(()()(((()()))())())", "(()()(((()()))()))()", "(()()(((()())))(()))", "(()()(((()())))()())", "(()()(((()())))())()", "(()()(((()()))))(())", "(()()(((()()))))()()", "(()()(((())((())))))", "(()()(((())(()()))))", "(()()(((())(())())))", "(()()(((())(()))()))", "(()()(((())(())))())", "(()()(((())(()))))()", "(()()(((())()(()))))", "(()()(((())()()())))", "(()()(((())()())()))", "(()()(((())()()))())", "(()()(((())()())))()", "(()()(((())())(())))", "(()()(((())())()()))", "(()()(((())())())())", "(()()(((())())()))()", "(()()(((())()))(()))", "(()()(((())()))()())", "(()()(((())()))())()", "(()()(((())())))(())", "(()()(((())())))()()", "(()()(((()))((()))))", "(()()(((()))(()())))", "(()()(((()))(())()))", "(()()(((()))(()))())", "(()()(((()))(())))()", "(()()(((()))()(())))", "(()()(((()))()()()))", "(()()(((()))()())())", "(()()(((()))()()))()", "(()()(((()))())(()))", "(()()(((()))())()())", "(()()(((()))())())()", "(()()(((()))()))(())", "(()()(((()))()))()()", "(()()(((())))((())))", "(()()(((())))(()()))", "(()()(((())))(())())", "(()()(((())))(()))()", "(()()(((())))()(()))", "(()()(((())))()()())", "(()()(((())))()())()", "(()()(((())))())(())", "(()()(((())))())()()", "(()()(((()))))((()))", "(()()(((()))))(()())", "(()()(((()))))(())()", "(()()(((()))))()(())", "(()()(((()))))()()()", "(()()((()(((()))))))", "(()()((()((()())))))", "(()()((()((())()))))", "(()()((()((()))())))", "(()()((()((())))()))", "(()()((()((()))))())", "(()()((()((())))))()", "(()()((()(()(())))))", "(()()((()(()()()))))", "(()()((()(()())())))", "(()()((()(()()))()))", "(()()((()(()())))())", "(()()((()(()()))))()", "(()()((()(())(()))))", "(()()((()(())()())))", "(()()((()(())())()))", "(()()((()(())()))())", "(()()((()(())())))()", "(()()((()(()))(())))", "(()()((()(()))()()))", "(()()((()(()))())())", "(()()((()(()))()))()", "(()()((()(())))(()))", "(()()((()(())))()())", "(()()((()(())))())()", "(()()((()(()))))(())", "(()()((()(()))))()()", "(()()((()()((())))))", "(()()((()()(()()))))", "(()()((()()(())())))", "(()()((()()(()))()))", "(()()((()()(())))())", "(()()((()()(()))))()", "(()()((()()()(()))))", "(()()((()()()()())))", "(()()((()()()())()))", "(()()((()()()()))())", "(()()((()()()())))()", "(()()((()()())(())))", "(()()((()()())()()))", "(()()((()()())())())", "(()()((()()())()))()", "(()()((()()()))(()))", "(()()((()()()))()())", "(()()((()()()))())()", "(()()((()()())))(())", "(()()((()()())))()()", "(()()((()())((()))))", "(()()((()())(()())))", "(()()((()())(())()))", "(()()((()())(()))())", "(()()((()())(())))()", "(()()((()())()(())))", "(()()((()())()()()))", "(()()((()())()())())", "(()()((()())()()))()", "(()()((()())())(()))", "(()()((()())())()())", "(()()((()())())())()", "(()()((()())()))(())", "(()()((()())()))()()", "(()()((()()))((())))", "(()()((()()))(()()))", "(()()((()()))(())())", "(()()((()()))(()))()", "(()()((()()))()(()))", "(()()((()()))()()())", "(()()((()()))()())()", "(()()((()()))())(())", "(()()((()()))())()()", "(()()((()())))((()))", "(()()((()())))(()())", "(()()((()())))(())()", "(()()((()())))()(())", "(()()((()())))()()()", "(()()((())(((())))))", "(()()((())((()()))))", "(()()((())((())())))", "(()()((())((()))()))", "(()()((())((())))())", "(()()((())((()))))()", "(()()((())(()(()))))", "(()()((())(()()())))", "(()()((())(()())()))", "(()()((())(()()))())", "(()()((())(()())))()", "(()()((())(())(())))", "(()()((())(())()()))", "(()()((())(())())())", "(()()((())(())()))()", "(()()((())(()))(()))", "(()()((())(()))()())", "(()()((())(()))())()", "(()()((())(())))(())", "(()()((())(())))()()", "(()()((())()((()))))", "(()()((())()(()())))", "(()()((())()(())()))", "(()()((())()(()))())", "(()()((())()(())))()", "(()()((())()()(())))", "(()()((())()()()()))", "(()()((())()()())())", "(()()((())()()()))()", "(()()((())()())(()))", "(()()((())()())()())", "(()()((())()())())()", "(()()((())()()))(())", "(()()((())()()))()()", "(()()((())())((())))", "(()()((())())(()()))", "(()()((())())(())())", "(()()((())())(()))()", "(()()((())())()(()))", "(()()((())())()()())", "(()()((())())()())()", "(()()((())())())(())", "(()()((())())())()()", "(()()((())()))((()))", "(()()((())()))(()())", "(()()((())()))(())()", "(()()((())()))()(())", "(()()((())()))()()()", "(()()((()))(((()))))", "(()()((()))((()())))", "(()()((()))((())()))", "(()()((()))((()))())", "(()()((()))((())))()", "(()()((()))(()(())))", "(()()((()))(()()()))", "(()()((()))(()())())", "(()()((()))(()()))()", "(()()((()))(())(()))", "(()()((()))(())()())", "(()()((()))(())())()", "(()()((()))(()))(())", "(()()((()))(()))()()", "(()()((()))()((())))", "(()()((()))()(()()))", "(()()((()))()(())())", "(()()((()))()(()))()", "(()()((()))()()(()))", "(()()((()))()()()())", "(()()((()))()()())()", "(()()((()))()())(())", "(()()((()))()())()()", "(()()((()))())((()))", "(()()((()))())(()())", "(()()((()))())(())()", "(()()((()))())()(())", "(()()((()))())()()()", "(()()((())))(((())))", "(()()((())))((()()))", "(()()((())))((())())", "(()()((())))((()))()", "(()()((())))(()(()))", "(()()((())))(()()())", "(()()((())))(()())()", "(()()((())))(())(())", "(()()((())))(())()()", "(()()((())))()((()))", "(()()((())))()(()())", "(()()((())))()(())()", "(()()((())))()()(())", "(()()((())))()()()()", "(()()(()((((()))))))", "(()()(()(((()())))))", "(()()(()(((())()))))", "(()()(()(((()))())))", "(()()(()(((())))()))", "(()()(()(((()))))())", "(()()(()(((())))))()", "(()()(()((()(())))))", "(()()(()((()()()))))", "(()()(()((()())())))", "(()()(()((()()))()))", "(()()(()((()())))())", "(()()(()((()()))))()", "(()()(()((())(()))))", "(()()(()((())()())))", "(()()(()((())())()))", "(()()(()((())()))())", "(()()(()((())())))()", "(()()(()((()))(())))", "(()()(()((()))()()))", "(()()(()((()))())())", "(()()(()((()))()))()", "(()()(()((())))(()))", "(()()(()((())))()())", "(()()(()((())))())()", "(()()(()((()))))(())", "(()()(()((()))))()()", "(()()(()(()((())))))", "(()()(()(()(()()))))", "(()()(()(()(())())))", "(()()(()(()(()))()))", "(()()(()(()(())))())", "(()()(()(()(()))))()", "(()()(()(()()(()))))", "(()()(()(()()()())))", "(()()(()(()()())()))", "(()()(()(()()()))())", "(()()(()(()()())))()", "(()()(()(()())(())))", "(()()(()(()())()()))", "(()()(()(()())())())", "(()()(()(()())()))()", "(()()(()(()()))(()))", "(()()(()(()()))()())", "(()()(()(()()))())()", "(()()(()(()())))(())", "(()()(()(()())))()()", "(()()(()(())((()))))", "(()()(()(())(()())))", "(()()(()(())(())()))", "(()()(()(())(()))())", "(()()(()(())(())))()", "(()()(()(())()(())))", "(()()(()(())()()()))", "(()()(()(())()())())", "(()()(()(())()()))()", "(()()(()(())())(()))", "(()()(()(())())()())", "(()()(()(())())())()", "(()()(()(())()))(())", "(()()(()(())()))()()", "(()()(()(()))((())))", "(()()(()(()))(()()))", "(()()(()(()))(())())", "(()()(()(()))(()))()", "(()()(()(()))()(()))", "(()()(()(()))()()())", "(()()(()(()))()())()", "(()()(()(()))())(())", "(()()(()(()))())()()", "(()()(()(())))((()))", "(()()(()(())))(()())", "(()()(()(())))(())()", "(()()(()(())))()(())", "(()()(()(())))()()()", "(()()(()()(((())))))", "(()()(()()((()()))))", "(()()(()()((())())))", "(()()(()()((()))()))", "(()()(()()((())))())", "(()()(()()((()))))()", "(()()(()()(()(()))))", "(()()(()()(()()())))", "(()()(()()(()())()))", "(()()(()()(()()))())", "(()()(()()(()())))()", "(()()(()()(())(())))", "(()()(()()(())()()))", "(()()(()()(())())())", "(()()(()()(())()))()", "(()()(()()(()))(()))", "(()()(()()(()))()())", "(()()(()()(()))())()", "(()()(()()(())))(())", "(()()(()()(())))()()", "(()()(()()()((()))))", "(()()(()()()(()())))", "(()()(()()()(())()))", "(()()(()()()(()))())", "(()()(()()()(())))()", "(()()(()()()()(())))", "(()()(()()()()()()))", "(()()(()()()()())())", "(()()(()()()()()))()", "(()()(()()()())(()))", "(()()(()()()())()())", "(()()(()()()())())()", "(()()(()()()()))(())", "(()()(()()()()))()()", "(()()(()()())((())))", "(()()(()()())(()()))", "(()()(()()())(())())", "(()()(()()())(()))()", "(()()(()()())()(()))", "(()()(()()())()()())", "(()()(()()())()())()", "(()()(()()())())(())", "(()()(()()())())()()", "(()()(()()()))((()))", "(()()(()()()))(()())", "(()()(()()()))(())()", "(()()(()()()))()(())", "(()()(()()()))()()()", "(()()(()())(((()))))", "(()()(()())((()())))", "(()()(()())((())()))", "(()()(()())((()))())", "(()()(()())((())))()", "(()()(()())(()(())))", "(()()(()())(()()()))", "(()()(()())(()())())", "(()()(()())(()()))()", "(()()(()())(())(()))", "(()()(()())(())()())", "(()()(()())(())())()", "(()()(()())(()))(())", "(()()(()())(()))()()", "(()()(()())()((())))", "(()()(()())()(()()))", "(()()(()())()(())())", "(()()(()())()(()))()", "(()()(()())()()(()))", "(()()(()())()()()())", "(()()(()())()()())()", "(()()(()())()())(())", "(()()(()())()())()()", "(()()(()())())((()))", "(()()(()())())(()())", "(()()(()())())(())()", "(()()(()())())()(())", "(()()(()())())()()()", "(()()(()()))(((())))", "(()()(()()))((()()))", "(()()(()()))((())())", "(()()(()()))((()))()", "(()()(()()))(()(()))", "(()()(()()))(()()())", "(()()(()()))(()())()", "(()()(()()))(())(())", "(()()(()()))(())()()", "(()()(()()))()((()))", "(()()(()()))()(()())", "(()()(()()))()(())()", "(()()(()()))()()(())", "(()()(()()))()()()()", "(()()(())((((())))))", "(()()(())(((()()))))", "(()()(())(((())())))", "(()()(())(((()))()))", "(()()(())(((())))())", "(()()(())(((()))))()", "(()()(())((()(()))))", "(()()(())((()()())))", "(()()(())((()())()))", "(()()(())((()()))())", "(()()(())((()())))()", "(()()(())((())(())))", "(()()(())((())()()))", "(()()(())((())())())", "(()()(())((())()))()", "(()()(())((()))(()))", "(()()(())((()))()())", "(()()(())((()))())()", "(()()(())((())))(())", "(()()(())((())))()()", "(()()(())(()((()))))", "(()()(())(()(()())))", "(()()(())(()(())()))", "(()()(())(()(()))())", "(()()(())(()(())))()", "(()()(())(()()(())))", "(()()(())(()()()()))", "(()()(())(()()())())", "(()()(())(()()()))()", "(()()(())(()())(()))", "(()()(())(()())()())", "(()()(())(()())())()", "(()()(())(()()))(())", "(()()(())(()()))()()", "(()()(())(())((())))", "(()()(())(())(()()))", "(()()(())(())(())())", "(()()(())(())(()))()", "(()()(())(())()(()))", "(()()(())(())()()())", "(()()(())(())()())()", "(()()(())(())())(())", "(()()(())(())())()()", "(()()(())(()))((()))", "(()()(())(()))(()())", "(()()(())(()))(())()", "(()()(())(()))()(())", "(()()(())(()))()()()", "(()()(())()(((()))))", "(()()(())()((()())))", "(()()(())()((())()))", "(()()(())()((()))())", "(()()(())()((())))()", "(()()(())()(()(())))", "(()()(())()(()()()))", "(()()(())()(()())())", "(()()(())()(()()))()", "(()()(())()(())(()))", "(()()(())()(())()())", "(()()(())()(())())()", "(()()(())()(()))(())", "(()()(())()(()))()()", "(()()(())()()((())))", "(()()(())()()(()()))", "(()()(())()()(())())", "(()()(())()()(()))()", "(()()(())()()()(()))", "(()()(())()()()()())", "(()()(())()()()())()", "(()()(())()()())(())", "(()()(())()()())()()", "(()()(())()())((()))", "(()()(())()())(()())", "(()()(())()())(())()", "(()()(())()())()(())", "(()()(())()())()()()", "(()()(())())(((())))", "(()()(())())((()()))", "(()()(())())((())())", "(()()(())())((()))()", "(()()(())())(()(()))", "(()()(())())(()()())", "(()()(())())(()())()", "(()()(())())(())(())", "(()()(())())(())()()", "(()()(())())()((()))", "(()()(())())()(()())", "(()()(())())()(())()", "(()()(())())()()(())", "(()()(())())()()()()", "(()()(()))((((()))))", "(()()(()))(((()())))", "(()()(()))(((())()))", "(()()(()))(((()))())", "(()()(()))(((())))()", "(()()(()))((()(())))", "(()()(()))((()()()))", "(()()(()))((()())())", "(()()(()))((()()))()", "(()()(()))((())(()))", "(()()(()))((())()())", "(()()(()))((())())()", "(()()(()))((()))(())", "(()()(()))((()))()()", "(()()(()))(()((())))", "(()()(()))(()(()()))", "(()()(()))(()(())())", "(()()(()))(()(()))()", "(()()(()))(()()(()))", "(()()(()))(()()()())", "(()()(()))(()()())()", "(()()(()))(()())(())", "(()()(()))(()())()()", "(()()(()))(())((()))", "(()()(()))(())(()())", "(()()(()))(())(())()", "(()()(()))(())()(())", "(()()(()))(())()()()", "(()()(()))()(((())))", "(()()(()))()((()()))", "(()()(()))()((())())", "(()()(()))()((()))()", "(()()(()))()(()(()))", "(()()(()))()(()()())", "(()()(()))()(()())()", "(()()(()))()(())(())", "(()()(()))()(())()()", "(()()(()))()()((()))", "(()()(()))()()(()())", "(()()(()))()()(())()", "(()()(()))()()()(())", "(()()(()))()()()()()", "(()()()(((((()))))))", "(()()()((((()())))))", "(()()()((((())()))))", "(()()()((((()))())))", "(()()()((((())))()))", "(()()()((((()))))())", "(()()()((((())))))()", "(()()()(((()(())))))", "(()()()(((()()()))))", "(()()()(((()())())))", "(()()()(((()()))()))", "(()()()(((()())))())", "(()()()(((()()))))()", "(()()()(((())(()))))", "(()()()(((())()())))", "(()()()(((())())()))", "(()()()(((())()))())", "(()()()(((())())))()", "(()()()(((()))(())))", "(()()()(((()))()()))", "(()()()(((()))())())", "(()()()(((()))()))()", "(()()()(((())))(()))", "(()()()(((())))()())", "(()()()(((())))())()", "(()()()(((()))))(())", "(()()()(((()))))()()", "(()()()((()((())))))", "(()()()((()(()()))))", "(()()()((()(())())))", "(()()()((()(()))()))", "(()()()((()(())))())", "(()()()((()(()))))()", "(()()()((()()(()))))", "(()()()((()()()())))", "(()()()((()()())()))", "(()()()((()()()))())", "(()()()((()()())))()", "(()()()((()())(())))", "(()()()((()())()()))", "(()()()((()())())())", "(()()()((()())()))()", "(()()()((()()))(()))", "(()()()((()()))()())", "(()()()((()()))())()", "(()()()((()())))(())", "(()()()((()())))()()", "(()()()((())((()))))", "(()()()((())(()())))", "(()()()((())(())()))", "(()()()((())(()))())", "(()()()((())(())))()", "(()()()((())()(())))", "(()()()((())()()()))", "(()()()((())()())())", "(()()()((())()()))()", "(()()()((())())(()))", "(()()()((())())()())", "(()()()((())())())()", "(()()()((())()))(())", "(()()()((())()))()()", "(()()()((()))((())))", "(()()()((()))(()()))", "(()()()((()))(())())", "(()()()((()))(()))()", "(()()()((()))()(()))", "(()()()((()))()()())", "(()()()((()))()())()", "(()()()((()))())(())", "(()()()((()))())()()", "(()()()((())))((()))", "(()()()((())))(()())", "(()()()((())))(())()", "(()()()((())))()(())", "(()()()((())))()()()", "(()()()(()(((())))))", "(()()()(()((()()))))", "(()()()(()((())())))", "(()()()(()((()))()))", "(()()()(()((())))())", "(()()()(()((()))))()", "(()()()(()(()(()))))", "(()()()(()(()()())))", "(()()()(()(()())()))", "(()()()(()(()()))())", "(()()()(()(()())))()", "(()()()(()(())(())))", "(()()()(()(())()()))", "(()()()(()(())())())", "(()()()(()(())()))()", "(()()()(()(()))(()))", "(()()()(()(()))()())", "(()()()(()(()))())()", "(()()()(()(())))(())", "(()()()(()(())))()()", "(()()()(()()((()))))", "(()()()(()()(()())))", "(()()()(()()(())()))", "(()()()(()()(()))())", "(()()()(()()(())))()", "(()()()(()()()(())))", "(()()()(()()()()()))", "(()()()(()()()())())", "(()()()(()()()()))()", "(()()()(()()())(()))", "(()()()(()()())()())", "(()()()(()()())())()", "(()()()(()()()))(())", "(()()()(()()()))()()", "(()()()(()())((())))", "(()()()(()())(()()))", "(()()()(()())(())())", "(()()()(()())(()))()", "(()()()(()())()(()))", "(()()()(()())()()())", "(()()()(()())()())()", "(()()()(()())())(())", "(()()()(()())())()()", "(()()()(()()))((()))", "(()()()(()()))(()())", "(()()()(()()))(())()", "(()()()(()()))()(())", "(()()()(()()))()()()", "(()()()(())(((()))))", "(()()()(())((()())))", "(()()()(())((())()))", "(()()()(())((()))())", "(()()()(())((())))()", "(()()()(())(()(())))", "(()()()(())(()()()))", "(()()()(())(()())())", "(()()()(())(()()))()", "(()()()(())(())(()))", "(()()()(())(())()())", "(()()()(())(())())()", "(()()()(())(()))(())", "(()()()(())(()))()()", "(()()()(())()((())))", "(()()()(())()(()()))", "(()()()(())()(())())", "(()()()(())()(()))()", "(()()()(())()()(()))", "(()()()(())()()()())", "(()()()(())()()())()", "(()()()(())()())(())", "(()()()(())()())()()", "(()()()(())())((()))", "(()()()(())())(()())", "(()()()(())())(())()", "(()()()(())())()(())", "(()()()(())())()()()", "(()()()(()))(((())))", "(()()()(()))((()()))", "(()()()(()))((())())", "(()()()(()))((()))()", "(()()()(()))(()(()))", "(()()()(()))(()()())", "(()()()(()))(()())()", "(()()()(()))(())(())", "(()()()(()))(())()()", "(()()()(()))()((()))", "(()()()(()))()(()())", "(()()()(()))()(())()", "(()()()(()))()()(())", "(()()()(()))()()()()", "(()()()()((((())))))", "(()()()()(((()()))))", "(()()()()(((())())))", "(()()()()(((()))()))", "(()()()()(((())))())", "(()()()()(((()))))()", "(()()()()((()(()))))", "(()()()()((()()())))", "(()()()()((()())()))", "(()()()()((()()))())", "(()()()()((()())))()", "(()()()()((())(())))", "(()()()()((())()()))", "(()()()()((())())())", "(()()()()((())()))()", "(()()()()((()))(()))", "(()()()()((()))()())", "(()()()()((()))())()", "(()()()()((())))(())", "(()()()()((())))()()", "(()()()()(()((()))))", "(()()()()(()(()())))", "(()()()()(()(())()))", "(()()()()(()(()))())", "(()()()()(()(())))()", "(()()()()(()()(())))", "(()()()()(()()()()))", "(()()()()(()()())())", "(()()()()(()()()))()", "(()()()()(()())(()))", "(()()()()(()())()())", "(()()()()(()())())()", "(()()()()(()()))(())", "(()()()()(()()))()()", "(()()()()(())((())))", "(()()()()(())(()()))", "(()()()()(())(())())", "(()()()()(())(()))()", "(()()()()(())()(()))", "(()()()()(())()()())", "(()()()()(())()())()", "(()()()()(())())(())", "(()()()()(())())()()", "(()()()()(()))((()))", "(()()()()(()))(()())", "(()()()()(()))(())()", "(()()()()(()))()(())", "(()()()()(()))()()()", "(()()()()()(((()))))", "(()()()()()((()())))", "(()()()()()((())()))", "(()()()()()((()))())", "(()()()()()((())))()", "(()()()()()(()(())))", "(()()()()()(()()()))", "(()()()()()(()())())", "(()()()()()(()()))()", "(()()()()()(())(()))", "(()()()()()(())()())", "(()()()()()(())())()", "(()()()()()(()))(())", "(()()()()()(()))()()", "(()()()()()()((())))", "(()()()()()()(()()))", "(()()()()()()(())())", "(()()()()()()(()))()", "(()()()()()()()(()))", "(()()()()()()()()())", "(()()()()()()()())()", "(()()()()()()())(())", "(()()()()()()())()()", "(()()()()()())((()))", "(()()()()()())(()())", "(()()()()()())(())()", "(()()()()()())()(())", "(()()()()()())()()()", "(()()()()())(((())))", "(()()()()())((()()))", "(()()()()())((())())", "(()()()()())((()))()", "(()()()()())(()(()))", "(()()()()())(()()())", "(()()()()())(()())()", "(()()()()())(())(())", "(()()()()())(())()()", "(()()()()())()((()))", "(()()()()())()(()())", "(()()()()())()(())()", "(()()()()())()()(())", "(()()()()())()()()()", "(()()()())((((()))))", "(()()()())(((()())))", "(()()()())(((())()))", "(()()()())(((()))())", "(()()()())(((())))()", "(()()()())((()(())))", "(()()()())((()()()))", "(()()()())((()())())", "(()()()())((()()))()", "(()()()())((())(()))", "(()()()())((())()())", "(()()()())((())())()", "(()()()())((()))(())", "(()()()())((()))()()", "(()()()())(()((())))", "(()()()())(()(()()))", "(()()()())(()(())())", "(()()()())(()(()))()", "(()()()())(()()(()))", "(()()()())(()()()())", "(()()()())(()()())()", "(()()()())(()())(())", "(()()()())(()())()()", "(()()()())(())((()))", "(()()()())(())(()())", "(()()()())(())(())()", "(()()()())(())()(())", "(()()()())(())()()()", "(()()()())()(((())))", "(()()()())()((()()))", "(()()()())()((())())", "(()()()())()((()))()", "(()()()())()(()(()))", "(()()()())()(()()())", "(()()()())()(()())()", "(()()()())()(())(())", "(()()()())()(())()()", "(()()()())()()((()))", "(()()()())()()(()())", "(()()()())()()(())()", "(()()()())()()()(())", "(()()()())()()()()()", "(()()())(((((())))))", "(()()())((((()()))))", "(()()())((((())())))", "(()()())((((()))()))", "(()()())((((())))())", "(()()())((((()))))()", "(()()())(((()(()))))", "(()()())(((()()())))", "(()()())(((()())()))", "(()()())(((()()))())", "(()()())(((()())))()", "(()()())(((())(())))", "(()()())(((())()()))", "(()()())(((())())())", "(()()())(((())()))()", "(()()())(((()))(()))", "(()()())(((()))()())", "(()()())(((()))())()", "(()()())(((())))(())", "(()()())(((())))()()", "(()()())((()((()))))", "(()()())((()(()())))", "(()()())((()(())()))", "(()()())((()(()))())", "(()()())((()(())))()", "(()()())((()()(())))", "(()()())((()()()()))", "(()()())((()()())())", "(()()())((()()()))()", "(()()())((()())(()))", "(()()())((()())()())", "(()()())((()())())()", "(()()())((()()))(())", "(()()())((()()))()()", "(()()())((())((())))", "(()()())((())(()()))", "(()()())((())(())())", "(()()())((())(()))()", "(()()())((())()(()))", "(()()())((())()()())", "(()()())((())()())()", "(()()())((())())(())", "(()()())((())())()()", "(()()())((()))((()))", "(()()())((()))(()())", "(()()())((()))(())()", "(()()())((()))()(())", "(()()())((()))()()()", "(()()())(()(((()))))", "(()()())(()((()())))", "(()()())(()((())()))", "(()()())(()((()))())", "(()()())(()((())))()", "(()()())(()(()(())))", "(()()())(()(()()()))", "(()()())(()(()())())", "(()()())(()(()()))()", "(()()())(()(())(()))", "(()()())(()(())()())", "(()()())(()(())())()", "(()()())(()(()))(())", "(()()())(()(()))()()", "(()()())(()()((())))", "(()()())(()()(()()))", "(()()())(()()(())())", "(()()())(()()(()))()", "(()()())(()()()(()))", "(()()())(()()()()())", "(()()())(()()()())()", "(()()())(()()())(())", "(()()())(()()())()()", "(()()())(()())((()))", "(()()())(()())(()())", "(()()())(()())(())()", "(()()())(()())()(())", "(()()())(()())()()()", "(()()())(())(((())))", "(()()())(())((()()))", "(()()())(())((())())", "(()()())(())((()))()", "(()()())(())(()(()))", "(()()())(())(()()())", "(()()())(())(()())()", "(()()())(())(())(())", "(()()())(())(())()()", "(()()())(())()((()))", "(()()())(())()(()())", "(()()())(())()(())()", "(()()())(())()()(())", "(()()())(())()()()()", "(()()())()((((()))))", "(()()())()(((()())))", "(()()())()(((())()))", "(()()())()(((()))())", "(()()())()(((())))()", "(()()())()((()(())))", "(()()())()((()()()))", "(()()())()((()())())", "(()()())()((()()))()", "(()()())()((())(()))", "(()()())()((())()())", "(()()())()((())())()", "(()()())()((()))(())", "(()()())()((()))()()", "(()()())()(()((())))", "(()()())()(()(()()))", "(()()())()(()(())())", "(()()())()(()(()))()", "(()()())()(()()(()))", "(()()())()(()()()())", "(()()())()(()()())()", "(()()())()(()())(())", "(()()())()(()())()()", "(()()())()(())((()))", "(()()())()(())(()())", "(()()())()(())(())()", "(()()())()(())()(())", "(()()())()(())()()()", "(()()())()()(((())))", "(()()())()()((()()))", "(()()())()()((())())", "(()()())()()((()))()", "(()()())()()(()(()))", "(()()())()()(()()())", "(()()())()()(()())()", "(()()())()()(())(())", "(()()())()()(())()()", "(()()())()()()((()))", "(()()())()()()(()())", "(()()())()()()(())()", "(()()())()()()()(())", "(()()())()()()()()()", "(()())((((((()))))))", "(()())(((((()())))))", "(()())(((((())()))))", "(()())(((((()))())))", "(()())(((((())))()))", "(()())(((((()))))())", "(()())(((((())))))()", "(()())((((()(())))))", "(()())((((()()()))))", "(()())((((()())())))", "(()())((((()()))()))", "(()())((((()())))())", "(()())((((()()))))()", "(()())((((())(()))))", "(()())((((())()())))", "(()())((((())())()))", "(()())((((())()))())", "(()())((((())())))()", "(()())((((()))(())))", "(()())((((()))()()))", "(()())((((()))())())", "(()())((((()))()))()", "(()())((((())))(()))", "(()())((((())))()())", "(()())((((())))())()", "(()())((((()))))(())", "(()())((((()))))()()", "(()())(((()((())))))", "(()())(((()(()()))))", "(()())(((()(())())))", "(()())(((()(()))()))", "(()())(((()(())))())", "(()())(((()(()))))()", "(()())(((()()(()))))", "(()())(((()()()())))", "(()())(((()()())()))", "(()())(((()()()))())", "(()())(((()()())))()", "(()())(((()())(())))", "(()())(((()())()()))", "(()())(((()())())())", "(()())(((()())()))()", "(()())(((()()))(()))", "(()())(((()()))()())", "(()())(((()()))())()", "(()())(((()())))(())", "(()())(((()())))()()", "(()())(((())((()))))", "(()())(((())(()())))", "(()())(((())(())()))", "(()())(((())(()))())", "(()())(((())(())))()", "(()())(((())()(())))", "(()())(((())()()()))", "(()())(((())()())())", "(()())(((())()()))()", "(()())(((())())(()))", "(()())(((())())()())", "(()())(((())())())()", "(()())(((())()))(())", "(()())(((())()))()()", "(()())(((()))((())))", "(()())(((()))(()()))", "(()())(((()))(())())", "(()())(((()))(()))()", "(()())(((()))()(()))", "(()())(((()))()()())", "(()())(((()))()())()", "(()())(((()))())(())", "(()())(((()))())()()", "(()())(((())))((()))", "(()())(((())))(()())", "(()())(((())))(())()", "(()())(((())))()(())", "(()())(((())))()()()", "(()())((()(((())))))", "(()())((()((()()))))", "(()())((()((())())))", "(()())((()((()))()))", "(()())((()((())))())", "(()())((()((()))))()", "(()())((()(()(()))))", "(()())((()(()()())))", "(()())((()(()())()))", "(()())((()(()()))())", "(()())((()(()())))()", "(()())((()(())(())))", "(()())((()(())()()))", "(()())((()(())())())", "(()())((()(())()))()", "(()())((()(()))(()))", "(()())((()(()))()())", "(()())((()(()))())()", "(()())((()(())))(())", "(()())((()(())))()()", "(()())((()()((()))))", "(()())((()()(()())))", "(()())((()()(())()))", "(()())((()()(()))())", "(()())((()()(())))()", "(()())((()()()(())))", "(()())((()()()()()))", "(()())((()()()())())", "(()())((()()()()))()", "(()())((()()())(()))", "(()())((()()())()())", "(()())((()()())())()", "(()())((()()()))(())", "(()())((()()()))()()", "(()())((()())((())))", "(()())((()())(()()))", "(()())((()())(())())", "(()())((()())(()))()", "(()())((()())()(()))", "(()())((()())()()())", "(()())((()())()())()", "(()())((()())())(())", "(()())((()())())()()", "(()())((()()))((()))", "(()())((()()))(()())", "(()())((()()))(())()", "(()())((()()))()(())", "(()())((()()))()()()", "(()())((())(((()))))", "(()())((())((()())))", "(()())((())((())()))", "(()())((())((()))())", "(()())((())((())))()", "(()())((())(()(())))", "(()())((())(()()()))", "(()())((())(()())())", "(()())((())(()()))()", "(()())((())(())(()))", "(()())((())(())()())", "(()())((())(())())()", "(()())((())(()))(())", "(()())((())(()))()()", "(()())((())()((())))", "(()())((())()(()()))", "(()())((())()(())())", "(()())((())()(()))()", "(()())((())()()(()))", "(()())((())()()()())", "(()())((())()()())()", "(()())((())()())(())", "(()())((())()())()()", "(()())((())())((()))", "(()())((())())(()())", "(()())((())())(())()", "(()())((())())()(())", "(()())((())())()()()", "(()())((()))(((())))", "(()())((()))((()()))", "(()())((()))((())())", "(()())((()))((()))()", "(()())((()))(()(()))", "(()())((()))(()()())", "(()())((()))(()())()", "(()())((()))(())(())", "(()())((()))(())()()", "(()())((()))()((()))", "(()())((()))()(()())", "(()())((()))()(())()", "(()())((()))()()(())", "(()())((()))()()()()", "(()())(()((((())))))", "(()())(()(((()()))))", "(()())(()(((())())))", "(()())(()(((()))()))", "(()())(()(((())))())", "(()())(()(((()))))()", "(()())(()((()(()))))", "(()())(()((()()())))", "(()())(()((()())()))", "(()())(()((()()))())", "(()())(()((()())))()", "(()())(()((())(())))", "(()())(()((())()()))", "(()())(()((())())())", "(()())(()((())()))()", "(()())(()((()))(()))", "(()())(()((()))()())", "(()())(()((()))())()", "(()())(()((())))(())", "(()())(()((())))()()", "(()())(()(()((()))))", "(()())(()(()(()())))", "(()())(()(()(())()))", "(()())(()(()(()))())", "(()())(()(()(())))()", "(()())(()(()()(())))", "(()())(()(()()()()))", "(()())(()(()()())())", "(()())(()(()()()))()", "(()())(()(()())(()))", "(()())(()(()())()())", "(()())(()(()())())()", "(()())(()(()()))(())", "(()())(()(()()))()()", "(()())(()(())((())))", "(()())(()(())(()()))", "(()())(()(())(())())", "(()())(()(())(()))()", "(()())(()(())()(()))", "(()())(()(())()()())", "(()())(()(())()())()", "(()())(()(())())(())", "(()())(()(())())()()", "(()())(()(()))((()))", "(()())(()(()))(()())", "(()())(()(()))(())()", "(()())(()(()))()(())", "(()())(()(()))()()()", "(()())(()()(((()))))", "(()())(()()((()())))", "(()())(()()((())()))", "(()())(()()((()))())", "(()())(()()((())))()", "(()())(()()(()(())))", "(()())(()()(()()()))", "(()())(()()(()())())", "(()())(()()(()()))()", "(()())(()()(())(()))", "(()())(()()(())()())", "(()())(()()(())())()", "(()())(()()(()))(())", "(()())(()()(()))()()", "(()())(()()()((())))", "(()())(()()()(()()))", "(()())(()()()(())())", "(()())(()()()(()))()", "(()())(()()()()(()))", "(()())(()()()()()())", "(()())(()()()()())()", "(()())(()()()())(())", "(()())(()()()())()()", "(()())(()()())((()))", "(()())(()()())(()())", "(()())(()()())(())()", "(()())(()()())()(())", "(()())(()()())()()()", "(()())(()())(((())))", "(()())(()())((()()))", "(()())(()())((())())", "(()())(()())((()))()", "(()())(()())(()(()))", "(()())(()())(()()())", "(()())(()())(()())()", "(()())(()())(())(())", "(()())(()())(())()()", "(()())(()())()((()))", "(()())(()())()(()())", "(()())(()())()(())()", "(()())(()())()()(())", "(()())(()())()()()()", "(()())(())((((()))))", "(()())(())(((()())))", "(()())(())(((())()))", "(()())(())(((()))())", "(()())(())(((())))()", "(()())(())((()(())))", "(()())(())((()()()))", "(()())(())((()())())", "(()())(())((()()))()", "(()())(())((())(()))", "(()())(())((())()())", "(()())(())((())())()", "(()())(())((()))(())", "(()())(())((()))()()", "(()())(())(()((())))", "(()())(())(()(()()))", "(()())(())(()(())())", "(()())(())(()(()))()", "(()())(())(()()(()))", "(()())(())(()()()())", "(()())(())(()()())()", "(()())(())(()())(())", "(()())(())(()())()()", "(()())(())(())((()))", "(()())(())(())(()())", "(()())(())(())(())()", "(()())(())(())()(())", "(()())(())(())()()()", "(()())(())()(((())))", "(()())(())()((()()))", "(()())(())()((())())", "(()())(())()((()))()", "(()())(())()(()(()))", "(()())(())()(()()())", "(()())(())()(()())()", "(()())(())()(())(())", "(()())(())()(())()()", "(()())(())()()((()))", "(()())(())()()(()())", "(()())(())()()(())()", "(()())(())()()()(())", "(()())(())()()()()()", "(()())()(((((())))))", "(()())()((((()()))))", "(()())()((((())())))", "(()())()((((()))()))", "(()())()((((())))())", "(()())()((((()))))()", "(()())()(((()(()))))", "(()())()(((()()())))", "(()())()(((()())()))", "(()())()(((()()))())", "(()())()(((()())))()", "(()())()(((())(())))", "(()())()(((())()()))", "(()())()(((())())())", "(()())()(((())()))()", "(()())()(((()))(()))", "(()())()(((()))()())", "(()())()(((()))())()", "(()())()(((())))(())", "(()())()(((())))()()", "(()())()((()((()))))", "(()())()((()(()())))", "(()())()((()(())()))", "(()())()((()(()))())", "(()())()((()(())))()", "(()())()((()()(())))", "(()())()((()()()()))", "(()())()((()()())())", "(()())()((()()()))()", "(()())()((()())(()))", "(()())()((()())()())", "(()())()((()())())()", "(()())()((()()))(())", "(()())()((()()))()()", "(()())()((())((())))", "(()())()((())(()()))", "(()())()((())(())())", "(()())()((())(()))()", "(()())()((())()(()))", "(()())()((())()()())", "(()())()((())()())()", "(()())()((())())(())", "(()())()((())())()()", "(()())()((()))((()))", "(()())()((()))(()())", "(()())()((()))(())()", "(()())()((()))()(())", "(()())()((()))()()()", "(()())()(()(((()))))", "(()())()(()((()())))", "(()())()(()((())()))", "(()())()(()((()))())", "(()())()(()((())))()", "(()())()(()(()(())))", "(()())()(()(()()()))", "(()())()(()(()())())", "(()())()(()(()()))()", "(()())()(()(())(()))", "(()())()(()(())()())", "(()())()(()(())())()", "(()())()(()(()))(())", "(()())()(()(()))()()", "(()())()(()()((())))", "(()())()(()()(()()))", "(()())()(()()(())())", "(()())()(()()(()))()", "(()())()(()()()(()))", "(()())()(()()()()())", "(()())()(()()()())()", "(()())()(()()())(())", "(()())()(()()())()()", "(()())()(()())((()))", "(()())()(()())(()())", "(()())()(()())(())()", "(()())()(()())()(())", "(()())()(()())()()()", "(()())()(())(((())))", "(()())()(())((()()))", "(()())()(())((())())", "(()())()(())((()))()", "(()())()(())(()(()))", "(()())()(())(()()())", "(()())()(())(()())()", "(()())()(())(())(())", "(()())()(())(())()()", "(()())()(())()((()))", "(()())()(())()(()())", "(()())()(())()(())()", "(()())()(())()()(())", "(()())()(())()()()()", "(()())()()((((()))))", "(()())()()(((()())))", "(()())()()(((())()))", "(()())()()(((()))())", "(()())()()(((())))()", "(()())()()((()(())))", "(()())()()((()()()))", "(()())()()((()())())", "(()())()()((()()))()", "(()())()()((())(()))", "(()())()()((())()())", "(()())()()((())())()", "(()())()()((()))(())", "(()())()()((()))()()", "(()())()()(()((())))", "(()())()()(()(()()))", "(()())()()(()(())())", "(()())()()(()(()))()", "(()())()()(()()(()))", "(()())()()(()()()())", "(()())()()(()()())()", "(()())()()(()())(())", "(()())()()(()())()()", "(()())()()(())((()))", "(()())()()(())(()())", "(()())()()(())(())()", "(()())()()(())()(())", "(()())()()(())()()()", "(()())()()()(((())))", "(()())()()()((()()))", "(()())()()()((())())", "(()())()()()((()))()", "(()())()()()(()(()))", "(()())()()()(()()())", "(()())()()()(()())()", "(()())()()()(())(())", "(()())()()()(())()()", "(()())()()()()((()))", "(()())()()()()(()())", "(()())()()()()(())()", "(()())()()()()()(())", "(()())()()()()()()()", "(())(((((((())))))))", "(())((((((()()))))))", "(())((((((())())))))", "(())((((((()))()))))", "(())((((((())))())))", "(())((((((()))))()))", "(())((((((())))))())", "(())((((((()))))))()", "(())(((((()(()))))))", "(())(((((()()())))))", "(())(((((()())()))))", "(())(((((()()))())))", "(())(((((()())))()))", "(())(((((()()))))())", "(())(((((()())))))()", "(())(((((())(())))))", "(())(((((())()()))))", "(())(((((())())())))", "(())(((((())()))()))", "(())(((((())())))())", "(())(((((())()))))()", "(())(((((()))(()))))", "(())(((((()))()())))", "(())(((((()))())()))", "(())(((((()))()))())", "(())(((((()))())))()", "(())(((((())))(())))", "(())(((((())))()()))", "(())(((((())))())())", "(())(((((())))()))()", "(())(((((()))))(()))", "(())(((((()))))()())", "(())(((((()))))())()", "(())(((((())))))(())", "(())(((((())))))()()", "(())((((()((()))))))", "(())((((()(()())))))", "(())((((()(())()))))", "(())((((()(()))())))", "(())((((()(())))()))", "(())((((()(()))))())", "(())((((()(())))))()", "(())((((()()(())))))", "(())((((()()()()))))", "(())((((()()())())))", "(())((((()()()))()))", "(())((((()()())))())", "(())((((()()()))))()", "(())((((()())(()))))", "(())((((()())()())))", "(())((((()())())()))", "(())((((()())()))())", "(())((((()())())))()", "(())((((()()))(())))", "(())((((()()))()()))", "(())((((()()))())())", "(())((((()()))()))()", "(())((((()())))(()))", "(())((((()())))()())", "(())((((()())))())()", "(())((((()()))))(())", "(())((((()()))))()()", "(())((((())((())))))", "(())((((())(()()))))", "(())((((())(())())))", "(())((((())(()))()))", "(())((((())(())))())", "(())((((())(()))))()", "(())((((())()(()))))", "(())((((())()()())))", "(())((((())()())()))", "(())((((())()()))())", "(())((((())()())))()", "(())((((())())(())))", "(())((((())())()()))", "(())((((())())())())", "(())((((())())()))()", "(())((((())()))(()))", "(())((((())()))()())", "(())((((())()))())()", "(())((((())())))(())", "(())((((())())))()()", "(())((((()))((()))))", "(())((((()))(()())))", "(())((((()))(())()))", "(())((((()))(()))())", "(())((((()))(())))()", "(())((((()))()(())))", "(())((((()))()()()))", "(())((((()))()())())", "(())((((()))()()))()", "(())((((()))())(()))", "(())((((()))())()())", "(())((((()))())())()", "(())((((()))()))(())", "(())((((()))()))()()", "(())((((())))((())))", "(())((((())))(()()))", "(())((((())))(())())", "(())((((())))(()))()", "(())((((())))()(()))", "(())((((())))()()())", "(())((((())))()())()", "(())((((())))())(())", "(())((((())))())()()", "(())((((()))))((()))", "(())((((()))))(()())", "(())((((()))))(())()", "(())((((()))))()(())", "(())((((()))))()()()", "(())(((()(((()))))))", "(())(((()((()())))))", "(())(((()((())()))))", "(())(((()((()))())))", "(())(((()((())))()))", "(())(((()((()))))())", "(())(((()((())))))()", "(())(((()(()(())))))", "(())(((()(()()()))))", "(())(((()(()())())))", "(())(((()(()()))()))", "(())(((()(()())))())", "(())(((()(()()))))()", "(())(((()(())(()))))", "(())(((()(())()())))", "(())(((()(())())()))", "(())(((()(())()))())", "(())(((()(())())))()", "(())(((()(()))(())))", "(())(((()(()))()()))", "(())(((()(()))())())", "(())(((()(()))()))()", "(())(((()(())))(()))", "(())(((()(())))()())", "(())(((()(())))())()", "(())(((()(()))))(())", "(())(((()(()))))()()", "(())(((()()((())))))", "(())(((()()(()()))))", "(())(((()()(())())))", "(())(((()()(()))()))", "(())(((()()(())))())", "(())(((()()(()))))()", "(())(((()()()(()))))", "(())(((()()()()())))", "(())(((()()()())()))", "(())(((()()()()))())", "(())(((()()()())))()", "(())(((()()())(())))", "(())(((()()())()()))", "(())(((()()())())())", "(())(((()()())()))()", "(())(((()()()))(()))", "(())(((()()()))()())", "(())(((()()()))())()", "(())(((()()())))(())", "(())(((()()())))()()", "(())(((()())((()))))", "(())(((()())(()())))", "(())(((()())(())()))", "(())(((()())(()))())", "(())(((()())(())))()", "(())(((()())()(())))", "(())(((()())()()()))", "(())(((()())()())())", "(())(((()())()()))()", "(())(((()())())(()))", "(())(((()())())()())", "(())(((()())())())()", "(())(((()())()))(())", "(())(((()())()))()()", "(())(((()()))((())))", "(())(((()()))(()()))", "(())(((()()))(())())", "(())(((()()))(()))()", "(())(((()()))()(()))", "(())(((()()))()()())", "(())(((()()))()())()", "(())(((()()))())(())", "(())(((()()))())()()", "(())(((()())))((()))", "(())(((()())))(()())", "(())(((()())))(())()", "(())(((()())))()(())", "(())(((()())))()()()", "(())(((())(((())))))", "(())(((())((()()))))", "(())(((())((())())))", "(())(((())((()))()))", "(())(((())((())))())", "(())(((())((()))))()", "(())(((())(()(()))))", "(())(((())(()()())))", "(())(((())(()())()))", "(())(((())(()()))())", "(())(((())(()())))()", "(())(((())(())(())))", "(())(((())(())()()))", "(())(((())(())())())", "(())(((())(())()))()", "(())(((())(()))(()))", "(())(((())(()))()())", "(())(((())(()))())()", "(())(((())(())))(())", "(())(((())(())))()()", "(())(((())()((()))))", "(())(((())()(()())))", "(())(((())()(())()))", "(())(((())()(()))())", "(())(((())()(())))()", "(())(((())()()(())))", "(())(((())()()()()))", "(())(((())()()())())", "(())(((())()()()))()", "(())(((())()())(()))", "(())(((())()())()())", "(())(((())()())())()", "(())(((())()()))(())", "(())(((())()()))()()", "(())(((())())((())))", "(())(((())())(()()))", "(())(((())())(())())", "(())(((())())(()))()", "(())(((())())()(()))", "(())(((())())()()())", "(())(((())())()())()", "(())(((())())())(())", "(())(((())())())()()", "(())(((())()))((()))", "(())(((())()))(()())", "(())(((())()))(())()", "(())(((())()))()(())", "(())(((())()))()()()", "(())(((()))(((()))))", "(())(((()))((()())))", "(())(((()))((())()))", "(())(((()))((()))())", "(())(((()))((())))()", "(())(((()))(()(())))", "(())(((()))(()()()))", "(())(((()))(()())())", "(())(((()))(()()))()", "(())(((()))(())(()))", "(())(((()))(())()())", "(())(((()))(())())()", "(())(((()))(()))(())", "(())(((()))(()))()()", "(())(((()))()((())))", "(())(((()))()(()()))", "(())(((()))()(())())", "(())(((()))()(()))()", "(())(((()))()()(()))", "(())(((()))()()()())", "(())(((()))()()())()", "(())(((()))()())(())", "(())(((()))()())()()", "(())(((()))())((()))", "(())(((()))())(()())", "(())(((()))())(())()", "(())(((()))())()(())", "(())(((()))())()()()", "(())(((())))(((())))", "(())(((())))((()()))", "(())(((())))((())())", "(())(((())))((()))()", "(())(((())))(()(()))", "(())(((())))(()()())", "(())(((())))(()())()", "(())(((())))(())(())", "(())(((())))(())()()", "(())(((())))()((()))", "(())(((())))()(()())", "(())(((())))()(())()", "(())(((())))()()(())", "(())(((())))()()()()", "(())((()((((()))))))", "(())((()(((()())))))", "(())((()(((())()))))", "(())((()(((()))())))", "(())((()(((())))()))", "(())((()(((()))))())", "(())((()(((())))))()", "(())((()((()(())))))", "(())((()((()()()))))", "(())((()((()())())))", "(())((()((()()))()))", "(())((()((()())))())", "(())((()((()()))))()", "(())((()((())(()))))", "(())((()((())()())))", "(())((()((())())()))", "(())((()((())()))())", "(())((()((())())))()", "(())((()((()))(())))", "(())((()((()))()()))", "(())((()((()))())())", "(())((()((()))()))()", "(())((()((())))(()))", "(())((()((())))()())", "(())((()((())))())()", "(())((()((()))))(())", "(())((()((()))))()()", "(())((()(()((())))))", "(())((()(()(()()))))", "(())((()(()(())())))", "(())((()(()(()))()))", "(())((()(()(())))())", "(())((()(()(()))))()", "(())((()(()()(()))))", "(())((()(()()()())))", "(())((()(()()())()))", "(())((()(()()()))())", "(())((()(()()())))()", "(())((()(()())(())))", "(())((()(()())()()))", "(())((()(()())())())", "(())((()(()())()))()", "(())((()(()()))(()))", "(())((()(()()))()())", "(())((()(()()))())()", "(())((()(()())))(())", "(())((()(()())))()()", "(())((()(())((()))))", "(())((()(())(()())))", "(())((()(())(())()))", "(())((()(())(()))())", "(())((()(())(())))()", "(())((()(())()(())))", "(())((()(())()()()))", "(())((()(())()())())", "(())((()(())()()))()", "(())((()(())())(()))", "(())((()(())())()())", "(())((()(())())())()", "(())((()(())()))(())", "(())((()(())()))()()", "(())((()(()))((())))", "(())((()(()))(()()))", "(())((()(()))(())())", "(())((()(()))(()))()", "(())((()(()))()(()))", "(())((()(()))()()())", "(())((()(()))()())()", "(())((()(()))())(())", "(())((()(()))())()()", "(())((()(())))((()))", "(())((()(())))(()())", "(())((()(())))(())()", "(())((()(())))()(())", "(())((()(())))()()()", "(())((()()(((())))))", "(())((()()((()()))))", "(())((()()((())())))", "(())((()()((()))()))", "(())((()()((())))())", "(())((()()((()))))()", "(())((()()(()(()))))", "(())((()()(()()())))", "(())((()()(()())()))", "(())((()()(()()))())", "(())((()()(()())))()", "(())((()()(())(())))", "(())((()()(())()()))", "(())((()()(())())())", "(())((()()(())()))()", "(())((()()(()))(()))", "(())((()()(()))()())", "(())((()()(()))())()", "(())((()()(())))(())", "(())((()()(())))()()", "(())((()()()((()))))", "(())((()()()(()())))", "(())((()()()(())()))", "(())((()()()(()))())", "(())((()()()(())))()", "(())((()()()()(())))", "(())((()()()()()()))", "(())((()()()()())())", "(())((()()()()()))()", "(())((()()()())(()))", "(())((()()()())()())", "(())((()()()())())()", "(())((()()()()))(())", "(())((()()()()))()()", "(())((()()())((())))", "(())((()()())(()()))", "(())((()()())(())())", "(())((()()())(()))()", "(())((()()())()(()))", "(())((()()())()()())", "(())((()()())()())()", "(())((()()())())(())", "(())((()()())())()()", "(())((()()()))((()))", "(())((()()()))(()())", "(())((()()()))(())()", "(())((()()()))()(())", "(())((()()()))()()()", "(())((()())(((()))))", "(())((()())((()())))", "(())((()())((())()))", "(())((()())((()))())", "(())((()())((())))()", "(())((()())(()(())))", "(())((()())(()()()))", "(())((()())(()())())", "(())((()())(()()))()", "(())((()())(())(()))", "(())((()())(())()())", "(())((()())(())())()", "(())((()())(()))(())", "(())((()())(()))()()", "(())((()())()((())))", "(())((()())()(()()))", "(())((()())()(())())", "(())((()())()(()))()", "(())((()())()()(()))", "(())((()())()()()())", "(())((()())()()())()", "(())((()())()())(())", "(())((()())()())()()", "(())((()())())((()))", "(())((()())())(()())", "(())((()())())(())()", "(())((()())())()(())", "(())((()())())()()()", "(())((()()))(((())))", "(())((()()))((()()))", "(())((()()))((())())", "(())((()()))((()))()", "(())((()()))(()(()))", "(())((()()))(()()())", "(())((()()))(()())()", "(())((()()))(())(())", "(())((()()))(())()()", "(())((()()))()((()))", "(())((()()))()(()())", "(())((()()))()(())()", "(())((()()))()()(())", "(())((()()))()()()()", "(())((())((((())))))", "(())((())(((()()))))", "(())((())(((())())))", "(())((())(((()))()))", "(())((())(((())))())", "(())((())(((()))))()", "(())((())((()(()))))", "(())((())((()()())))", "(())((())((()())()))", "(())((())((()()))())", "(())((())((()())))()", "(())((())((())(())))", "(())((())((())()()))", "(())((())((())())())", "(())((())((())()))()", "(())((())((()))(()))", "(())((())((()))()())", "(())((())((()))())()", "(())((())((())))(())", "(())((())((())))()()", "(())((())(()((()))))", "(())((())(()(()())))", "(())((())(()(())()))", "(())((())(()(()))())", "(())((())(()(())))()", "(())((())(()()(())))", "(())((())(()()()()))", "(())((())(()()())())", "(())((())(()()()))()", "(())((())(()())(()))", "(())((())(()())()())", "(())((())(()())())()", "(())((())(()()))(())", "(())((())(()()))()()", "(())((())(())((())))", "(())((())(())(()()))", "(())((())(())(())())", "(())((())(())(()))()", "(())((())(())()(()))", "(())((())(())()()())", "(())((())(())()())()", "(())((())(())())(())", "(())((())(())())()()", "(())((())(()))((()))", "(())((())(()))(()())", "(())((())(()))(())()", "(())((())(()))()(())", "(())((())(()))()()()", "(())((())()(((()))))", "(())((())()((()())))", "(())((())()((())()))", "(())((())()((()))())", "(())((())()((())))()", "(())((())()(()(())))", "(())((())()(()()()))", "(())((())()(()())())", "(())((())()(()()))()", "(())((())()(())(()))", "(())((())()(())()())", "(())((())()(())())()", "(())((())()(()))(())", "(())((())()(()))()()", "(())((())()()((())))", "(())((())()()(()()))", "(())((())()()(())())", "(())((())()()(()))()", "(())((())()()()(()))", "(())((())()()()()())", "(())((())()()()())()", "(())((())()()())(())", "(())((())()()())()()", "(())((())()())((()))", "(())((())()())(()())", "(())((())()())(())()", "(())((())()())()(())", "(())((())()())()()()", "(())((())())(((())))", "(())((())())((()()))", "(())((())())((())())", "(())((())())((()))()", "(())((())())(()(()))", "(())((())())(()()())", "(())((())())(()())()", "(())((())())(())(())", "(())((())())(())()()", "(())((())())()((()))", "(())((())())()(()())", "(())((())())()(())()", "(())((())())()()(())", "(())((())())()()()()", "(())((()))((((()))))", "(())((()))(((()())))", "(())((()))(((())()))", "(())((()))(((()))())", "(())((()))(((())))()", "(())((()))((()(())))", "(())((()))((()()()))", "(())((()))((()())())", "(())((()))((()()))()", "(())((()))((())(()))", "(())((()))((())()())", "(())((()))((())())()", "(())((()))((()))(())", "(())((()))((()))()()", "(())((()))(()((())))", "(())((()))(()(()()))", "(())((()))(()(())())", "(())((()))(()(()))()", "(())((()))(()()(()))", "(())((()))(()()()())", "(())((()))(()()())()", "(())((()))(()())(())", "(())((()))(()())()()", "(())((()))(())((()))", "(())((()))(())(()())", "(())((()))(())(())()", "(())((()))(())()(())", "(())((()))(())()()()", "(())((()))()(((())))", "(())((()))()((()()))", "(())((()))()((())())", "(())((()))()((()))()", "(())((()))()(()(()))", "(())((()))()(()()())", "(())((()))()(()())()", "(())((()))()(())(())", "(())((()))()(())()()", "(())((()))()()((()))", "(())((()))()()(()())", "(())((()))()()(())()", "(())((()))()()()(())", "(())((()))()()()()()", "(())(()(((((()))))))", "(())(()((((()())))))", "(())(()((((())()))))", "(())(()((((()))())))", "(())(()((((())))()))", "(())(()((((()))))())", "(())(()((((())))))()", "(())(()(((()(())))))", "(())(()(((()()()))))", "(())(()(((()())())))", "(())(()(((()()))()))", "(())(()(((()())))())", "(())(()(((()()))))()", "(())(()(((())(()))))", "(())(()(((())()())))", "(())(()(((())())()))", "(())(()(((())()))())", "(())(()(((())())))()", "(())(()(((()))(())))", "(())(()(((()))()()))", "(())(()(((()))())())", "(())(()(((()))()))()", "(())(()(((())))(()))", "(())(()(((())))()())", "(())(()(((())))())()", "(())(()(((()))))(())", "(())(()(((()))))()()", "(())(()((()((())))))", "(())(()((()(()()))))", "(())(()((()(())())))", "(())(()((()(()))()))", "(())(()((()(())))())", "(())(()((()(()))))()", "(())(()((()()(()))))", "(())(()((()()()())))", "(())(()((()()())()))", "(())(()((()()()))())", "(())(()((()()())))()", "(())(()((()())(())))", "(())(()((()())()()))", "(())(()((()())())())", "(())(()((()())()))()", "(())(()((()()))(()))", "(())(()((()()))()())", "(())(()((()()))())()", "(())(()((()())))(())", "(())(()((()())))()()", "(())(()((())((()))))", "(())(()((())(()())))", "(())(()((())(())()))", "(())(()((())(()))())", "(())(()((())(())))()", "(())(()((())()(())))", "(())(()((())()()()))", "(())(()((())()())())", "(())(()((())()()))()", "(())(()((())())(()))", "(())(()((())())()())", "(())(()((())())())()", "(())(()((())()))(())", "(())(()((())()))()()", "(())(()((()))((())))", "(())(()((()))(()()))", "(())(()((()))(())())", "(())(()((()))(()))()", "(())(()((()))()(()))", "(())(()((()))()()())", "(())(()((()))()())()", "(())(()((()))())(())", "(())(()((()))())()()", "(())(()((())))((()))", "(())(()((())))(()())", "(())(()((())))(())()", "(())(()((())))()(())", "(())(()((())))()()()", "(())(()(()(((())))))", "(())(()(()((()()))))", "(())(()(()((())())))", "(())(()(()((()))()))", "(())(()(()((())))())", "(())(()(()((()))))()", "(())(()(()(()(()))))", "(())(()(()(()()())))", "(())(()(()(()())()))", "(())(()(()(()()))())", "(())(()(()(()())))()", "(())(()(()(())(())))", "(())(()(()(())()()))", "(())(()(()(())())())", "(())(()(()(())()))()", "(())(()(()(()))(()))", "(())(()(()(()))()())", "(())(()(()(()))())()", "(())(()(()(())))(())", "(())(()(()(())))()()", "(())(()(()()((()))))", "(())(()(()()(()())))", "(())(()(()()(())()))", "(())(()(()()(()))())", "(())(()(()()(())))()", "(())(()(()()()(())))", "(())(()(()()()()()))", "(())(()(()()()())())", "(())(()(()()()()))()", "(())(()(()()())(()))", "(())(()(()()())()())", "(())(()(()()())())()", "(())(()(()()()))(())", "(())(()(()()()))()()", "(())(()(()())((())))", "(())(()(()())(()()))", "(())(()(()())(())())", "(())(()(()())(()))()", "(())(()(()())()(()))", "(())(()(()())()()())", "(())(()(()())()())()", "(())(()(()())())(())", "(())(()(()())())()()", "(())(()(()()))((()))", "(())(()(()()))(()())", "(())(()(()()))(())()", "(())(()(()()))()(())", "(())(()(()()))()()()", "(())(()(())(((()))))", "(())(()(())((()())))", "(())(()(())((())()))", "(())(()(())((()))())", "(())(()(())((())))()", "(())(()(())(()(())))", "(())(()(())(()()()))", "(())(()(())(()())())", "(())(()(())(()()))()", "(())(()(())(())(()))", "(())(()(())(())()())", "(())(()(())(())())()", "(())(()(())(()))(())", "(())(()(())(()))()()", "(())(()(())()((())))", "(())(()(())()(()()))", "(())(()(())()(())())", "(())(()(())()(()))()", "(())(()(())()()(()))", "(())(()(())()()()())", "(())(()(())()()())()", "(())(()(())()())(())", "(())(()(())()())()()", "(())(()(())())((()))", "(())(()(())())(()())", "(())(()(())())(())()", "(())(()(())())()(())", "(())(()(())())()()()", "(())(()(()))(((())))", "(())(()(()))((()()))", "(())(()(()))((())())", "(())(()(()))((()))()", "(())(()(()))(()(()))", "(())(()(()))(()()())", "(())(()(()))(()())()", "(())(()(()))(())(())", "(())(()(()))(())()()", "(())(()(()))()((()))", "(())(()(()))()(()())", "(())(()(()))()(())()", "(())(()(()))()()(())", "(())(()(()))()()()()", "(())(()()((((())))))", "(())(()()(((()()))))", "(())(()()(((())())))", "(())(()()(((()))()))", "(())(()()(((())))())", "(())(()()(((()))))()", "(())(()()((()(()))))", "(())(()()((()()())))", "(())(()()((()())()))", "(())(()()((()()))())", "(())(()()((()())))()", "(())(()()((())(())))", "(())(()()((())()()))", "(())(()()((())())())", "(())(()()((())()))()", "(())(()()((()))(()))", "(())(()()((()))()())", "(())(()()((()))())()", "(())(()()((())))(())", "(())(()()((())))()()", "(())(()()(()((()))))", "(())(()()(()(()())))", "(())(()()(()(())()))", "(())(()()(()(()))())", "(())(()()(()(())))()", "(())(()()(()()(())))", "(())(()()(()()()()))", "(())(()()(()()())())", "(())(()()(()()()))()", "(())(()()(()())(()))", "(())(()()(()())()())", "(())(()()(()())())()", "(())(()()(()()))(())", "(())(()()(()()))()()", "(())(()()(())((())))", "(())(()()(())(()()))", "(())(()()(())(())())", "(())(()()(())(()))()", "(())(()()(())()(()))", "(())(()()(())()()())", "(())(()()(())()())()", "(())(()()(())())(())", "(())(()()(())())()()", "(())(()()(()))((()))", "(())(()()(()))(()())", "(())(()()(()))(())()", "(())(()()(()))()(())", "(())(()()(()))()()()", "(())(()()()(((()))))", "(())(()()()((()())))", "(())(()()()((())()))", "(())(()()()((()))())", "(())(()()()((())))()", "(())(()()()(()(())))", "(())(()()()(()()()))", "(())(()()()(()())())", "(())(()()()(()()))()", "(())(()()()(())(()))", "(())(()()()(())()())", "(())(()()()(())())()", "(())(()()()(()))(())", "(())(()()()(()))()()", "(())(()()()()((())))", "(())(()()()()(()()))", "(())(()()()()(())())", "(())(()()()()(()))()", "(())(()()()()()(()))", "(())(()()()()()()())", "(())(()()()()()())()", "(())(()()()()())(())", "(())(()()()()())()()", "(())(()()()())((()))", "(())(()()()())(()())", "(())(()()()())(())()", "(())(()()()())()(())", "(())(()()()())()()()", "(())(()()())(((())))", "(())(()()())((()()))", "(())(()()())((())())", "(())(()()())((()))()", "(())(()()())(()(()))", "(())(()()())(()()())", "(())(()()())(()())()", "(())(()()())(())(())", "(())(()()())(())()()", "(())(()()())()((()))", "(())(()()())()(()())", "(())(()()())()(())()", "(())(()()())()()(())", "(())(()()())()()()()", "(())(()())((((()))))", "(())(()())(((()())))", "(())(()())(((())()))", "(())(()())(((()))())", "(())(()())(((())))()", "(())(()())((()(())))", "(())(()())((()()()))", "(())(()())((()())())", "(())(()())((()()))()", "(())(()())((())(()))", "(())(()())((())()())", "(())(()())((())())()", "(())(()())((()))(())", "(())(()())((()))()()", "(())(()())(()((())))", "(())(()())(()(()()))", "(())(()())(()(())())", "(())(()())(()(()))()", "(())(()())(()()(()))", "(())(()())(()()()())", "(())(()())(()()())()", "(())(()())(()())(())", "(())(()())(()())()()", "(())(()())(())((()))", "(())(()())(())(()())", "(())(()())(())(())()", "(())(()())(())()(())", "(())(()())(())()()()", "(())(()())()(((())))", "(())(()())()((()()))", "(())(()())()((())())", "(())(()())()((()))()", "(())(()())()(()(()))", "(())(()())()(()()())", "(())(()())()(()())()", "(())(()())()(())(())", "(())(()())()(())()()", "(())(()())()()((()))", "(())(()())()()(()())", "(())(()())()()(())()", "(())(()())()()()(())", "(())(()())()()()()()", "(())(())(((((())))))", "(())(())((((()()))))", "(())(())((((())())))", "(())(())((((()))()))", "(())(())((((())))())", "(())(())((((()))))()", "(())(())(((()(()))))", "(())(())(((()()())))", "(())(())(((()())()))", "(())(())(((()()))())", "(())(())(((()())))()", "(())(())(((())(())))", "(())(())(((())()()))", "(())(())(((())())())", "(())(())(((())()))()", "(())(())(((()))(()))", "(())(())(((()))()())", "(())(())(((()))())()", "(())(())(((())))(())", "(())(())(((())))()()", "(())(())((()((()))))", "(())(())((()(()())))", "(())(())((()(())()))", "(())(())((()(()))())", "(())(())((()(())))()", "(())(())((()()(())))", "(())(())((()()()()))", "(())(())((()()())())", "(())(())((()()()))()", "(())(())((()())(()))", "(())(())((()())()())", "(())(())((()())())()", "(())(())((()()))(())", "(())(())((()()))()()", "(())(())((())((())))", "(())(())((())(()()))", "(())(())((())(())())", "(())(())((())(()))()", "(())(())((())()(()))", "(())(())((())()()())", "(())(())((())()())()", "(())(())((())())(())", "(())(())((())())()()", "(())(())((()))((()))", "(())(())((()))(()())", "(())(())((()))(())()", "(())(())((()))()(())", "(())(())((()))()()()", "(())(())(()(((()))))", "(())(())(()((()())))", "(())(())(()((())()))", "(())(())(()((()))())", "(())(())(()((())))()", "(())(())(()(()(())))", "(())(())(()(()()()))", "(())(())(()(()())())", "(())(())(()(()()))()", "(())(())(()(())(()))", "(())(())(()(())()())", "(())(())(()(())())()", "(())(())(()(()))(())", "(())(())(()(()))()()", "(())(())(()()((())))", "(())(())(()()(()()))", "(())(())(()()(())())", "(())(())(()()(()))()", "(())(())(()()()(()))", "(())(())(()()()()())", "(())(())(()()()())()", "(())(())(()()())(())", "(())(())(()()())()()", "(())(())(()())((()))", "(())(())(()())(()())", "(())(())(()())(())()", "(())(())(()())()(())", "(())(())(()())()()()", "(())(())(())(((())))", "(())(())(())((()()))", "(())(())(())((())())", "(())(())(())((()))()", "(())(())(())(()(()))", "(())(())(())(()()())", "(())(())(())(()())()", "(())(())(())(())(())", "(())(())(())(())()()", "(())(())(())()((()))", "(())(())(())()(()())", "(())(())(())()(())()", "(())(())(())()()(())", "(())(())(())()()()()", "(())(())()((((()))))", "(())(())()(((()())))", "(())(())()(((())()))", "(())(())()(((()))())", "(())(())()(((())))()", "(())(())()((()(())))", "(())(())()((()()()))", "(())(())()((()())())", "(())(())()((()()))()", "(())(())()((())(()))", "(())(())()((())()())", "(())(())()((())())()", "(())(())()((()))(())", "(())(())()((()))()()", "(())(())()(()((())))", "(())(())()(()(()()))", "(())(())()(()(())())", "(())(())()(()(()))()", "(())(())()(()()(()))", "(())(())()(()()()())", "(())(())()(()()())()", "(())(())()(()())(())", "(())(())()(()())()()", "(())(())()(())((()))", "(())(())()(())(()())", "(())(())()(())(())()", "(())(())()(())()(())", "(())(())()(())()()()", "(())(())()()(((())))", "(())(())()()((()()))", "(())(())()()((())())", "(())(())()()((()))()", "(())(())()()(()(()))", "(())(())()()(()()())", "(())(())()()(()())()", "(())(())()()(())(())", "(())(())()()(())()()", "(())(())()()()((()))", "(())(())()()()(()())", "(())(())()()()(())()", "(())(())()()()()(())", "(())(())()()()()()()", "(())()((((((()))))))", "(())()(((((()())))))", "(())()(((((())()))))", "(())()(((((()))())))", "(())()(((((())))()))", "(())()(((((()))))())", "(())()(((((())))))()", "(())()((((()(())))))", "(())()((((()()()))))", "(())()((((()())())))", "(())()((((()()))()))", "(())()((((()())))())", "(())()((((()()))))()", "(())()((((())(()))))", "(())()((((())()())))", "(())()((((())())()))", "(())()((((())()))())", "(())()((((())())))()", "(())()((((()))(())))", "(())()((((()))()()))", "(())()((((()))())())", "(())()((((()))()))()", "(())()((((())))(()))", "(())()((((())))()())", "(())()((((())))())()", "(())()((((()))))(())", "(())()((((()))))()()", "(())()(((()((())))))", "(())()(((()(()()))))", "(())()(((()(())())))", "(())()(((()(()))()))", "(())()(((()(())))())", "(())()(((()(()))))()", "(())()(((()()(()))))", "(())()(((()()()())))", "(())()(((()()())()))", "(())()(((()()()))())", "(())()(((()()())))()", "(())()(((()())(())))", "(())()(((()())()()))", "(())()(((()())())())", "(())()(((()())()))()", "(())()(((()()))(()))", "(())()(((()()))()())", "(())()(((()()))())()", "(())()(((()())))(())", "(())()(((()())))()()", "(())()(((())((()))))", "(())()(((())(()())))", "(())()(((())(())()))", "(())()(((())(()))())", "(())()(((())(())))()", "(())()(((())()(())))", "(())()(((())()()()))", "(())()(((())()())())", "(())()(((())()()))()", "(())()(((())())(()))", "(())()(((())())()())", "(())()(((())())())()", "(())()(((())()))(())", "(())()(((())()))()()", "(())()(((()))((())))", "(())()(((()))(()()))", "(())()(((()))(())())", "(())()(((()))(()))()", "(())()(((()))()(()))", "(())()(((()))()()())", "(())()(((()))()())()", "(())()(((()))())(())", "(())()(((()))())()()", "(())()(((())))((()))", "(())()(((())))(()())", "(())()(((())))(())()", "(())()(((())))()(())", "(())()(((())))()()()", "(())()((()(((())))))", "(())()((()((()()))))", "(())()((()((())())))", "(())()((()((()))()))", "(())()((()((())))())", "(())()((()((()))))()", "(())()((()(()(()))))", "(())()((()(()()())))", "(())()((()(()())()))", "(())()((()(()()))())", "(())()((()(()())))()", "(())()((()(())(())))", "(())()((()(())()()))", "(())()((()(())())())", "(())()((()(())()))()", "(())()((()(()))(()))", "(())()((()(()))()())", "(())()((()(()))())()", "(())()((()(())))(())", "(())()((()(())))()()", "(())()((()()((()))))", "(())()((()()(()())))", "(())()((()()(())()))", "(())()((()()(()))())", "(())()((()()(())))()", "(())()((()()()(())))", "(())()((()()()()()))", "(())()((()()()())())", "(())()((()()()()))()", "(())()((()()())(()))", "(())()((()()())()())", "(())()((()()())())()", "(())()((()()()))(())", "(())()((()()()))()()", "(())()((()())((())))", "(())()((()())(()()))", "(())()((()())(())())", "(())()((()())(()))()", "(())()((()())()(()))", "(())()((()())()()())", "(())()((()())()())()", "(())()((()())())(())", "(())()((()())())()()", "(())()((()()))((()))", "(())()((()()))(()())", "(())()((()()))(())()", "(())()((()()))()(())", "(())()((()()))()()()", "(())()((())(((()))))", "(())()((())((()())))", "(())()((())((())()))", "(())()((())((()))())", "(())()((())((())))()", "(())()((())(()(())))", "(())()((())(()()()))", "(())()((())(()())())", "(())()((())(()()))()", "(())()((())(())(()))", "(())()((())(())()())", "(())()((())(())())()", "(())()((())(()))(())", "(())()((())(()))()()", "(())()((())()((())))", "(())()((())()(()()))", "(())()((())()(())())", "(())()((())()(()))()", "(())()((())()()(()))", "(())()((())()()()())", "(())()((())()()())()", "(())()((())()())(())", "(())()((())()())()()", "(())()((())())((()))", "(())()((())())(()())", "(())()((())())(())()", "(())()((())())()(())", "(())()((())())()()()", "(())()((()))(((())))", "(())()((()))((()()))", "(())()((()))((())())", "(())()((()))((()))()", "(())()((()))(()(()))", "(())()((()))(()()())", "(())()((()))(()())()", "(())()((()))(())(())", "(())()((()))(())()()", "(())()((()))()((()))", "(())()((()))()(()())", "(())()((()))()(())()", "(())()((()))()()(())", "(())()((()))()()()()", "(())()(()((((())))))", "(())()(()(((()()))))", "(())()(()(((())())))", "(())()(()(((()))()))", "(())()(()(((())))())", "(())()(()(((()))))()", "(())()(()((()(()))))", "(())()(()((()()())))", "(())()(()((()())()))", "(())()(()((()()))())", "(())()(()((()())))()", "(())()(()((())(())))", "(())()(()((())()()))", "(())()(()((())())())", "(())()(()((())()))()", "(())()(()((()))(()))", "(())()(()((()))()())", "(())()(()((()))())()", "(())()(()((())))(())", "(())()(()((())))()()", "(())()(()(()((()))))", "(())()(()(()(()())))", "(())()(()(()(())()))", "(())()(()(()(()))())", "(())()(()(()(())))()", "(())()(()(()()(())))", "(())()(()(()()()()))", "(())()(()(()()())())", "(())()(()(()()()))()", "(())()(()(()())(()))", "(())()(()(()())()())", "(())()(()(()())())()", "(())()(()(()()))(())", "(())()(()(()()))()()", "(())()(()(())((())))", "(())()(()(())(()()))", "(())()(()(())(())())", "(())()(()(())(()))()", "(())()(()(())()(()))", "(())()(()(())()()())", "(())()(()(())()())()", "(())()(()(())())(())", "(())()(()(())())()()", "(())()(()(()))((()))", "(())()(()(()))(()())", "(())()(()(()))(())()", "(())()(()(()))()(())", "(())()(()(()))()()()", "(())()(()()(((()))))", "(())()(()()((()())))", "(())()(()()((())()))", "(())()(()()((()))())", "(())()(()()((())))()", "(())()(()()(()(())))", "(())()(()()(()()()))", "(())()(()()(()())())", "(())()(()()(()()))()", "(())()(()()(())(()))", "(())()(()()(())()())", "(())()(()()(())())()", "(())()(()()(()))(())", "(())()(()()(()))()()", "(())()(()()()((())))", "(())()(()()()(()()))", "(())()(()()()(())())", "(())()(()()()(()))()", "(())()(()()()()(()))", "(())()(()()()()()())", "(())()(()()()()())()", "(())()(()()()())(())", "(())()(()()()())()()", "(())()(()()())((()))", "(())()(()()())(()())", "(())()(()()())(())()", "(())()(()()())()(())", "(())()(()()())()()()", "(())()(()())(((())))", "(())()(()())((()()))", "(())()(()())((())())", "(())()(()())((()))()", "(())()(()())(()(()))", "(())()(()())(()()())", "(())()(()())(()())()", "(())()(()())(())(())", "(())()(()())(())()()", "(())()(()())()((()))", "(())()(()())()(()())", "(())()(()())()(())()", "(())()(()())()()(())", "(())()(()())()()()()", "(())()(())((((()))))", "(())()(())(((()())))", "(())()(())(((())()))", "(())()(())(((()))())", "(())()(())(((())))()", "(())()(())((()(())))", "(())()(())((()()()))", "(())()(())((()())())", "(())()(())((()()))()", "(())()(())((())(()))", "(())()(())((())()())", "(())()(())((())())()", "(())()(())((()))(())", "(())()(())((()))()()", "(())()(())(()((())))", "(())()(())(()(()()))", "(())()(())(()(())())", "(())()(())(()(()))()", "(())()(())(()()(()))", "(())()(())(()()()())", "(())()(())(()()())()", "(())()(())(()())(())", "(())()(())(()())()()", "(())()(())(())((()))", "(())()(())(())(()())", "(())()(())(())(())()", "(())()(())(())()(())", "(())()(())(())()()()", "(())()(())()(((())))", "(())()(())()((()()))", "(())()(())()((())())", "(())()(())()((()))()", "(())()(())()(()(()))", "(())()(())()(()()())", "(())()(())()(()())()", "(())()(())()(())(())", "(())()(())()(())()()", "(())()(())()()((()))", "(())()(())()()(()())", "(())()(())()()(())()", "(())()(())()()()(())", "(())()(())()()()()()", "(())()()(((((())))))", "(())()()((((()()))))", "(())()()((((())())))", "(())()()((((()))()))", "(())()()((((())))())", "(())()()((((()))))()", "(())()()(((()(()))))", "(())()()(((()()())))", "(())()()(((()())()))", "(())()()(((()()))())", "(())()()(((()())))()", "(())()()(((())(())))", "(())()()(((())()()))", "(())()()(((())())())", "(())()()(((())()))()", "(())()()(((()))(()))", "(())()()(((()))()())", "(())()()(((()))())()", "(())()()(((())))(())", "(())()()(((())))()()", "(())()()((()((()))))", "(())()()((()(()())))", "(())()()((()(())()))", "(())()()((()(()))())", "(())()()((()(())))()", "(())()()((()()(())))", "(())()()((()()()()))", "(())()()((()()())())", "(())()()((()()()))()", "(())()()((()())(()))", "(())()()((()())()())", "(())()()((()())())()", "(())()()((()()))(())", "(())()()((()()))()()", "(())()()((())((())))", "(())()()((())(()()))", "(())()()((())(())())", "(())()()((())(()))()", "(())()()((())()(()))", "(())()()((())()()())", "(())()()((())()())()", "(())()()((())())(())", "(())()()((())())()()", "(())()()((()))((()))", "(())()()((()))(()())", "(())()()((()))(())()", "(())()()((()))()(())", "(())()()((()))()()()", "(())()()(()(((()))))", "(())()()(()((()())))", "(())()()(()((())()))", "(())()()(()((()))())", "(())()()(()((())))()", "(())()()(()(()(())))", "(())()()(()(()()()))", "(())()()(()(()())())", "(())()()(()(()()))()", "(())()()(()(())(()))", "(())()()(()(())()())", "(())()()(()(())())()", "(())()()(()(()))(())", "(())()()(()(()))()()", "(())()()(()()((())))", "(())()()(()()(()()))", "(())()()(()()(())())", "(())()()(()()(()))()", "(())()()(()()()(()))", "(())()()(()()()()())", "(())()()(()()()())()", "(())()()(()()())(())", "(())()()(()()())()()", "(())()()(()())((()))", "(())()()(()())(()())", "(())()()(()())(())()", "(())()()(()())()(())", "(())()()(()())()()()", "(())()()(())(((())))", "(())()()(())((()()))", "(())()()(())((())())", "(())()()(())((()))()", "(())()()(())(()(()))", "(())()()(())(()()())", "(())()()(())(()())()", "(())()()(())(())(())", "(())()()(())(())()()", "(())()()(())()((()))", "(())()()(())()(()())", "(())()()(())()(())()", "(())()()(())()()(())", "(())()()(())()()()()", "(())()()()((((()))))", "(())()()()(((()())))", "(())()()()(((())()))", "(())()()()(((()))())", "(())()()()(((())))()", "(())()()()((()(())))", "(())()()()((()()()))", "(())()()()((()())())", "(())()()()((()()))()", "(())()()()((())(()))", "(())()()()((())()())", "(())()()()((())())()", "(())()()()((()))(())", "(())()()()((()))()()", "(())()()()(()((())))", "(())()()()(()(()()))", "(())()()()(()(())())", "(())()()()(()(()))()", "(())()()()(()()(()))", "(())()()()(()()()())", "(())()()()(()()())()", "(())()()()(()())(())", "(())()()()(()())()()", "(())()()()(())((()))", "(())()()()(())(()())", "(())()()()(())(())()", "(())()()()(())()(())", "(())()()()(())()()()", "(())()()()()(((())))", "(())()()()()((()()))", "(())()()()()((())())", "(())()()()()((()))()", "(())()()()()(()(()))", "(())()()()()(()()())", "(())()()()()(()())()", "(())()()()()(())(())", "(())()()()()(())()()", "(())()()()()()((()))", "(())()()()()()(()())", "(())()()()()()(())()", "(())()()()()()()(())", "(())()()()()()()()()", "()((((((((()))))))))", "()(((((((()())))))))", "()(((((((())()))))))", "()(((((((()))())))))", "()(((((((())))()))))", "()(((((((()))))())))", "()(((((((())))))()))", "()(((((((()))))))())", "()(((((((())))))))()", "()((((((()(())))))))", "()((((((()()()))))))", "()((((((()())())))))", "()((((((()()))()))))", "()((((((()())))())))", "()((((((()()))))()))", "()((((((()())))))())", "()((((((()()))))))()", "()((((((())(()))))))", "()((((((())()())))))", "()((((((())())()))))", "()((((((())()))())))", "()((((((())())))()))", "()((((((())()))))())", "()((((((())())))))()", "()((((((()))(())))))", "()((((((()))()()))))", "()((((((()))())())))", "()((((((()))()))()))", "()((((((()))())))())", "()((((((()))()))))()", "()((((((())))(()))))", "()((((((())))()())))", "()((((((())))())()))", "()((((((())))()))())", "()((((((())))())))()", "()((((((()))))(())))", "()((((((()))))()()))", "()((((((()))))())())", "()((((((()))))()))()", "()((((((())))))(()))", "()((((((())))))()())", "()((((((())))))())()", "()((((((()))))))(())", "()((((((()))))))()()", "()(((((()((())))))))", "()(((((()(()()))))))", "()(((((()(())())))))", "()(((((()(()))()))))", "()(((((()(())))())))", "()(((((()(()))))()))", "()(((((()(())))))())", "()(((((()(()))))))()", "()(((((()()(()))))))", "()(((((()()()())))))", "()(((((()()())()))))", "()(((((()()()))())))", "()(((((()()())))()))", "()(((((()()()))))())", "()(((((()()())))))()", "()(((((()())(())))))", "()(((((()())()()))))", "()(((((()())())())))", "()(((((()())()))()))", "()(((((()())())))())", "()(((((()())()))))()", "()(((((()()))(()))))", "()(((((()()))()())))", "()(((((()()))())()))", "()(((((()()))()))())", "()(((((()()))())))()", "()(((((()())))(())))", "()(((((()())))()()))", "()(((((()())))())())", "()(((((()())))()))()", "()(((((()()))))(()))", "()(((((()()))))()())", "()(((((()()))))())()", "()(((((()())))))(())", "()(((((()())))))()()", "()(((((())((()))))))", "()(((((())(()())))))", "()(((((())(())()))))", "()(((((())(()))())))", "()(((((())(())))()))", "()(((((())(()))))())", "()(((((())(())))))()", "()(((((())()(())))))", "()(((((())()()()))))", "()(((((())()())())))", "()(((((())()()))()))", "()(((((())()())))())", "()(((((())()()))))()", "()(((((())())(()))))", "()(((((())())()())))", "()(((((())())())()))", "()(((((())())()))())", "()(((((())())())))()", "()(((((())()))(())))", "()(((((())()))()()))", "()(((((())()))())())", "()(((((())()))()))()", "()(((((())())))(()))", "()(((((())())))()())", "()(((((())())))())()", "()(((((())()))))(())", "()(((((())()))))()()", "()(((((()))((())))))", "()(((((()))(()()))))", "()(((((()))(())())))", "()(((((()))(()))()))", "()(((((()))(())))())", "()(((((()))(()))))()", "()(((((()))()(()))))", "()(((((()))()()())))", "()(((((()))()())()))", "()(((((()))()()))())", "()(((((()))()())))()", "()(((((()))())(())))", "()(((((()))())()()))", "()(((((()))())())())", "()(((((()))())()))()", "()(((((()))()))(()))", "()(((((()))()))()())", "()(((((()))()))())()", "()(((((()))())))(())", "()(((((()))())))()()", "()(((((())))((()))))", "()(((((())))(()())))", "()(((((())))(())()))", "()(((((())))(()))())", "()(((((())))(())))()", "()(((((())))()(())))", "()(((((())))()()()))", "()(((((())))()())())", "()(((((())))()()))()", "()(((((())))())(()))", "()(((((())))())()())", "()(((((())))())())()", "()(((((())))()))(())", "()(((((())))()))()()", "()(((((()))))((())))", "()(((((()))))(()()))", "()(((((()))))(())())", "()(((((()))))(()))()", "()(((((()))))()(()))", "()(((((()))))()()())", "()(((((()))))()())()", "()(((((()))))())(())", "()(((((()))))())()()", "()(((((())))))((()))", "()(((((())))))(()())", "()(((((())))))(())()", "()(((((())))))()(())", "()(((((())))))()()()", "()((((()(((())))))))", "()((((()((()()))))))", "()((((()((())())))))", "()((((()((()))()))))", "()((((()((())))())))", "()((((()((()))))()))", "()((((()((())))))())", "()((((()((()))))))()", "()((((()(()(()))))))", "()((((()(()()())))))", "()((((()(()())()))))", "()((((()(()()))())))", "()((((()(()())))()))", "()((((()(()()))))())", "()((((()(()())))))()", "()((((()(())(())))))", "()((((()(())()()))))", "()((((()(())())())))", "()((((()(())()))()))", "()((((()(())())))())", "()((((()(())()))))()", "()((((()(()))(()))))", "()((((()(()))()())))", "()((((()(()))())()))", "()((((()(()))()))())", "()((((()(()))())))()", "()((((()(())))(())))", "()((((()(())))()()))", "()((((()(())))())())", "()((((()(())))()))()", "()((((()(()))))(()))", "()((((()(()))))()())", "()((((()(()))))())()", "()((((()(())))))(())", "()((((()(())))))()()", "()((((()()((()))))))", "()((((()()(()())))))", "()((((()()(())()))))", "()((((()()(()))())))", "()((((()()(())))()))", "()((((()()(()))))())", "()((((()()(())))))()", "()((((()()()(())))))", "()((((()()()()()))))", "()((((()()()())())))", "()((((()()()()))()))", "()((((()()()())))())", "()((((()()()()))))()", "()((((()()())(()))))", "()((((()()())()())))", "()((((()()())())()))", "()((((()()())()))())", "()((((()()())())))()", "()((((()()()))(())))", "()((((()()()))()()))", "()((((()()()))())())", "()((((()()()))()))()", "()((((()()())))(()))", "()((((()()())))()())", "()((((()()())))())()", "()((((()()()))))(())", "()((((()()()))))()()", "()((((()())((())))))", "()((((()())(()()))))", "()((((()())(())())))", "()((((()())(()))()))", "()((((()())(())))())", "()((((()())(()))))()", "()((((()())()(()))))", "()((((()())()()())))", "()((((()())()())()))", "()((((()())()()))())", "()((((()())()())))()", "()((((()())())(())))", "()((((()())())()()))", "()((((()())())())())", "()((((()())())()))()", "()((((()())()))(()))", "()((((()())()))()())", "()((((()())()))())()", "()((((()())())))(())", "()((((()())())))()()", "()((((()()))((()))))", "()((((()()))(()())))", "()((((()()))(())()))", "()((((()()))(()))())", "()((((()()))(())))()", "()((((()()))()(())))", "()((((()()))()()()))", "()((((()()))()())())", "()((((()()))()()))()", "()((((()()))())(()))", "()((((()()))())()())", "()((((()()))())())()", "()((((()()))()))(())", "()((((()()))()))()()", "()((((()())))((())))", "()((((()())))(()()))", "()((((()())))(())())", "()((((()())))(()))()", "()((((()())))()(()))", "()((((()())))()()())", "()((((()())))()())()", "()((((()())))())(())", "()((((()())))())()()", "()((((()()))))((()))", "()((((()()))))(()())", "()((((()()))))(())()", "()((((()()))))()(())", "()((((()()))))()()()", "()((((())(((()))))))", "()((((())((()())))))", "()((((())((())()))))", "()((((())((()))())))", "()((((())((())))()))", "()((((())((()))))())", "()((((())((())))))()", "()((((())(()(())))))", "()((((())(()()()))))", "()((((())(()())())))", "()((((())(()()))()))", "()((((())(()())))())", "()((((())(()()))))()", "()((((())(())(()))))", "()((((())(())()())))", "()((((())(())())()))", "()((((())(())()))())", "()((((())(())())))()", "()((((())(()))(())))", "()((((())(()))()()))", "()((((())(()))())())", "()((((())(()))()))()", "()((((())(())))(()))", "()((((())(())))()())", "()((((())(())))())()", "()((((())(()))))(())", "()((((())(()))))()()", "()((((())()((())))))", "()((((())()(()()))))", "()((((())()(())())))", "()((((())()(()))()))", "()((((())()(())))())", "()((((())()(()))))()", "()((((())()()(()))))", "()((((())()()()())))", "()((((())()()())()))", "()((((())()()()))())", "()((((())()()())))()", "()((((())()())(())))", "()((((())()())()()))", "()((((())()())())())", "()((((())()())()))()", "()((((())()()))(()))", "()((((())()()))()())", "()((((())()()))())()", "()((((())()())))(())", "()((((())()())))()()", "()((((())())((()))))", "()((((())())(()())))", "()((((())())(())()))", "()((((())())(()))())", "()((((())())(())))()", "()((((())())()(())))", "()((((())())()()()))", "()((((())())()())())", "()((((())())()()))()", "()((((())())())(()))", "()((((())())())()())", "()((((())())())())()", "()((((())())()))(())", "()((((())())()))()()", "()((((())()))((())))", "()((((())()))(()()))", "()((((())()))(())())", "()((((())()))(()))()", "()((((())()))()(()))", "()((((())()))()()())", "()((((())()))()())()", "()((((())()))())(())", "()((((())()))())()()", "()((((())())))((()))", "()((((())())))(()())", "()((((())())))(())()", "()((((())())))()(())", "()((((())())))()()()", "()((((()))(((())))))", "()((((()))((()()))))", "()((((()))((())())))", "()((((()))((()))()))", "()((((()))((())))())", "()((((()))((()))))()", "()((((()))(()(()))))", "()((((()))(()()())))", "()((((()))(()())()))", "()((((()))(()()))())", "()((((()))(()())))()", "()((((()))(())(())))", "()((((()))(())()()))", "()((((()))(())())())", "()((((()))(())()))()", "()((((()))(()))(()))", "()((((()))(()))()())", "()((((()))(()))())()", "()((((()))(())))(())", "()((((()))(())))()()", "()((((()))()((()))))", "()((((()))()(()())))", "()((((()))()(())()))", "()((((()))()(()))())", "()((((()))()(())))()", "()((((()))()()(())))", "()((((()))()()()()))", "()((((()))()()())())", "()((((()))()()()))()", "()((((()))()())(()))", "()((((()))()())()())", "()((((()))()())())()", "()((((()))()()))(())", "()((((()))()()))()()", "()((((()))())((())))", "()((((()))())(()()))", "()((((()))())(())())", "()((((()))())(()))()", "()((((()))())()(()))", "()((((()))())()()())", "()((((()))())()())()", "()((((()))())())(())", "()((((()))())())()()", "()((((()))()))((()))", "()((((()))()))(()())", "()((((()))()))(())()", "()((((()))()))()(())", "()((((()))()))()()()", "()((((())))(((()))))", "()((((())))((()())))", "()((((())))((())()))", "()((((())))((()))())", "()((((())))((())))()", "()((((())))(()(())))", "()((((())))(()()()))", "()((((())))(()())())", "()((((())))(()()))()", "()((((())))(())(()))", "()((((())))(())()())", "()((((())))(())())()", "()((((())))(()))(())", "()((((())))(()))()()", "()((((())))()((())))", "()((((())))()(()()))", "()((((())))()(())())", "()((((())))()(()))()", "()((((())))()()(()))", "()((((())))()()()())", "()((((())))()()())()", "()((((())))()())(())", "()((((())))()())()()", "()((((())))())((()))", "()((((())))())(()())", "()((((())))())(())()", "()((((())))())()(())", "()((((())))())()()()", "()((((()))))(((())))", "()((((()))))((()()))", "()((((()))))((())())", "()((((()))))((()))()", "()((((()))))(()(()))", "()((((()))))(()()())", "()((((()))))(()())()", "()((((()))))(())(())", "()((((()))))(())()()", "()((((()))))()((()))", "()((((()))))()(()())", "()((((()))))()(())()", "()((((()))))()()(())", "()((((()))))()()()()", "()(((()((((())))))))", "()(((()(((()()))))))", "()(((()(((())())))))", "()(((()(((()))()))))", "()(((()(((())))())))", "()(((()(((()))))()))", "()(((()(((())))))())", "()(((()(((()))))))()", "()(((()((()(()))))))", "()(((()((()()())))))", "()(((()((()())()))))", "()(((()((()()))())))", "()(((()((()())))()))", "()(((()((()()))))())", "()(((()((()())))))()", "()(((()((())(())))))", "()(((()((())()()))))", "()(((()((())())())))", "()(((()((())()))()))", "()(((()((())())))())", "()(((()((())()))))()", "()(((()((()))(()))))", "()(((()((()))()())))", "()(((()((()))())()))", "()(((()((()))()))())", "()(((()((()))())))()", "()(((()((())))(())))", "()(((()((())))()()))", "()(((()((())))())())", "()(((()((())))()))()", "()(((()((()))))(()))", "()(((()((()))))()())", "()(((()((()))))())()", "()(((()((())))))(())", "()(((()((())))))()()", "()(((()(()((()))))))", "()(((()(()(()())))))", "()(((()(()(())()))))", "()(((()(()(()))())))", "()(((()(()(())))()))", "()(((()(()(()))))())", "()(((()(()(())))))()", "()(((()(()()(())))))", "()(((()(()()()()))))", "()(((()(()()())())))", "()(((()(()()()))()))", "()(((()(()()())))())", "()(((()(()()()))))()", "()(((()(()())(()))))", "()(((()(()())()())))", "()(((()(()())())()))", "()(((()(()())()))())", "()(((()(()())())))()", "()(((()(()()))(())))", "()(((()(()()))()()))", "()(((()(()()))())())", "()(((()(()()))()))()", "()(((()(()())))(()))", "()(((()(()())))()())", "()(((()(()())))())()", "()(((()(()()))))(())", "()(((()(()()))))()()", "()(((()(())((())))))", "()(((()(())(()()))))", "()(((()(())(())())))", "()(((()(())(()))()))", "()(((()(())(())))())", "()(((()(())(()))))()", "()(((()(())()(()))))", "()(((()(())()()())))", "()(((()(())()())()))", "()(((()(())()()))())", "()(((()(())()())))()", "()(((()(())())(())))", "()(((()(())())()()))", "()(((()(())())())())", "()(((()(())())()))()", "()(((()(())()))(()))", "()(((()(())()))()())", "()(((()(())()))())()", "()(((()(())())))(())", "()(((()(())())))()()", "()(((()(()))((()))))", "()(((()(()))(()())))", "()(((()(()))(())()))", "()(((()(()))(()))())", "()(((()(()))(())))()", "()(((()(()))()(())))", "()(((()(()))()()()))", "()(((()(()))()())())", "()(((()(()))()()))()", "()(((()(()))())(()))", "()(((()(()))())()())", "()(((()(()))())())()", "()(((()(()))()))(())", "()(((()(()))()))()()", "()(((()(())))((())))", "()(((()(())))(()()))", "()(((()(())))(())())", "()(((()(())))(()))()", "()(((()(())))()(()))", "()(((()(())))()()())", "()(((()(())))()())()", "()(((()(())))())(())", "()(((()(())))())()()", "()(((()(()))))((()))", "()(((()(()))))(()())", "()(((()(()))))(())()", "()(((()(()))))()(())", "()(((()(()))))()()()", "()(((()()(((()))))))", "()(((()()((()())))))", "()(((()()((())()))))", "()(((()()((()))())))", "()(((()()((())))()))", "()(((()()((()))))())", "()(((()()((())))))()", "()(((()()(()(())))))", "()(((()()(()()()))))", "()(((()()(()())())))", "()(((()()(()()))()))", "()(((()()(()())))())", "()(((()()(()()))))()", "()(((()()(())(()))))", "()(((()()(())()())))", "()(((()()(())())()))", "()(((()()(())()))())", "()(((()()(())())))()", "()(((()()(()))(())))", "()(((()()(()))()()))", "()(((()()(()))())())", "()(((()()(()))()))()", "()(((()()(())))(()))", "()(((()()(())))()())", "()(((()()(())))())()", "()(((()()(()))))(())", "()(((()()(()))))()()", "()(((()()()((())))))", "()(((()()()(()()))))", "()(((()()()(())())))", "()(((()()()(()))()))", "()(((()()()(())))())", "()(((()()()(()))))()", "()(((()()()()(()))))", "()(((()()()()()())))", "()(((()()()()())()))", "()(((()()()()()))())", "()(((()()()()())))()", "()(((()()()())(())))", "()(((()()()())()()))", "()(((()()()())())())", "()(((()()()())()))()", "()(((()()()()))(()))", "()(((()()()()))()())", "()(((()()()()))())()", "()(((()()()())))(())", "()(((()()()())))()()", "()(((()()())((()))))", "()(((()()())(()())))", "()(((()()())(())()))", "()(((()()())(()))())", "()(((()()())(())))()", "()(((()()())()(())))", "()(((()()())()()()))", "()(((()()())()())())", "()(((()()())()()))()", "()(((()()())())(()))", "()(((()()())())()())", "()(((()()())())())()", "()(((()()())()))(())", "()(((()()())()))()()", "()(((()()()))((())))", "()(((()()()))(()()))", "()(((()()()))(())())", "()(((()()()))(()))()", "()(((()()()))()(()))", "()(((()()()))()()())", "()(((()()()))()())()", "()(((()()()))())(())", "()(((()()()))())()()", "()(((()()())))((()))", "()(((()()())))(()())", "()(((()()())))(())()", "()(((()()())))()(())", "()(((()()())))()()()", "()(((()())(((())))))", "()(((()())((()()))))", "()(((()())((())())))", "()(((()())((()))()))", "()(((()())((())))())", "()(((()())((()))))()", "()(((()())(()(()))))", "()(((()())(()()())))", "()(((()())(()())()))", "()(((()())(()()))())", "()(((()())(()())))()", "()(((()())(())(())))", "()(((()())(())()()))", "()(((()())(())())())", "()(((()())(())()))()", "()(((()())(()))(()))", "()(((()())(()))()())", "()(((()())(()))())()", "()(((()())(())))(())", "()(((()())(())))()()", "()(((()())()((()))))", "()(((()())()(()())))", "()(((()())()(())()))", "()(((()())()(()))())", "()(((()())()(())))()", "()(((()())()()(())))", "()(((()())()()()()))", "()(((()())()()())())", "()(((()())()()()))()", "()(((()())()())(()))", "()(((()())()())()())", "()(((()())()())())()", "()(((()())()()))(())", "()(((()())()()))()()", "()(((()())())((())))", "()(((()())())(()()))", "()(((()())())(())())", "()(((()())())(()))()", "()(((()())())()(()))", "()(((()())())()()())", "()(((()())())()())()", "()(((()())())())(())", "()(((()())())())()()", "()(((()())()))((()))", "()(((()())()))(()())", "()(((()())()))(())()", "()(((()())()))()(())", "()(((()())()))()()()", "()(((()()))(((()))))", "()(((()()))((()())))", "()(((()()))((())()))", "()(((()()))((()))())", "()(((()()))((())))()", "()(((()()))(()(())))", "()(((()()))(()()()))", "()(((()()))(()())())", "()(((()()))(()()))()", "()(((()()))(())(()))", "()(((()()))(())()())", "()(((()()))(())())()", "()(((()()))(()))(())", "()(((()()))(()))()()", "()(((()()))()((())))", "()(((()()))()(()()))", "()(((()()))()(())())", "()(((()()))()(()))()", "()(((()()))()()(()))", "()(((()()))()()()())", "()(((()()))()()())()", "()(((()()))()())(())", "()(((()()))()())()()", "()(((()()))())((()))", "()(((()()))())(()())", "()(((()()))())(())()", "()(((()()))())()(())", "()(((()()))())()()()", "()(((()())))(((())))", "()(((()())))((()()))", "()(((()())))((())())", "()(((()())))((()))()", "()(((()())))(()(()))", "()(((()())))(()()())", "()(((()())))(()())()", "()(((()())))(())(())", "()(((()())))(())()()", "()(((()())))()((()))", "()(((()())))()(()())", "()(((()())))()(())()", "()(((()())))()()(())", "()(((()())))()()()()", "()(((())((((()))))))", "()(((())(((()())))))", "()(((())(((())()))))", "()(((())(((()))())))", "()(((())(((())))()))", "()(((())(((()))))())", "()(((())(((())))))()", "()(((())((()(())))))", "()(((())((()()()))))", "()(((())((()())())))", "()(((())((()()))()))", "()(((())((()())))())", "()(((())((()()))))()", "()(((())((())(()))))", "()(((())((())()())))", "()(((())((())())()))", "()(((())((())()))())", "()(((())((())())))()", "()(((())((()))(())))", "()(((())((()))()()))", "()(((())((()))())())", "()(((())((()))()))()", "()(((())((())))(()))", "()(((())((())))()())", "()(((())((())))())()", "()(((())((()))))(())", "()(((())((()))))()()", "()(((())(()((())))))", "()(((())(()(()()))))", "()(((())(()(())())))", "()(((())(()(()))()))", "()(((())(()(())))())", "()(((())(()(()))))()", "()(((())(()()(()))))", "()(((())(()()()())))", "()(((())(()()())()))", "()(((())(()()()))())", "()(((())(()()())))()", "()(((())(()())(())))", "()(((())(()())()()))", "()(((())(()())())())", "()(((())(()())()))()", "()(((())(()()))(()))", "()(((())(()()))()())", "()(((())(()()))())()", "()(((())(()())))(())", "()(((())(()())))()()", "()(((())(())((()))))", "()(((())(())(()())))", "()(((())(())(())()))", "()(((())(())(()))())", "()(((())(())(())))()", "()(((())(())()(())))", "()(((())(())()()()))", "()(((())(())()())())", "()(((())(())()()))()", "()(((())(())())(()))", "()(((())(())())()())", "()(((())(())())())()", "()(((())(())()))(())", "()(((())(())()))()()", "()(((())(()))((())))", "()(((())(()))(()()))", "()(((())(()))(())())", "()(((())(()))(()))()", "()(((())(()))()(()))", "()(((())(()))()()())", "()(((())(()))()())()", "()(((())(()))())(())", "()(((())(()))())()()", "()(((())(())))((()))", "()(((())(())))(()())", "()(((())(())))(())()", "()(((())(())))()(())", "()(((())(())))()()()", "()(((())()(((())))))", "()(((())()((()()))))", "()(((())()((())())))", "()(((())()((()))()))", "()(((())()((())))())", "()(((())()((()))))()", "()(((())()(()(()))))", "()(((())()(()()())))", "()(((())()(()())()))", "()(((())()(()()))())", "()(((())()(()())))()", "()(((())()(())(())))", "()(((())()(())()()))", "()(((())()(())())())", "()(((())()(())()))()", "()(((())()(()))(()))", "()(((())()(()))()())", "()(((())()(()))())()", "()(((())()(())))(())", "()(((())()(())))()()", "()(((())()()((()))))", "()(((())()()(()())))", "()(((())()()(())()))", "()(((())()()(()))())", "()(((())()()(())))()", "()(((())()()()(())))", "()(((())()()()()()))", "()(((())()()()())())", "()(((())()()()()))()", "()(((())()()())(()))", "()(((())()()())()())", "()(((())()()())())()", "()(((())()()()))(())", "()(((())()()()))()()", "()(((())()())((())))", "()(((())()())(()()))", "()(((())()())(())())", "()(((())()())(()))()", "()(((())()())()(()))", "()(((())()())()()())", "()(((())()())()())()", "()(((())()())())(())", "()(((())()())())()()", "()(((())()()))((()))", "()(((())()()))(()())", "()(((())()()))(())()", "()(((())()()))()(())", "()(((())()()))()()()", "()(((())())(((()))))", "()(((())())((()())))", "()(((())())((())()))", "()(((())())((()))())", "()(((())())((())))()", "()(((())())(()(())))", "()(((())())(()()()))", "()(((())())(()())())", "()(((())())(()()))()", "()(((())())(())(()))", "()(((())())(())()())", "()(((())())(())())()", "()(((())())(()))(())", "()(((())())(()))()()", "()(((())())()((())))", "()(((())())()(()()))", "()(((())())()(())())", "()(((())())()(()))()", "()(((())())()()(()))", "()(((())())()()()())", "()(((())())()()())()", "()(((())())()())(())", "()(((())())()())()()", "()(((())())())((()))", "()(((())())())(()())", "()(((())())())(())()", "()(((())())())()(())", "()(((())())())()()()", "()(((())()))(((())))", "()(((())()))((()()))", "()(((())()))((())())", "()(((())()))((()))()", "()(((())()))(()(()))", "()(((())()))(()()())", "()(((())()))(()())()", "()(((())()))(())(())", "()(((())()))(())()()", "()(((())()))()((()))", "()(((())()))()(()())", "()(((())()))()(())()", "()(((())()))()()(())", "()(((())()))()()()()", "()(((()))((((())))))", "()(((()))(((()()))))", "()(((()))(((())())))", "()(((()))(((()))()))", "()(((()))(((())))())", "()(((()))(((()))))()", "()(((()))((()(()))))", "()(((()))((()()())))", "()(((()))((()())()))", "()(((()))((()()))())", "()(((()))((()())))()", "()(((()))((())(())))", "()(((()))((())()()))", "()(((()))((())())())", "()(((()))((())()))()", "()(((()))((()))(()))", "()(((()))((()))()())", "()(((()))((()))())()", "()(((()))((())))(())", "()(((()))((())))()()", "()(((()))(()((()))))", "()(((()))(()(()())))", "()(((()))(()(())()))", "()(((()))(()(()))())", "()(((()))(()(())))()", "()(((()))(()()(())))", "()(((()))(()()()()))", "()(((()))(()()())())", "()(((()))(()()()))()", "()(((()))(()())(()))", "()(((()))(()())()())", "()(((()))(()())())()", "()(((()))(()()))(())", "()(((()))(()()))()()", "()(((()))(())((())))", "()(((()))(())(()()))", "()(((()))(())(())())", "()(((()))(())(()))()", "()(((()))(())()(()))", "()(((()))(())()()())", "()(((()))(())()())()", "()(((()))(())())(())", "()(((()))(())())()()", "()(((()))(()))((()))", "()(((()))(()))(()())", "()(((()))(()))(())()", "()(((()))(()))()(())", "()(((()))(()))()()()", "()(((()))()(((()))))", "()(((()))()((()())))", "()(((()))()((())()))", "()(((()))()((()))())", "()(((()))()((())))()", "()(((()))()(()(())))", "()(((()))()(()()()))", "()(((()))()(()())())", "()(((()))()(()()))()", "()(((()))()(())(()))", "()(((()))()(())()())", "()(((()))()(())())()", "()(((()))()(()))(())", "()(((()))()(()))()()", "()(((()))()()((())))", "()(((()))()()(()()))", "()(((()))()()(())())", "()(((()))()()(()))()", "()(((()))()()()(()))", "()(((()))()()()()())", "()(((()))()()()())()", "()(((()))()()())(())", "()(((()))()()())()()", "()(((()))()())((()))", "()(((()))()())(()())", "()(((()))()())(())()", "()(((()))()())()(())", "()(((()))()())()()()", "()(((()))())(((())))", "()(((()))())((()()))", "()(((()))())((())())", "()(((()))())((()))()", "()(((()))())(()(()))", "()(((()))())(()()())", "()(((()))())(()())()", "()(((()))())(())(())", "()(((()))())(())()()", "()(((()))())()((()))", "()(((()))())()(()())", "()(((()))())()(())()", "()(((()))())()()(())", "()(((()))())()()()()", "()(((())))((((()))))", "()(((())))(((()())))", "()(((())))(((())()))", "()(((())))(((()))())", "()(((())))(((())))()", "()(((())))((()(())))", "()(((())))((()()()))", "()(((())))((()())())", "()(((())))((()()))()", "()(((())))((())(()))", "()(((())))((())()())", "()(((())))((())())()", "()(((())))((()))(())", "()(((())))((()))()()", "()(((())))(()((())))", "()(((())))(()(()()))", "()(((())))(()(())())", "()(((())))(()(()))()", "()(((())))(()()(()))", "()(((())))(()()()())", "()(((())))(()()())()", "()(((())))(()())(())", "()(((())))(()())()()", "()(((())))(())((()))", "()(((())))(())(()())", "()(((())))(())(())()", "()(((())))(())()(())", "()(((())))(())()()()", "()(((())))()(((())))", "()(((())))()((()()))", "()(((())))()((())())", "()(((())))()((()))()", "()(((())))()(()(()))", "()(((())))()(()()())", "()(((())))()(()())()", "()(((())))()(())(())", "()(((())))()(())()()", "()(((())))()()((()))", "()(((())))()()(()())", "()(((())))()()(())()", "()(((())))()()()(())", "()(((())))()()()()()", "()((()(((((())))))))", "()((()((((()()))))))", "()((()((((())())))))", "()((()((((()))()))))", "()((()((((())))())))", "()((()((((()))))()))", "()((()((((())))))())", "()((()((((()))))))()", "()((()(((()(()))))))", "()((()(((()()())))))", "()((()(((()())()))))", "()((()(((()()))())))", "()((()(((()())))()))", "()((()(((()()))))())", "()((()(((()())))))()", "()((()(((())(())))))", "()((()(((())()()))))", "()((()(((())())())))", "()((()(((())()))()))", "()((()(((())())))())", "()((()(((())()))))()", "()((()(((()))(()))))", "()((()(((()))()())))", "()((()(((()))())()))", "()((()(((()))()))())", "()((()(((()))())))()", "()((()(((())))(())))", "()((()(((())))()()))", "()((()(((())))())())", "()((()(((())))()))()", "()((()(((()))))(()))", "()((()(((()))))()())", "()((()(((()))))())()", "()((()(((())))))(())", "()((()(((())))))()()", "()((()((()((()))))))", "()((()((()(()())))))", "()((()((()(())()))))", "()((()((()(()))())))", "()((()((()(())))()))", "()((()((()(()))))())", "()((()((()(())))))()", "()((()((()()(())))))", "()((()((()()()()))))", "()((()((()()())())))", "()((()((()()()))()))", "()((()((()()())))())", "()((()((()()()))))()", "()((()((()())(()))))", "()((()((()())()())))", "()((()((()())())()))", "()((()((()())()))())", "()((()((()())())))()", "()((()((()()))(())))", "()((()((()()))()()))", "()((()((()()))())())", "()((()((()()))()))()", "()((()((()())))(()))", "()((()((()())))()())", "()((()((()())))())()", "()((()((()()))))(())", "()((()((()()))))()()", "()((()((())((())))))", "()((()((())(()()))))", "()((()((())(())())))", "()((()((())(()))()))", "()((()((())(())))())", "()((()((())(()))))()", "()((()((())()(()))))", "()((()((())()()())))", "()((()((())()())()))", "()((()((())()()))())", "()((()((())()())))()", "()((()((())())(())))", "()((()((())())()()))", "()((()((())())())())", "()((()((())())()))()", "()((()((())()))(()))", "()((()((())()))()())", "()((()((())()))())()", "()((()((())())))(())", "()((()((())())))()()", "()((()((()))((()))))", "()((()((()))(()())))", "()((()((()))(())()))", "()((()((()))(()))())", "()((()((()))(())))()", "()((()((()))()(())))", "()((()((()))()()()))", "()((()((()))()())())", "()((()((()))()()))()", "()((()((()))())(()))", "()((()((()))())()())", "()((()((()))())())()", "()((()((()))()))(())", "()((()((()))()))()()", "()((()((())))((())))", "()((()((())))(()()))", "()((()((())))(())())", "()((()((())))(()))()", "()((()((())))()(()))", "()((()((())))()()())", "()((()((())))()())()", "()((()((())))())(())", "()((()((())))())()()", "()((()((()))))((()))", "()((()((()))))(()())", "()((()((()))))(())()", "()((()((()))))()(())", "()((()((()))))()()()", "()((()(()(((()))))))", "()((()(()((()())))))", "()((()(()((())()))))", "()((()(()((()))())))", "()((()(()((())))()))", "()((()(()((()))))())", "()((()(()((())))))()", "()((()(()(()(())))))", "()((()(()(()()()))))", "()((()(()(()())())))", "()((()(()(()()))()))", "()((()(()(()())))())", "()((()(()(()()))))()", "()((()(()(())(()))))", "()((()(()(())()())))", "()((()(()(())())()))", "()((()(()(())()))())", "()((()(()(())())))()", "()((()(()(()))(())))", "()((()(()(()))()()))", "()((()(()(()))())())", "()((()(()(()))()))()", "()((()(()(())))(()))", "()((()(()(())))()())", "()((()(()(())))())()", "()((()(()(()))))(())", "()((()(()(()))))()()", "()((()(()()((())))))", "()((()(()()(()()))))", "()((()(()()(())())))", "()((()(()()(()))()))", "()((()(()()(())))())", "()((()(()()(()))))()", "()((()(()()()(()))))", "()((()(()()()()())))", "()((()(()()()())()))", "()((()(()()()()))())", "()((()(()()()())))()", "()((()(()()())(())))", "()((()(()()())()()))", "()((()(()()())())())", "()((()(()()())()))()", "()((()(()()()))(()))", "()((()(()()()))()())", "()((()(()()()))())()", "()((()(()()())))(())", "()((()(()()())))()()", "()((()(()())((()))))", "()((()(()())(()())))", "()((()(()())(())()))", "()((()(()())(()))())", "()((()(()())(())))()", "()((()(()())()(())))", "()((()(()())()()()))", "()((()(()())()())())", "()((()(()())()()))()", "()((()(()())())(()))", "()((()(()())())()())", "()((()(()())())())()", "()((()(()())()))(())", "()((()(()())()))()()", "()((()(()()))((())))", "()((()(()()))(()()))", "()((()(()()))(())())", "()((()(()()))(()))()", "()((()(()()))()(()))", "()((()(()()))()()())", "()((()(()()))()())()", "()((()(()()))())(())", "()((()(()()))())()()", "()((()(()())))((()))", "()((()(()())))(()())", "()((()(()())))(())()", "()((()(()())))()(())", "()((()(()())))()()()", "()((()(())(((())))))", "()((()(())((()()))))", "()((()(())((())())))", "()((()(())((()))()))", "()((()(())((())))())", "()((()(())((()))))()", "()((()(())(()(()))))", "()((()(())(()()())))", "()((()(())(()())()))", "()((()(())(()()))())", "()((()(())(()())))()", "()((()(())(())(())))", "()((()(())(())()()))", "()((()(())(())())())", "()((()(())(())()))()", "()((()(())(()))(()))", "()((()(())(()))()())", "()((()(())(()))())()", "()((()(())(())))(())", "()((()(())(())))()()", "()((()(())()((()))))", "()((()(())()(()())))", "()((()(())()(())()))", "()((()(())()(()))())", "()((()(())()(())))()", "()((()(())()()(())))", "()((()(())()()()()))", "()((()(())()()())())", "()((()(())()()()))()", "()((()(())()())(()))", "()((()(())()())()())", "()((()(())()())())()", "()((()(())()()))(())", "()((()(())()()))()()", "()((()(())())((())))", "()((()(())())(()()))", "()((()(())())(())())", "()((()(())())(()))()", "()((()(())())()(()))", "()((()(())())()()())", "()((()(())())()())()", "()((()(())())())(())", "()((()(())())())()()", "()((()(())()))((()))", "()((()(())()))(()())", "()((()(())()))(())()", "()((()(())()))()(())", "()((()(())()))()()()", "()((()(()))(((()))))", "()((()(()))((()())))", "()((()(()))((())()))", "()((()(()))((()))())", "()((()(()))((())))()", "()((()(()))(()(())))", "()((()(()))(()()()))", "()((()(()))(()())())", "()((()(()))(()()))()", "()((()(()))(())(()))", "()((()(()))(())()())", "()((()(()))(())())()", "()((()(()))(()))(())", "()((()(()))(()))()()", "()((()(()))()((())))", "()((()(()))()(()()))", "()((()(()))()(())())", "()((()(()))()(()))()", "()((()(()))()()(()))", "()((()(()))()()()())", "()((()(()))()()())()", "()((()(()))()())(())", "()((()(()))()())()()", "()((()(()))())((()))", "()((()(()))())(()())", "()((()(()))())(())()", "()((()(()))())()(())", "()((()(()))())()()()", "()((()(())))(((())))", "()((()(())))((()()))", "()((()(())))((())())", "()((()(())))((()))()", "()((()(())))(()(()))", "()((()(())))(()()())", "()((()(())))(()())()", "()((()(())))(())(())", "()((()(())))(())()()", "()((()(())))()((()))", "()((()(())))()(()())", "()((()(())))()(())()", "()((()(())))()()(())", "()((()(())))()()()()", "()((()()((((()))))))", "()((()()(((()())))))", "()((()()(((())()))))", "()((()()(((()))())))", "()((()()(((())))()))", "()((()()(((()))))())", "()((()()(((())))))()", "()((()()((()(())))))", "()((()()((()()()))))", "()((()()((()())())))", "()((()()((()()))()))", "()((()()((()())))())", "()((()()((()()))))()", "()((()()((())(()))))", "()((()()((())()())))", "()((()()((())())()))", "()((()()((())()))())", "()((()()((())())))()", "()((()()((()))(())))", "()((()()((()))()()))", "()((()()((()))())())", "()((()()((()))()))()", "()((()()((())))(()))", "()((()()((())))()())", "()((()()((())))())()", "()((()()((()))))(())", "()((()()((()))))()()", "()((()()(()((())))))", "()((()()(()(()()))))", "()((()()(()(())())))", "()((()()(()(()))()))", "()((()()(()(())))())", "()((()()(()(()))))()", "()((()()(()()(()))))", "()((()()(()()()())))", "()((()()(()()())()))", "()((()()(()()()))())", "()((()()(()()())))()", "()((()()(()())(())))", "()((()()(()())()()))", "()((()()(()())())())", "()((()()(()())()))()", "()((()()(()()))(()))", "()((()()(()()))()())", "()((()()(()()))())()", "()((()()(()())))(())", "()((()()(()())))()()", "()((()()(())((()))))", "()((()()(())(()())))", "()((()()(())(())()))", "()((()()(())(()))())", "()((()()(())(())))()", "()((()()(())()(())))", "()((()()(())()()()))", "()((()()(())()())())", "()((()()(())()()))()", "()((()()(())())(()))", "()((()()(())())()())", "()((()()(())())())()", "()((()()(())()))(())", "()((()()(())()))()()", "()((()()(()))((())))", "()((()()(()))(()()))", "()((()()(()))(())())", "()((()()(()))(()))()", "()((()()(()))()(()))", "()((()()(()))()()())", "()((()()(()))()())()", "()((()()(()))())(())", "()((()()(()))())()()", "()((()()(())))((()))", "()((()()(())))(()())", "()((()()(())))(())()", "()((()()(())))()(())", "()((()()(())))()()()", "()((()()()(((())))))", "()((()()()((()()))))", "()((()()()((())())))", "()((()()()((()))()))", "()((()()()((())))())", "()((()()()((()))))()", "()((()()()(()(()))))", "()((()()()(()()())))", "()((()()()(()())()))", "()((()()()(()()))())", "()((()()()(()())))()", "()((()()()(())(())))", "()((()()()(())()()))", "()((()()()(())())())", "()((()()()(())()))()", "()((()()()(()))(()))", "()((()()()(()))()())", "()((()()()(()))())()", "()((()()()(())))(())", "()((()()()(())))()()", "()((()()()()((()))))", "()((()()()()(()())))", "()((()()()()(())()))", "()((()()()()(()))())", "()((()()()()(())))()", "()((()()()()()(())))", "()((()()()()()()()))", "()((()()()()()())())", "()((()()()()()()))()", "()((()()()()())(()))", "()((()()()()())()())", "()((()()()()())())()", "()((()()()()()))(())", "()((()()()()()))()()", "()((()()()())((())))", "()((()()()())(()()))", "()((()()()())(())())", "()((()()()())(()))()", "()((()()()())()(()))", "()((()()()())()()())", "()((()()()())()())()", "()((()()()())())(())", "()((()()()())())()()", "()((()()()()))((()))", "()((()()()()))(()())", "()((()()()()))(())()", "()((()()()()))()(())", "()((()()()()))()()()", "()((()()())(((()))))", "()((()()())((()())))", "()((()()())((())()))", "()((()()())((()))())", "()((()()())((())))()", "()((()()())(()(())))", "()((()()())(()()()))", "()((()()())(()())())", "()((()()())(()()))()", "()((()()())(())(()))", "()((()()())(())()())", "()((()()())(())())()", "()((()()())(()))(())", "()((()()())(()))()()", "()((()()())()((())))", "()((()()())()(()()))", "()((()()())()(())())", "()((()()())()(()))()", "()((()()())()()(()))", "()((()()())()()()())", "()((()()())()()())()", "()((()()())()())(())", "()((()()())()())()()", "()((()()())())((()))", "()((()()())())(()())", "()((()()())())(())()", "()((()()())())()(())", "()((()()())())()()()", "()((()()()))(((())))", "()((()()()))((()()))", "()((()()()))((())())", "()((()()()))((()))()", "()((()()()))(()(()))", "()((()()()))(()()())", "()((()()()))(()())()", "()((()()()))(())(())", "()((()()()))(())()()", "()((()()()))()((()))", "()((()()()))()(()())", "()((()()()))()(())()", "()((()()()))()()(())", "()((()()()))()()()()", "()((()())((((())))))", "()((()())(((()()))))", "()((()())(((())())))", "()((()())(((()))()))", "()((()())(((())))())", "()((()())(((()))))()", "()((()())((()(()))))", "()((()())((()()())))", "()((()())((()())()))", "()((()())((()()))())", "()((()())((()())))()", "()((()())((())(())))", "()((()())((())()()))", "()((()())((())())())", "()((()())((())()))()", "()((()())((()))(()))", "()((()())((()))()())", "()((()())((()))())()", "()((()())((())))(())", "()((()())((())))()()", "()((()())(()((()))))", "()((()())(()(()())))", "()((()())(()(())()))", "()((()())(()(()))())", "()((()())(()(())))()", "()((()())(()()(())))", "()((()())(()()()()))", "()((()())(()()())())", "()((()())(()()()))()", "()((()())(()())(()))", "()((()())(()())()())", "()((()())(()())())()", "()((()())(()()))(())", "()((()())(()()))()()", "()((()())(())((())))", "()((()())(())(()()))", "()((()())(())(())())", "()((()())(())(()))()", "()((()())(())()(()))", "()((()())(())()()())", "()((()())(())()())()", "()((()())(())())(())", "()((()())(())())()()", "()((()())(()))((()))", "()((()())(()))(()())", "()((()())(()))(())()", "()((()())(()))()(())", "()((()())(()))()()()", "()((()())()(((()))))", "()((()())()((()())))", "()((()())()((())()))", "()((()())()((()))())", "()((()())()((())))()", "()((()())()(()(())))", "()((()())()(()()()))", "()((()())()(()())())", "()((()())()(()()))()", "()((()())()(())(()))", "()((()())()(())()())", "()((()())()(())())()", "()((()())()(()))(())", "()((()())()(()))()()", "()((()())()()((())))", "()((()())()()(()()))", "()((()())()()(())())", "()((()())()()(()))()", "()((()())()()()(()))", "()((()())()()()()())", "()((()())()()()())()", "()((()())()()())(())", "()((()())()()())()()", "()((()())()())((()))", "()((()())()())(()())", "()((()())()())(())()", "()((()())()())()(())", "()((()())()())()()()", "()((()())())(((())))", "()((()())())((()()))", "()((()())())((())())", "()((()())())((()))()", "()((()())())(()(()))", "()((()())())(()()())", "()((()())())(()())()", "()((()())())(())(())", "()((()())())(())()()", "()((()())())()((()))", "()((()())())()(()())", "()((()())())()(())()", "()((()())())()()(())", "()((()())())()()()()", "()((()()))((((()))))", "()((()()))(((()())))", "()((()()))(((())()))", "()((()()))(((()))())", "()((()()))(((())))()", "()((()()))((()(())))", "()((()()))((()()()))", "()((()()))((()())())", "()((()()))((()()))()", "()((()()))((())(()))", "()((()()))((())()())", "()((()()))((())())()", "()((()()))((()))(())", "()((()()))((()))()()", "()((()()))(()((())))", "()((()()))(()(()()))", "()((()()))(()(())())", "()((()()))(()(()))()", "()((()()))(()()(()))", "()((()()))(()()()())", "()((()()))(()()())()", "()((()()))(()())(())", "()((()()))(()())()()", "()((()()))(())((()))", "()((()()))(())(()())", "()((()()))(())(())()", "()((()()))(())()(())", "()((()()))(())()()()", "()((()()))()(((())))", "()((()()))()((()()))", "()((()()))()((())())", "()((()()))()((()))()", "()((()()))()(()(()))", "()((()()))()(()()())", "()((()()))()(()())()", "()((()()))()(())(())", "()((()()))()(())()()", "()((()()))()()((()))", "()((()()))()()(()())", "()((()()))()()(())()", "()((()()))()()()(())", "()((()()))()()()()()", "()((())(((((()))))))", "()((())((((()())))))", "()((())((((())()))))", "()((())((((()))())))", "()((())((((())))()))", "()((())((((()))))())", "()((())((((())))))()", "()((())(((()(())))))", "()((())(((()()()))))", "()((())(((()())())))", "()((())(((()()))()))", "()((())(((()())))())", "()((())(((()()))))()", "()((())(((())(()))))", "()((())(((())()())))", "()((())(((())())()))", "()((())(((())()))())", "()((())(((())())))()", "()((())(((()))(())))", "()((())(((()))()()))", "()((())(((()))())())", "()((())(((()))()))()", "()((())(((())))(()))", "()((())(((())))()())", "()((())(((())))())()", "()((())(((()))))(())", "()((())(((()))))()()", "()((())((()((())))))", "()((())((()(()()))))", "()((())((()(())())))", "()((())((()(()))()))", "()((())((()(())))())", "()((())((()(()))))()", "()((())((()()(()))))", "()((())((()()()())))", "()((())((()()())()))", "()((())((()()()))())", "()((())((()()())))()", "()((())((()())(())))", "()((())((()())()()))", "()((())((()())())())", "()((())((()())()))()", "()((())((()()))(()))", "()((())((()()))()())", "()((())((()()))())()", "()((())((()())))(())", "()((())((()())))()()", "()((())((())((()))))", "()((())((())(()())))", "()((())((())(())()))", "()((())((())(()))())", "()((())((())(())))()", "()((())((())()(())))", "()((())((())()()()))", "()((())((())()())())", "()((())((())()()))()", "()((())((())())(()))", "()((())((())())()())", "()((())((())())())()", "()((())((())()))(())", "()((())((())()))()()", "()((())((()))((())))", "()((())((()))(()()))", "()((())((()))(())())", "()((())((()))(()))()", "()((())((()))()(()))", "()((())((()))()()())", "()((())((()))()())()", "()((())((()))())(())", "()((())((()))())()()", "()((())((())))((()))", "()((())((())))(()())", "()((())((())))(())()", "()((())((())))()(())", "()((())((())))()()()", "()((())(()(((())))))", "()((())(()((()()))))", "()((())(()((())())))", "()((())(()((()))()))", "()((())(()((())))())", "()((())(()((()))))()", "()((())(()(()(()))))", "()((())(()(()()())))", "()((())(()(()())()))", "()((())(()(()()))())", "()((())(()(()())))()", "()((())(()(())(())))", "()((())(()(())()()))", "()((())(()(())())())", "()((())(()(())()))()", "()((())(()(()))(()))", "()((())(()(()))()())", "()((())(()(()))())()", "()((())(()(())))(())", "()((())(()(())))()()", "()((())(()()((()))))", "()((())(()()(()())))", "()((())(()()(())()))", "()((())(()()(()))())", "()((())(()()(())))()", "()((())(()()()(())))", "()((())(()()()()()))", "()((())(()()()())())", "()((())(()()()()))()", "()((())(()()())(()))", "()((())(()()())()())", "()((())(()()())())()", "()((())(()()()))(())", "()((())(()()()))()()", "()((())(()())((())))", "()((())(()())(()()))", "()((())(()())(())())", "()((())(()())(()))()", "()((())(()())()(()))", "()((())(()())()()())", "()((())(()())()())()", "()((())(()())())(())", "()((())(()())())()()", "()((())(()()))((()))", "()((())(()()))(()())", "()((())(()()))(())()", "()((())(()()))()(())", "()((())(()()))()()()", "()((())(())(((()))))", "()((())(())((()())))", "()((())(())((())()))", "()((())(())((()))())", "()((())(())((())))()", "()((())(())(()(())))", "()((())(())(()()()))", "()((())(())(()())())", "()((())(())(()()))()", "()((())(())(())(()))", "()((())(())(())()())", "()((())(())(())())()", "()((())(())(()))(())", "()((())(())(()))()()", "()((())(())()((())))", "()((())(())()(()()))", "()((())(())()(())())", "()((())(())()(()))()", "()((())(())()()(()))", "()((())(())()()()())", "()((())(())()()())()", "()((())(())()())(())", "()((())(())()())()()", "()((())(())())((()))", "()((())(())())(()())", "()((())(())())(())()", "()((())(())())()(())", "()((())(())())()()()", "()((())(()))(((())))", "()((())(()))((()()))", "()((())(()))((())())", "()((())(()))((()))()", "()((())(()))(()(()))", "()((())(()))(()()())", "()((())(()))(()())()", "()((())(()))(())(())", "()((())(()))(())()()", "()((())(()))()((()))", "()((())(()))()(()())", "()((())(()))()(())()", "()((())(()))()()(())", "()((())(()))()()()()", "()((())()((((())))))", "()((())()(((()()))))", "()((())()(((())())))", "()((())()(((()))()))", "()((())()(((())))())", "()((())()(((()))))()", "()((())()((()(()))))", "()((())()((()()())))", "()((())()((()())()))", "()((())()((()()))())", "()((())()((()())))()", "()((())()((())(())))", "()((())()((())()()))", "()((())()((())())())", "()((())()((())()))()", "()((())()((()))(()))", "()((())()((()))()())", "()((())()((()))())()", "()((())()((())))(())", "()((())()((())))()()", "()((())()(()((()))))", "()((())()(()(()())))", "()((())()(()(())()))", "()((())()(()(()))())", "()((())()(()(())))()", "()((())()(()()(())))", "()((())()(()()()()))", "()((())()(()()())())", "()((())()(()()()))()", "()((())()(()())(()))", "()((())()(()())()())", "()((())()(()())())()", "()((())()(()()))(())", "()((())()(()()))()()", "()((())()(())((())))", "()((())()(())(()()))", "()((())()(())(())())", "()((())()(())(()))()", "()((())()(())()(()))", "()((())()(())()()())", "()((())()(())()())()", "()((())()(())())(())", "()((())()(())())()()", "()((())()(()))((()))", "()((())()(()))(()())", "()((())()(()))(())()", "()((())()(()))()(())", "()((())()(()))()()()", "()((())()()(((()))))", "()((())()()((()())))", "()((())()()((())()))", "()((())()()((()))())", "()((())()()((())))()", "()((())()()(()(())))", "()((())()()(()()()))", "()((())()()(()())())", "()((())()()(()()))()", "()((())()()(())(()))", "()((())()()(())()())", "()((())()()(())())()", "()((())()()(()))(())", "()((())()()(()))()()", "()((())()()()((())))", "()((())()()()(()()))", "()((())()()()(())())", "()((())()()()(()))()", "()((())()()()()(()))", "()((())()()()()()())", "()((())()()()()())()", "()((())()()()())(())", "()((())()()()())()()", "()((())()()())((()))", "()((())()()())(()())", "()((())()()())(())()", "()((())()()())()(())", "()((())()()())()()()", "()((())()())(((())))", "()((())()())((()()))", "()((())()())((())())", "()((())()())((()))()", "()((())()())(()(()))", "()((())()())(()()())", "()((())()())(()())()", "()((())()())(())(())", "()((())()())(())()()", "()((())()())()((()))", "()((())()())()(()())", "()((())()())()(())()", "()((())()())()()(())", "()((())()())()()()()", "()((())())((((()))))", "()((())())(((()())))", "()((())())(((())()))", "()((())())(((()))())", "()((())())(((())))()", "()((())())((()(())))", "()((())())((()()()))", "()((())())((()())())", "()((())())((()()))()", "()((())())((())(()))", "()((())())((())()())", "()((())())((())())()", "()((())())((()))(())", "()((())())((()))()()", "()((())())(()((())))", "()((())())(()(()()))", "()((())())(()(())())", "()((())())(()(()))()", "()((())())(()()(()))", "()((())())(()()()())", "()((())())(()()())()", "()((())())(()())(())", "()((())())(()())()()", "()((())())(())((()))", "()((())())(())(()())", "()((())())(())(())()", "()((())())(())()(())", "()((())())(())()()()", "()((())())()(((())))", "()((())())()((()()))", "()((())())()((())())", "()((())())()((()))()", "()((())())()(()(()))", "()((())())()(()()())", "()((())())()(()())()", "()((())())()(())(())", "()((())())()(())()()", "()((())())()()((()))", "()((())())()()(()())", "()((())())()()(())()", "()((())())()()()(())", "()((())())()()()()()", "()((()))(((((())))))", "()((()))((((()()))))", "()((()))((((())())))", "()((()))((((()))()))", "()((()))((((())))())", "()((()))((((()))))()", "()((()))(((()(()))))", "()((()))(((()()())))", "()((()))(((()())()))", "()((()))(((()()))())", "()((()))(((()())))()", "()((()))(((())(())))", "()((()))(((())()()))", "()((()))(((())())())", "()((()))(((())()))()", "()((()))(((()))(()))", "()((()))(((()))()())", "()((()))(((()))())()", "()((()))(((())))(())", "()((()))(((())))()()", "()((()))((()((()))))", "()((()))((()(()())))", "()((()))((()(())()))", "()((()))((()(()))())", "()((()))((()(())))()", "()((()))((()()(())))", "()((()))((()()()()))", "()((()))((()()())())", "()((()))((()()()))()", "()((()))((()())(()))", "()((()))((()())()())", "()((()))((()())())()", "()((()))((()()))(())", "()((()))((()()))()()", "()((()))((())((())))", "()((()))((())(()()))", "()((()))((())(())())", "()((()))((())(()))()", "()((()))((())()(()))", "()((()))((())()()())", "()((()))((())()())()", "()((()))((())())(())", "()((()))((())())()()", "()((()))((()))((()))", "()((()))((()))(()())", "()((()))((()))(())()", "()((()))((()))()(())", "()((()))((()))()()()", "()((()))(()(((()))))", "()((()))(()((()())))", "()((()))(()((())()))", "()((()))(()((()))())", "()((()))(()((())))()", "()((()))(()(()(())))", "()((()))(()(()()()))", "()((()))(()(()())())", "()((()))(()(()()))()", "()((()))(()(())(()))", "()((()))(()(())()())", "()((()))(()(())())()", "()((()))(()(()))(())", "()((()))(()(()))()()", "()((()))(()()((())))", "()((()))(()()(()()))", "()((()))(()()(())())", "()((()))(()()(()))()", "()((()))(()()()(()))", "()((()))(()()()()())", "()((()))(()()()())()", "()((()))(()()())(())", "()((()))(()()())()()", "()((()))(()())((()))", "()((()))(()())(()())", "()((()))(()())(())()", "()((()))(()())()(())", "()((()))(()())()()()", "()((()))(())(((())))", "()((()))(())((()()))", "()((()))(())((())())", "()((()))(())((()))()", "()((()))(())(()(()))", "()((()))(())(()()())", "()((()))(())(()())()", "()((()))(())(())(())", "()((()))(())(())()()", "()((()))(())()((()))", "()((()))(())()(()())", "()((()))(())()(())()", "()((()))(())()()(())", "()((()))(())()()()()", "()((()))()((((()))))", "()((()))()(((()())))", "()((()))()(((())()))", "()((()))()(((()))())", "()((()))()(((())))()", "()((()))()((()(())))", "()((()))()((()()()))", "()((()))()((()())())", "()((()))()((()()))()", "()((()))()((())(()))", "()((()))()((())()())", "()((()))()((())())()", "()((()))()((()))(())", "()((()))()((()))()()", "()((()))()(()((())))", "()((()))()(()(()()))", "()((()))()(()(())())", "()((()))()(()(()))()", "()((()))()(()()(()))", "()((()))()(()()()())", "()((()))()(()()())()", "()((()))()(()())(())", "()((()))()(()())()()", "()((()))()(())((()))", "()((()))()(())(()())", "()((()))()(())(())()", "()((()))()(())()(())", "()((()))()(())()()()", "()((()))()()(((())))", "()((()))()()((()()))", "()((()))()()((())())", "()((()))()()((()))()", "()((()))()()(()(()))", "()((()))()()(()()())", "()((()))()()(()())()", "()((()))()()(())(())", "()((()))()()(())()()", "()((()))()()()((()))", "()((()))()()()(()())", "()((()))()()()(())()", "()((()))()()()()(())", "()((()))()()()()()()", "()(()((((((())))))))", "()(()(((((()()))))))", "()(()(((((())())))))", "()(()(((((()))()))))", "()(()(((((())))())))", "()(()(((((()))))()))", "()(()(((((())))))())", "()(()(((((()))))))()", "()(()((((()(()))))))", "()(()((((()()())))))", "()(()((((()())()))))", "()(()((((()()))())))", "()(()((((()())))()))", "()(()((((()()))))())", "()(()((((()())))))()", "()(()((((())(())))))", "()(()((((())()()))))", "()(()((((())())())))", "()(()((((())()))()))", "()(()((((())())))())", "()(()((((())()))))()", "()(()((((()))(()))))", "()(()((((()))()())))", "()(()((((()))())()))", "()(()((((()))()))())", "()(()((((()))())))()", "()(()((((())))(())))", "()(()((((())))()()))", "()(()((((())))())())", "()(()((((())))()))()", "()(()((((()))))(()))", "()(()((((()))))()())", "()(()((((()))))())()", "()(()((((())))))(())", "()(()((((())))))()()", "()(()(((()((()))))))", "()(()(((()(()())))))", "()(()(((()(())()))))", "()(()(((()(()))())))", "()(()(((()(())))()))", "()(()(((()(()))))())", "()(()(((()(())))))()", "()(()(((()()(())))))", "()(()(((()()()()))))", "()(()(((()()())())))", "()(()(((()()()))()))", "()(()(((()()())))())", "()(()(((()()()))))()", "()(()(((()())(()))))", "()(()(((()())()())))", "()(()(((()())())()))", "()(()(((()())()))())", "()(()(((()())())))()", "()(()(((()()))(())))", "()(()(((()()))()()))", "()(()(((()()))())())", "()(()(((()()))()))()", "()(()(((()())))(()))", "()(()(((()())))()())", "()(()(((()())))())()", "()(()(((()()))))(())", "()(()(((()()))))()()", "()(()(((())((())))))", "()(()(((())(()()))))", "()(()(((())(())())))", "()(()(((())(()))()))", "()(()(((())(())))())", "()(()(((())(()))))()", "()(()(((())()(()))))", "()(()(((())()()())))", "()(()(((())()())()))", "()(()(((())()()))())", "()(()(((())()())))()", "()(()(((())())(())))", "()(()(((())())()()))", "()(()(((())())())())", "()(()(((())())()))()", "()(()(((())()))(()))", "()(()(((())()))()())", "()(()(((())()))())()", "()(()(((())())))(())", "()(()(((())())))()()", "()(()(((()))((()))))", "()(()(((()))(()())))", "()(()(((()))(())()))", "()(()(((()))(()))())", "()(()(((()))(())))()", "()(()(((()))()(())))", "()(()(((()))()()()))", "()(()(((()))()())())", "()(()(((()))()()))()", "()(()(((()))())(()))", "()(()(((()))())()())", "()(()(((()))())())()", "()(()(((()))()))(())", "()(()(((()))()))()()", "()(()(((())))((())))", "()(()(((())))(()()))", "()(()(((())))(())())", "()(()(((())))(()))()", "()(()(((())))()(()))", "()(()(((())))()()())", "()(()(((())))()())()", "()(()(((())))())(())", "()(()(((())))())()()", "()(()(((()))))((()))", "()(()(((()))))(()())", "()(()(((()))))(())()", "()(()(((()))))()(())", "()(()(((()))))()()()", "()(()((()(((()))))))", "()(()((()((()())))))", "()(()((()((())()))))", "()(()((()((()))())))", "()(()((()((())))()))", "()(()((()((()))))())", "()(()((()((())))))()", "()(()((()(()(())))))", "()(()((()(()()()))))", "()(()((()(()())())))", "()(()((()(()()))()))", "()(()((()(()())))())", "()(()((()(()()))))()", "()(()((()(())(()))))", "()(()((()(())()())))", "()(()((()(())())()))", "()(()((()(())()))())", "()(()((()(())())))()", "()(()((()(()))(())))", "()(()((()(()))()()))", "()(()((()(()))())())", "()(()((()(()))()))()", "()(()((()(())))(()))", "()(()((()(())))()())", "()(()((()(())))())()", "()(()((()(()))))(())", "()(()((()(()))))()()", "()(()((()()((())))))", "()(()((()()(()()))))", "()(()((()()(())())))", "()(()((()()(()))()))", "()(()((()()(())))())", "()(()((()()(()))))()", "()(()((()()()(()))))", "()(()((()()()()())))", "()(()((()()()())()))", "()(()((()()()()))())", "()(()((()()()())))()", "()(()((()()())(())))", "()(()((()()())()()))", "()(()((()()())())())", "()(()((()()())()))()", "()(()((()()()))(()))", "()(()((()()()))()())", "()(()((()()()))())()", "()(()((()()())))(())", "()(()((()()())))()()", "()(()((()())((()))))", "()(()((()())(()())))", "()(()((()())(())()))", "()(()((()())(()))())", "()(()((()())(())))()", "()(()((()())()(())))", "()(()((()())()()()))", "()(()((()())()())())", "()(()((()())()()))()", "()(()((()())())(()))", "()(()((()())())()())", "()(()((()())())())()", "()(()((()())()))(())", "()(()((()())()))()()", "()(()((()()))((())))", "()(()((()()))(()()))", "()(()((()()))(())())", "()(()((()()))(()))()", "()(()((()()))()(()))", "()(()((()()))()()())", "()(()((()()))()())()", "()(()((()()))())(())", "()(()((()()))())()()", "()(()((()())))((()))", "()(()((()())))(()())", "()(()((()())))(())()", "()(()((()())))()(())", "()(()((()())))()()()", "()(()((())(((())))))", "()(()((())((()()))))", "()(()((())((())())))", "()(()((())((()))()))", "()(()((())((())))())", "()(()((())((()))))()", "()(()((())(()(()))))", "()(()((())(()()())))", "()(()((())(()())()))", "()(()((())(()()))())", "()(()((())(()())))()", "()(()((())(())(())))", "()(()((())(())()()))", "()(()((())(())())())", "()(()((())(())()))()", "()(()((())(()))(()))", "()(()((())(()))()())", "()(()((())(()))())()", "()(()((())(())))(())", "()(()((())(())))()()", "()(()((())()((()))))", "()(()((())()(()())))", "()(()((())()(())()))", "()(()((())()(()))())", "()(()((())()(())))()", "()(()((())()()(())))", "()(()((())()()()()))", "()(()((())()()())())", "()(()((())()()()))()", "()(()((())()())(()))", "()(()((())()())()())", "()(()((())()())())()", "()(()((())()()))(())", "()(()((())()()))()()", "()(()((())())((())))", "()(()((())())(()()))", "()(()((())())(())())", "()(()((())())(()))()", "()(()((())())()(()))", "()(()((())())()()())", "()(()((())())()())()", "()(()((())())())(())", "()(()((())())())()()", "()(()((())()))((()))", "()(()((())()))(()())", "()(()((())()))(())()", "()(()((())()))()(())", "()(()((())()))()()()", "()(()((()))(((()))))", "()(()((()))((()())))", "()(()((()))((())()))", "()(()((()))((()))())", "()(()((()))((())))()", "()(()((()))(()(())))", "()(()((()))(()()()))", "()(()((()))(()())())", "()(()((()))(()()))()", "()(()((()))(())(()))", "()(()((()))(())()())", "()(()((()))(())())()", "()(()((()))(()))(())", "()(()((()))(()))()()", "()(()((()))()((())))", "()(()((()))()(()()))", "()(()((()))()(())())", "()(()((()))()(()))()", "()(()((()))()()(()))", "()(()((()))()()()())", "()(()((()))()()())()", "()(()((()))()())(())", "()(()((()))()())()()", "()(()((()))())((()))", "()(()((()))())(()())", "()(()((()))())(())()", "()(()((()))())()(())", "()(()((()))())()()()", "()(()((())))(((())))", "()(()((())))((()()))", "()(()((())))((())())", "()(()((())))((()))()", "()(()((())))(()(()))", "()(()((())))(()()())", "()(()((())))(()())()", "()(()((())))(())(())", "()(()((())))(())()()", "()(()((())))()((()))", "()(()((())))()(()())", "()(()((())))()(())()", "()(()((())))()()(())", "()(()((())))()()()()", "()(()(()((((()))))))", "()(()(()(((()())))))", "()(()(()(((())()))))", "()(()(()(((()))())))", "()(()(()(((())))()))", "()(()(()(((()))))())", "()(()(()(((())))))()", "()(()(()((()(())))))", "()(()(()((()()()))))", "()(()(()((()())())))", "()(()(()((()()))()))", "()(()(()((()())))())", "()(()(()((()()))))()", "()(()(()((())(()))))", "()(()(()((())()())))", "()(()(()((())())()))", "()(()(()((())()))())", "()(()(()((())())))()", "()(()(()((()))(())))", "()(()(()((()))()()))", "()(()(()((()))())())", "()(()(()((()))()))()", "()(()(()((())))(()))", "()(()(()((())))()())", "()(()(()((())))())()", "()(()(()((()))))(())", "()(()(()((()))))()()", "()(()(()(()((())))))", "()(()(()(()(()()))))", "()(()(()(()(())())))", "()(()(()(()(()))()))", "()(()(()(()(())))())", "()(()(()(()(()))))()", "()(()(()(()()(()))))", "()(()(()(()()()())))", "()(()(()(()()())()))", "()(()(()(()()()))())", "()(()(()(()()())))()", "()(()(()(()())(())))", "()(()(()(()())()()))", "()(()(()(()())())())", "()(()(()(()())()))()", "()(()(()(()()))(()))", "()(()(()(()()))()())", "()(()(()(()()))())()", "()(()(()(()())))(())", "()(()(()(()())))()()", "()(()(()(())((()))))", "()(()(()(())(()())))", "()(()(()(())(())()))", "()(()(()(())(()))())", "()(()(()(())(())))()", "()(()(()(())()(())))", "()(()(()(())()()()))", "()(()(()(())()())())", "()(()(()(())()()))()", "()(()(()(())())(()))", "()(()(()(())())()())", "()(()(()(())())())()", "()(()(()(())()))(())", "()(()(()(())()))()()", "()(()(()(()))((())))", "()(()(()(()))(()()))", "()(()(()(()))(())())", "()(()(()(()))(()))()", "()(()(()(()))()(()))", "()(()(()(()))()()())", "()(()(()(()))()())()", "()(()(()(()))())(())", "()(()(()(()))())()()", "()(()(()(())))((()))", "()(()(()(())))(()())", "()(()(()(())))(())()", "()(()(()(())))()(())", "()(()(()(())))()()()", "()(()(()()(((())))))", "()(()(()()((()()))))", "()(()(()()((())())))", "()(()(()()((()))()))", "()(()(()()((())))())", "()(()(()()((()))))()", "()(()(()()(()(()))))", "()(()(()()(()()())))", "()(()(()()(()())()))", "()(()(()()(()()))())", "()(()(()()(()())))()", "()(()(()()(())(())))", "()(()(()()(())()()))", "()(()(()()(())())())", "()(()(()()(())()))()", "()(()(()()(()))(()))", "()(()(()()(()))()())", "()(()(()()(()))())()", "()(()(()()(())))(())", "()(()(()()(())))()()", "()(()(()()()((()))))", "()(()(()()()(()())))", "()(()(()()()(())()))", "()(()(()()()(()))())", "()(()(()()()(())))()", "()(()(()()()()(())))", "()(()(()()()()()()))", "()(()(()()()()())())", "()(()(()()()()()))()", "()(()(()()()())(()))", "()(()(()()()())()())", "()(()(()()()())())()", "()(()(()()()()))(())", "()(()(()()()()))()()", "()(()(()()())((())))", "()(()(()()())(()()))", "()(()(()()())(())())", "()(()(()()())(()))()", "()(()(()()())()(()))", "()(()(()()())()()())", "()(()(()()())()())()", "()(()(()()())())(())", "()(()(()()())())()()", "()(()(()()()))((()))", "()(()(()()()))(()())", "()(()(()()()))(())()", "()(()(()()()))()(())", "()(()(()()()))()()()", "()(()(()())(((()))))", "()(()(()())((()())))", "()(()(()())((())()))", "()(()(()())((()))())", "()(()(()())((())))()", "()(()(()())(()(())))", "()(()(()())(()()()))", "()(()(()())(()())())", "()(()(()())(()()))()", "()(()(()())(())(()))", "()(()(()())(())()())", "()(()(()())(())())()", "()(()(()())(()))(())", "()(()(()())(()))()()", "()(()(()())()((())))", "()(()(()())()(()()))", "()(()(()())()(())())", "()(()(()())()(()))()", "()(()(()())()()(()))", "()(()(()())()()()())", "()(()(()())()()())()", "()(()(()())()())(())", "()(()(()())()())()()", "()(()(()())())((()))", "()(()(()())())(()())", "()(()(()())())(())()", "()(()(()())())()(())", "()(()(()())())()()()", "()(()(()()))(((())))", "()(()(()()))((()()))", "()(()(()()))((())())", "()(()(()()))((()))()", "()(()(()()))(()(()))", "()(()(()()))(()()())", "()(()(()()))(()())()", "()(()(()()))(())(())", "()(()(()()))(())()()", "()(()(()()))()((()))", "()(()(()()))()(()())", "()(()(()()))()(())()", "()(()(()()))()()(())", "()(()(()()))()()()()", "()(()(())((((())))))", "()(()(())(((()()))))", "()(()(())(((())())))", "()(()(())(((()))()))", "()(()(())(((())))())", "()(()(())(((()))))()", "()(()(())((()(()))))", "()(()(())((()()())))", "()(()(())((()())()))", "()(()(())((()()))())", "()(()(())((()())))()", "()(()(())((())(())))", "()(()(())((())()()))", "()(()(())((())())())", "()(()(())((())()))()", "()(()(())((()))(()))", "()(()(())((()))()())", "()(()(())((()))())()", "()(()(())((())))(())", "()(()(())((())))()()", "()(()(())(()((()))))", "()(()(())(()(()())))", "()(()(())(()(())()))", "()(()(())(()(()))())", "()(()(())(()(())))()", "()(()(())(()()(())))", "()(()(())(()()()()))", "()(()(())(()()())())", "()(()(())(()()()))()", "()(()(())(()())(()))", "()(()(())(()())()())", "()(()(())(()())())()", "()(()(())(()()))(())", "()(()(())(()()))()()", "()(()(())(())((())))", "()(()(())(())(()()))", "()(()(())(())(())())", "()(()(())(())(()))()", "()(()(())(())()(()))", "()(()(())(())()()())", "()(()(())(())()())()", "()(()(())(())())(())", "()(()(())(())())()()", "()(()(())(()))((()))", "()(()(())(()))(()())", "()(()(())(()))(())()", "()(()(())(()))()(())", "()(()(())(()))()()()", "()(()(())()(((()))))", "()(()(())()((()())))", "()(()(())()((())()))", "()(()(())()((()))())", "()(()(())()((())))()", "()(()(())()(()(())))", "()(()(())()(()()()))", "()(()(())()(()())())", "()(()(())()(()()))()", "()(()(())()(())(()))", "()(()(())()(())()())", "()(()(())()(())())()", "()(()(())()(()))(())", "()(()(())()(()))()()", "()(()(())()()((())))", "()(()(())()()(()()))", "()(()(())()()(())())", "()(()(())()()(()))()", "()(()(())()()()(()))", "()(()(())()()()()())", "()(()(())()()()())()", "()(()(())()()())(())", "()(()(())()()())()()", "()(()(())()())((()))", "()(()(())()())(()())", "()(()(())()())(())()", "()(()(())()())()(())", "()(()(())()())()()()", "()(()(())())(((())))", "()(()(())())((()()))", "()(()(())())((())())", "()(()(())())((()))()", "()(()(())())(()(()))", "()(()(())())(()()())", "()(()(())())(()())()", "()(()(())())(())(())", "()(()(())())(())()()", "()(()(())())()((()))", "()(()(())())()(()())", "()(()(())())()(())()", "()(()(())())()()(())", "()(()(())())()()()()", "()(()(()))((((()))))", "()(()(()))(((()())))", "()(()(()))(((())()))", "()(()(()))(((()))())", "()(()(()))(((())))()", "()(()(()))((()(())))", "()(()(()))((()()()))", "()(()(()))((()())())", "()(()(()))((()()))()", "()(()(()))((())(()))", "()(()(()))((())()())", "()(()(()))((())())()", "()(()(()))((()))(())", "()(()(()))((()))()()", "()(()(()))(()((())))", "()(()(()))(()(()()))", "()(()(()))(()(())())", "()(()(()))(()(()))()", "()(()(()))(()()(()))", "()(()(()))(()()()())", "()(()(()))(()()())()", "()(()(()))(()())(())", "()(()(()))(()())()()", "()(()(()))(())((()))", "()(()(()))(())(()())", "()(()(()))(())(())()", "()(()(()))(())()(())", "()(()(()))(())()()()", "()(()(()))()(((())))", "()(()(()))()((()()))", "()(()(()))()((())())", "()(()(()))()((()))()", "()(()(()))()(()(()))", "()(()(()))()(()()())", "()(()(()))()(()())()", "()(()(()))()(())(())", "()(()(()))()(())()()", "()(()(()))()()((()))", "()(()(()))()()(()())", "()(()(()))()()(())()", "()(()(()))()()()(())", "()(()(()))()()()()()", "()(()()(((((()))))))", "()(()()((((()())))))", "()(()()((((())()))))", "()(()()((((()))())))", "()(()()((((())))()))", "()(()()((((()))))())", "()(()()((((())))))()", "()(()()(((()(())))))", "()(()()(((()()()))))", "()(()()(((()())())))", "()(()()(((()()))()))", "()(()()(((()())))())", "()(()()(((()()))))()", "()(()()(((())(()))))", "()(()()(((())()())))", "()(()()(((())())()))", "()(()()(((())()))())", "()(()()(((())())))()", "()(()()(((()))(())))", "()(()()(((()))()()))", "()(()()(((()))())())", "()(()()(((()))()))()", "()(()()(((())))(()))", "()(()()(((())))()())", "()(()()(((())))())()", "()(()()(((()))))(())", "()(()()(((()))))()()", "()(()()((()((())))))", "()(()()((()(()()))))", "()(()()((()(())())))", "()(()()((()(()))()))", "()(()()((()(())))())", "()(()()((()(()))))()", "()(()()((()()(()))))", "()(()()((()()()())))", "()(()()((()()())()))", "()(()()((()()()))())", "()(()()((()()())))()", "()(()()((()())(())))", "()(()()((()())()()))", "()(()()((()())())())", "()(()()((()())()))()", "()(()()((()()))(()))", "()(()()((()()))()())", "()(()()((()()))())()", "()(()()((()())))(())", "()(()()((()())))()()", "()(()()((())((()))))", "()(()()((())(()())))", "()(()()((())(())()))", "()(()()((())(()))())", "()(()()((())(())))()", "()(()()((())()(())))", "()(()()((())()()()))", "()(()()((())()())())", "()(()()((())()()))()", "()(()()((())())(()))", "()(()()((())())()())", "()(()()((())())())()", "()(()()((())()))(())", "()(()()((())()))()()", "()(()()((()))((())))", "()(()()((()))(()()))", "()(()()((()))(())())", "()(()()((()))(()))()", "()(()()((()))()(()))", "()(()()((()))()()())", "()(()()((()))()())()", "()(()()((()))())(())", "()(()()((()))())()()", "()(()()((())))((()))", "()(()()((())))(()())", "()(()()((())))(())()", "()(()()((())))()(())", "()(()()((())))()()()", "()(()()(()(((())))))", "()(()()(()((()()))))", "()(()()(()((())())))", "()(()()(()((()))()))", "()(()()(()((())))())", "()(()()(()((()))))()", "()(()()(()(()(()))))", "()(()()(()(()()())))", "()(()()(()(()())()))", "()(()()(()(()()))())", "()(()()(()(()())))()", "()(()()(()(())(())))", "()(()()(()(())()()))", "()(()()(()(())())())", "()(()()(()(())()))()", "()(()()(()(()))(()))", "()(()()(()(()))()())", "()(()()(()(()))())()", "()(()()(()(())))(())", "()(()()(()(())))()()", "()(()()(()()((()))))", "()(()()(()()(()())))", "()(()()(()()(())()))", "()(()()(()()(()))())", "()(()()(()()(())))()", "()(()()(()()()(())))", "()(()()(()()()()()))", "()(()()(()()()())())", "()(()()(()()()()))()", "()(()()(()()())(()))", "()(()()(()()())()())", "()(()()(()()())())()", "()(()()(()()()))(())", "()(()()(()()()))()()", "()(()()(()())((())))", "()(()()(()())(()()))", "()(()()(()())(())())", "()(()()(()())(()))()", "()(()()(()())()(()))", "()(()()(()())()()())", "()(()()(()())()())()", "()(()()(()())())(())", "()(()()(()())())()()", "()(()()(()()))((()))", "()(()()(()()))(()())", "()(()()(()()))(())()", "()(()()(()()))()(())", "()(()()(()()))()()()", "()(()()(())(((()))))", "()(()()(())((()())))", "()(()()(())((())()))", "()(()()(())((()))())", "()(()()(())((())))()", "()(()()(())(()(())))", "()(()()(())(()()()))", "()(()()(())(()())())", "()(()()(())(()()))()", "()(()()(())(())(()))", "()(()()(())(())()())", "()(()()(())(())())()", "()(()()(())(()))(())", "()(()()(())(()))()()", "()(()()(())()((())))", "()(()()(())()(()()))", "()(()()(())()(())())", "()(()()(())()(()))()", "()(()()(())()()(()))", "()(()()(())()()()())", "()(()()(())()()())()", "()(()()(())()())(())", "()(()()(())()())()()", "()(()()(())())((()))", "()(()()(())())(()())", "()(()()(())())(())()", "()(()()(())())()(())", "()(()()(())())()()()", "()(()()(()))(((())))", "()(()()(()))((()()))", "()(()()(()))((())())", "()(()()(()))((()))()", "()(()()(()))(()(()))", "()(()()(()))(()()())", "()(()()(()))(()())()", "()(()()(()))(())(())", "()(()()(()))(())()()", "()(()()(()))()((()))", "()(()()(()))()(()())", "()(()()(()))()(())()", "()(()()(()))()()(())", "()(()()(()))()()()()", "()(()()()((((())))))", "()(()()()(((()()))))", "()(()()()(((())())))", "()(()()()(((()))()))", "()(()()()(((())))())", "()(()()()(((()))))()", "()(()()()((()(()))))", "()(()()()((()()())))", "()(()()()((()())()))", "()(()()()((()()))())", "()(()()()((()())))()", "()(()()()((())(())))", "()(()()()((())()()))", "()(()()()((())())())", "()(()()()((())()))()", "()(()()()((()))(()))", "()(()()()((()))()())", "()(()()()((()))())()", "()(()()()((())))(())", "()(()()()((())))()()", "()(()()()(()((()))))", "()(()()()(()(()())))", "()(()()()(()(())()))", "()(()()()(()(()))())", "()(()()()(()(())))()", "()(()()()(()()(())))", "()(()()()(()()()()))", "()(()()()(()()())())", "()(()()()(()()()))()", "()(()()()(()())(()))", "()(()()()(()())()())", "()(()()()(()())())()", "()(()()()(()()))(())", "()(()()()(()()))()()", "()(()()()(())((())))", "()(()()()(())(()()))", "()(()()()(())(())())", "()(()()()(())(()))()", "()(()()()(())()(()))", "()(()()()(())()()())", "()(()()()(())()())()", "()(()()()(())())(())", "()(()()()(())())()()", "()(()()()(()))((()))", "()(()()()(()))(()())", "()(()()()(()))(())()", "()(()()()(()))()(())", "()(()()()(()))()()()", "()(()()()()(((()))))", "()(()()()()((()())))", "()(()()()()((())()))", "()(()()()()((()))())", "()(()()()()((())))()", "()(()()()()(()(())))", "()(()()()()(()()()))", "()(()()()()(()())())", "()(()()()()(()()))()", "()(()()()()(())(()))", "()(()()()()(())()())", "()(()()()()(())())()", "()(()()()()(()))(())", "()(()()()()(()))()()", "()(()()()()()((())))", "()(()()()()()(()()))", "()(()()()()()(())())", "()(()()()()()(()))()", "()(()()()()()()(()))", "()(()()()()()()()())", "()(()()()()()()())()", "()(()()()()()())(())", "()(()()()()()())()()", "()(()()()()())((()))", "()(()()()()())(()())", "()(()()()()())(())()", "()(()()()()())()(())", "()(()()()()())()()()", "()(()()()())(((())))", "()(()()()())((()()))", "()(()()()())((())())", "()(()()()())((()))()", "()(()()()())(()(()))", "()(()()()())(()()())", "()(()()()())(()())()", "()(()()()())(())(())", "()(()()()())(())()()", "()(()()()())()((()))", "()(()()()())()(()())", "()(()()()())()(())()", "()(()()()())()()(())", "()(()()()())()()()()", "()(()()())((((()))))", "()(()()())(((()())))", "()(()()())(((())()))", "()(()()())(((()))())", "()(()()())(((())))()", "()(()()())((()(())))", "()(()()())((()()()))", "()(()()())((()())())", "()(()()())((()()))()", "()(()()())((())(()))", "()(()()())((())()())", "()(()()())((())())()", "()(()()())((()))(())", "()(()()())((()))()()", "()(()()())(()((())))", "()(()()())(()(()()))", "()(()()())(()(())())", "()(()()())(()(()))()", "()(()()())(()()(()))", "()(()()())(()()()())", "()(()()())(()()())()", "()(()()())(()())(())", "()(()()())(()())()()", "()(()()())(())((()))", "()(()()())(())(()())", "()(()()())(())(())()", "()(()()())(())()(())", "()(()()())(())()()()", "()(()()())()(((())))", "()(()()())()((()()))", "()(()()())()((())())", "()(()()())()((()))()", "()(()()())()(()(()))", "()(()()())()(()()())", "()(()()())()(()())()", "()(()()())()(())(())", "()(()()())()(())()()", "()(()()())()()((()))", "()(()()())()()(()())", "()(()()())()()(())()", "()(()()())()()()(())", "()(()()())()()()()()", "()(()())(((((())))))", "()(()())((((()()))))", "()(()())((((())())))", "()(()())((((()))()))", "()(()())((((())))())", "()(()())((((()))))()", "()(()())(((()(()))))", "()(()())(((()()())))", "()(()())(((()())()))", "()(()())(((()()))())", "()(()())(((()())))()", "()(()())(((())(())))", "()(()())(((())()()))", "()(()())(((())())())", "()(()())(((())()))()", "()(()())(((()))(()))", "()(()())(((()))()())", "()(()())(((()))())()", "()(()())(((())))(())", "()(()())(((())))()()", "()(()())((()((()))))", "()(()())((()(()())))", "()(()())((()(())()))", "()(()())((()(()))())", "()(()())((()(())))()", "()(()())((()()(())))", "()(()())((()()()()))", "()(()())((()()())())", "()(()())((()()()))()", "()(()())((()())(()))", "()(()())((()())()())", "()(()())((()())())()", "()(()())((()()))(())", "()(()())((()()))()()", "()(()())((())((())))", "()(()())((())(()()))", "()(()())((())(())())", "()(()())((())(()))()", "()(()())((())()(()))", "()(()())((())()()())", "()(()())((())()())()", "()(()())((())())(())", "()(()())((())())()()", "()(()())((()))((()))", "()(()())((()))(()())", "()(()())((()))(())()", "()(()())((()))()(())", "()(()())((()))()()()", "()(()())(()(((()))))", "()(()())(()((()())))", "()(()())(()((())()))", "()(()())(()((()))())", "()(()())(()((())))()", "()(()())(()(()(())))", "()(()())(()(()()()))", "()(()())(()(()())())", "()(()())(()(()()))()", "()(()())(()(())(()))", "()(()())(()(())()())", "()(()())(()(())())()", "()(()())(()(()))(())", "()(()())(()(()))()()", "()(()())(()()((())))", "()(()())(()()(()()))", "()(()())(()()(())())", "()(()())(()()(()))()", "()(()())(()()()(()))", "()(()())(()()()()())", "()(()())(()()()())()", "()(()())(()()())(())", "()(()())(()()())()()", "()(()())(()())((()))", "()(()())(()())(()())", "()(()())(()())(())()", "()(()())(()())()(())", "()(()())(()())()()()", "()(()())(())(((())))", "()(()())(())((()()))", "()(()())(())((())())", "()(()())(())((()))()", "()(()())(())(()(()))", "()(()())(())(()()())", "()(()())(())(()())()", "()(()())(())(())(())", "()(()())(())(())()()", "()(()())(())()((()))", "()(()())(())()(()())", "()(()())(())()(())()", "()(()())(())()()(())", "()(()())(())()()()()", "()(()())()((((()))))", "()(()())()(((()())))", "()(()())()(((())()))", "()(()())()(((()))())", "()(()())()(((())))()", "()(()())()((()(())))", "()(()())()((()()()))", "()(()())()((()())())", "()(()())()((()()))()", "()(()())()((())(()))", "()(()())()((())()())", "()(()())()((())())()", "()(()())()((()))(())", "()(()())()((()))()()", "()(()())()(()((())))", "()(()())()(()(()()))", "()(()())()(()(())())", "()(()())()(()(()))()", "()(()())()(()()(()))", "()(()())()(()()()())", "()(()())()(()()())()", "()(()())()(()())(())", "()(()())()(()())()()", "()(()())()(())((()))", "()(()())()(())(()())", "()(()())()(())(())()", "()(()())()(())()(())", "()(()())()(())()()()", "()(()())()()(((())))", "()(()())()()((()()))", "()(()())()()((())())", "()(()())()()((()))()", "()(()())()()(()(()))", "()(()())()()(()()())", "()(()())()()(()())()", "()(()())()()(())(())", "()(()())()()(())()()", "()(()())()()()((()))", "()(()())()()()(()())", "()(()())()()()(())()", "()(()())()()()()(())", "()(()())()()()()()()", "()(())((((((()))))))", "()(())(((((()())))))", "()(())(((((())()))))", "()(())(((((()))())))", "()(())(((((())))()))", "()(())(((((()))))())", "()(())(((((())))))()", "()(())((((()(())))))", "()(())((((()()()))))", "()(())((((()())())))", "()(())((((()()))()))", "()(())((((()())))())", "()(())((((()()))))()", "()(())((((())(()))))", "()(())((((())()())))", "()(())((((())())()))", "()(())((((())()))())", "()(())((((())())))()", "()(())((((()))(())))", "()(())((((()))()()))", "()(())((((()))())())", "()(())((((()))()))()", "()(())((((())))(()))", "()(())((((())))()())", "()(())((((())))())()", "()(())((((()))))(())", "()(())((((()))))()()", "()(())(((()((())))))", "()(())(((()(()()))))", "()(())(((()(())())))", "()(())(((()(()))()))", "()(())(((()(())))())", "()(())(((()(()))))()", "()(())(((()()(()))))", "()(())(((()()()())))", "()(())(((()()())()))", "()(())(((()()()))())", "()(())(((()()())))()", "()(())(((()())(())))", "()(())(((()())()()))", "()(())(((()())())())", "()(())(((()())()))()", "()(())(((()()))(()))", "()(())(((()()))()())", "()(())(((()()))())()", "()(())(((()())))(())", "()(())(((()())))()()", "()(())(((())((()))))", "()(())(((())(()())))", "()(())(((())(())()))", "()(())(((())(()))())", "()(())(((())(())))()", "()(())(((())()(())))", "()(())(((())()()()))", "()(())(((())()())())", "()(())(((())()()))()", "()(())(((())())(()))", "()(())(((())())()())", "()(())(((())())())()", "()(())(((())()))(())", "()(())(((())()))()()", "()(())(((()))((())))", "()(())(((()))(()()))", "()(())(((()))(())())", "()(())(((()))(()))()", "()(())(((()))()(()))", "()(())(((()))()()())", "()(())(((()))()())()", "()(())(((()))())(())", "()(())(((()))())()()", "()(())(((())))((()))", "()(())(((())))(()())", "()(())(((())))(())()", "()(())(((())))()(())", "()(())(((())))()()()", "()(())((()(((())))))", "()(())((()((()()))))", "()(())((()((())())))", "()(())((()((()))()))", "()(())((()((())))())", "()(())((()((()))))()", "()(())((()(()(()))))", "()(())((()(()()())))", "()(())((()(()())()))", "()(())((()(()()))())", "()(())((()(()())))()", "()(())((()(())(())))", "()(())((()(())()()))", "()(())((()(())())())", "()(())((()(())()))()", "()(())((()(()))(()))", "()(())((()(()))()())", "()(())((()(()))())()", "()(())((()(())))(())", "()(())((()(())))()()", "()(())((()()((()))))", "()(())((()()(()())))", "()(())((()()(())()))", "()(())((()()(()))())", "()(())((()()(())))()", "()(())((()()()(())))", "()(())((()()()()()))", "()(())((()()()())())", "()(())((()()()()))()", "()(())((()()())(()))", "()(())((()()())()())", "()(())((()()())())()", "()(())((()()()))(())", "()(())((()()()))()()", "()(())((()())((())))", "()(())((()())(()()))", "()(())((()())(())())", "()(())((()())(()))()", "()(())((()())()(()))", "()(())((()())()()())", "()(())((()())()())()", "()(())((()())())(())", "()(())((()())())()()", "()(())((()()))((()))", "()(())((()()))(()())", "()(())((()()))(())()", "()(())((()()))()(())", "()(())((()()))()()()", "()(())((())(((()))))", "()(())((())((()())))", "()(())((())((())()))", "()(())((())((()))())", "()(())((())((())))()", "()(())((())(()(())))", "()(())((())(()()()))", "()(())((())(()())())", "()(())((())(()()))()", "()(())((())(())(()))", "()(())((())(())()())", "()(())((())(())())()", "()(())((())(()))(())", "()(())((())(()))()()", "()(())((())()((())))", "()(())((())()(()()))", "()(())((())()(())())", "()(())((())()(()))()", "()(())((())()()(()))", "()(())((())()()()())", "()(())((())()()())()", "()(())((())()())(())", "()(())((())()())()()", "()(())((())())((()))", "()(())((())())(()())", "()(())((())())(())()", "()(())((())())()(())", "()(())((())())()()()", "()(())((()))(((())))", "()(())((()))((()()))", "()(())((()))((())())", "()(())((()))((()))()", "()(())((()))(()(()))", "()(())((()))(()()())", "()(())((()))(()())()", "()(())((()))(())(())", "()(())((()))(())()()", "()(())((()))()((()))", "()(())((()))()(()())", "()(())((()))()(())()", "()(())((()))()()(())", "()(())((()))()()()()", "()(())(()((((())))))", "()(())(()(((()()))))", "()(())(()(((())())))", "()(())(()(((()))()))", "()(())(()(((())))())", "()(())(()(((()))))()", "()(())(()((()(()))))", "()(())(()((()()())))", "()(())(()((()())()))", "()(())(()((()()))())", "()(())(()((()())))()", "()(())(()((())(())))", "()(())(()((())()()))", "()(())(()((())())())", "()(())(()((())()))()", "()(())(()((()))(()))", "()(())(()((()))()())", "()(())(()((()))())()", "()(())(()((())))(())", "()(())(()((())))()()", "()(())(()(()((()))))", "()(())(()(()(()())))", "()(())(()(()(())()))", "()(())(()(()(()))())", "()(())(()(()(())))()", "()(())(()(()()(())))", "()(())(()(()()()()))", "()(())(()(()()())())", "()(())(()(()()()))()", "()(())(()(()())(()))", "()(())(()(()())()())", "()(())(()(()())())()", "()(())(()(()()))(())", "()(())(()(()()))()()", "()(())(()(())((())))", "()(())(()(())(()()))", "()(())(()(())(())())", "()(())(()(())(()))()", "()(())(()(())()(()))", "()(())(()(())()()())", "()(())(()(())()())()", "()(())(()(())())(())", "()(())(()(())())()()", "()(())(()(()))((()))", "()(())(()(()))(()())", "()(())(()(()))(())()", "()(())(()(()))()(())", "()(())(()(()))()()()", "()(())(()()(((()))))", "()(())(()()((()())))", "()(())(()()((())()))", "()(())(()()((()))())", "()(())(()()((())))()", "()(())(()()(()(())))", "()(())(()()(()()()))", "()(())(()()(()())())", "()(())(()()(()()))()", "()(())(()()(())(()))", "()(())(()()(())()())", "()(())(()()(())())()", "()(())(()()(()))(())", "()(())(()()(()))()()", "()(())(()()()((())))", "()(())(()()()(()()))", "()(())(()()()(())())", "()(())(()()()(()))()", "()(())(()()()()(()))", "()(())(()()()()()())", "()(())(()()()()())()", "()(())(()()()())(())", "()(())(()()()())()()", "()(())(()()())((()))", "()(())(()()())(()())", "()(())(()()())(())()", "()(())(()()())()(())", "()(())(()()())()()()", "()(())(()())(((())))", "()(())(()())((()()))", "()(())(()())((())())", "()(())(()())((()))()", "()(())(()())(()(()))", "()(())(()())(()()())", "()(())(()())(()())()", "()(())(()())(())(())", "()(())(()())(())()()", "()(())(()())()((()))", "()(())(()())()(()())", "()(())(()())()(())()", "()(())(()())()()(())", "()(())(()())()()()()", "()(())(())((((()))))", "()(())(())(((()())))", "()(())(())(((())()))", "()(())(())(((()))())", "()(())(())(((())))()", "()(())(())((()(())))", "()(())(())((()()()))", "()(())(())((()())())", "()(())(())((()()))()", "()(())(())((())(()))", "()(())(())((())()())", "()(())(())((())())()", "()(())(())((()))(())", "()(())(())((()))()()", "()(())(())(()((())))", "()(())(())(()(()()))", "()(())(())(()(())())", "()(())(())(()(()))()", "()(())(())(()()(()))", "()(())(())(()()()())", "()(())(())(()()())()", "()(())(())(()())(())", "()(())(())(()())()()", "()(())(())(())((()))", "()(())(())(())(()())", "()(())(())(())(())()", "()(())(())(())()(())", "()(())(())(())()()()", "()(())(())()(((())))", "()(())(())()((()()))", "()(())(())()((())())", "()(())(())()((()))()", "()(())(())()(()(()))", "()(())(())()(()()())", "()(())(())()(()())()", "()(())(())()(())(())", "()(())(())()(())()()", "()(())(())()()((()))", "()(())(())()()(()())", "()(())(())()()(())()", "()(())(())()()()(())", "()(())(())()()()()()", "()(())()(((((())))))", "()(())()((((()()))))", "()(())()((((())())))", "()(())()((((()))()))", "()(())()((((())))())", "()(())()((((()))))()", "()(())()(((()(()))))", "()(())()(((()()())))", "()(())()(((()())()))", "()(())()(((()()))())", "()(())()(((()())))()", "()(())()(((())(())))", "()(())()(((())()()))", "()(())()(((())())())", "()(())()(((())()))()", "()(())()(((()))(()))", "()(())()(((()))()())", "()(())()(((()))())()", "()(())()(((())))(())", "()(())()(((())))()()", "()(())()((()((()))))", "()(())()((()(()())))", "()(())()((()(())()))", "()(())()((()(()))())", "()(())()((()(())))()", "()(())()((()()(())))", "()(())()((()()()()))", "()(())()((()()())())", "()(())()((()()()))()", "()(())()((()())(()))", "()(())()((()())()())", "()(())()((()())())()", "()(())()((()()))(())", "()(())()((()()))()()", "()(())()((())((())))", "()(())()((())(()()))", "()(())()((())(())())", "()(())()((())(()))()", "()(())()((())()(()))", "()(())()((())()()())", "()(())()((())()())()", "()(())()((())())(())", "()(())()((())())()()", "()(())()((()))((()))", "()(())()((()))(()())", "()(())()((()))(())()", "()(())()((()))()(())", "()(())()((()))()()()", "()(())()(()(((()))))", "()(())()(()((()())))", "()(())()(()((())()))", "()(())()(()((()))())", "()(())()(()((())))()", "()(())()(()(()(())))", "()(())()(()(()()()))", "()(())()(()(()())())", "()(())()(()(()()))()", "()(())()(()(())(()))", "()(())()(()(())()())", "()(())()(()(())())()", "()(())()(()(()))(())", "()(())()(()(()))()()", "()(())()(()()((())))", "()(())()(()()(()()))", "()(())()(()()(())())", "()(())()(()()(()))()", "()(())()(()()()(()))", "()(())()(()()()()())", "()(())()(()()()())()", "()(())()(()()())(())", "()(())()(()()())()()", "()(())()(()())((()))", "()(())()(()())(()())", "()(())()(()())(())()", "()(())()(()())()(())", "()(())()(()())()()()", "()(())()(())(((())))", "()(())()(())((()()))", "()(())()(())((())())", "()(())()(())((()))()", "()(())()(())(()(()))", "()(())()(())(()()())", "()(())()(())(()())()", "()(())()(())(())(())", "()(())()(())(())()()", "()(())()(())()((()))", "()(())()(())()(()())", "()(())()(())()(())()", "()(())()(())()()(())", "()(())()(())()()()()", "()(())()()((((()))))", "()(())()()(((()())))", "()(())()()(((())()))", "()(())()()(((()))())", "()(())()()(((())))()", "()(())()()((()(())))", "()(())()()((()()()))", "()(())()()((()())())", "()(())()()((()()))()", "()(())()()((())(()))", "()(())()()((())()())", "()(())()()((())())()", "()(())()()((()))(())", "()(())()()((()))()()", "()(())()()(()((())))", "()(())()()(()(()()))", "()(())()()(()(())())", "()(())()()(()(()))()", "()(())()()(()()(()))", "()(())()()(()()()())", "()(())()()(()()())()", "()(())()()(()())(())", "()(())()()(()())()()", "()(())()()(())((()))", "()(())()()(())(()())", "()(())()()(())(())()", "()(())()()(())()(())", "()(())()()(())()()()", "()(())()()()(((())))", "()(())()()()((()()))", "()(())()()()((())())", "()(())()()()((()))()", "()(())()()()(()(()))", "()(())()()()(()()())", "()(())()()()(()())()", "()(())()()()(())(())", "()(())()()()(())()()", "()(())()()()()((()))", "()(())()()()()(()())", "()(())()()()()(())()", "()(())()()()()()(())", "()(())()()()()()()()", "()()(((((((())))))))", "()()((((((()()))))))", "()()((((((())())))))", "()()((((((()))()))))", "()()((((((())))())))", "()()((((((()))))()))", "()()((((((())))))())", "()()((((((()))))))()", "()()(((((()(()))))))", "()()(((((()()())))))", "()()(((((()())()))))", "()()(((((()()))())))", "()()(((((()())))()))", "()()(((((()()))))())", "()()(((((()())))))()", "()()(((((())(())))))", "()()(((((())()()))))", "()()(((((())())())))", "()()(((((())()))()))", "()()(((((())())))())", "()()(((((())()))))()", "()()(((((()))(()))))", "()()(((((()))()())))", "()()(((((()))())()))", "()()(((((()))()))())", "()()(((((()))())))()", "()()(((((())))(())))", "()()(((((())))()()))", "()()(((((())))())())", "()()(((((())))()))()", "()()(((((()))))(()))", "()()(((((()))))()())", "()()(((((()))))())()", "()()(((((())))))(())", "()()(((((())))))()()", "()()((((()((()))))))", "()()((((()(()())))))", "()()((((()(())()))))", "()()((((()(()))())))", "()()((((()(())))()))", "()()((((()(()))))())", "()()((((()(())))))()", "()()((((()()(())))))", "()()((((()()()()))))", "()()((((()()())())))", "()()((((()()()))()))", "()()((((()()())))())", "()()((((()()()))))()", "()()((((()())(()))))", "()()((((()())()())))", "()()((((()())())()))", "()()((((()())()))())", "()()((((()())())))()", "()()((((()()))(())))", "()()((((()()))()()))", "()()((((()()))())())", "()()((((()()))()))()", "()()((((()())))(()))", "()()((((()())))()())", "()()((((()())))())()", "()()((((()()))))(())", "()()((((()()))))()()", "()()((((())((())))))", "()()((((())(()()))))", "()()((((())(())())))", "()()((((())(()))()))", "()()((((())(())))())", "()()((((())(()))))()", "()()((((())()(()))))", "()()((((())()()())))", "()()((((())()())()))", "()()((((())()()))())", "()()((((())()())))()", "()()((((())())(())))", "()()((((())())()()))", "()()((((())())())())", "()()((((())())()))()", "()()((((())()))(()))", "()()((((())()))()())", "()()((((())()))())()", "()()((((())())))(())", "()()((((())())))()()", "()()((((()))((()))))", "()()((((()))(()())))", "()()((((()))(())()))", "()()((((()))(()))())", "()()((((()))(())))()", "()()((((()))()(())))", "()()((((()))()()()))", "()()((((()))()())())", "()()((((()))()()))()", "()()((((()))())(()))", "()()((((()))())()())", "()()((((()))())())()", "()()((((()))()))(())", "()()((((()))()))()()", "()()((((())))((())))", "()()((((())))(()()))", "()()((((())))(())())", "()()((((())))(()))()", "()()((((())))()(()))", "()()((((())))()()())", "()()((((())))()())()", "()()((((())))())(())", "()()((((())))())()()", "()()((((()))))((()))", "()()((((()))))(()())", "()()((((()))))(())()", "()()((((()))))()(())", "()()((((()))))()()()", "()()(((()(((()))))))", "()()(((()((()())))))", "()()(((()((())()))))", "()()(((()((()))())))", "()()(((()((())))()))", "()()(((()((()))))())", "()()(((()((())))))()", "()()(((()(()(())))))", "()()(((()(()()()))))", "()()(((()(()())())))", "()()(((()(()()))()))", "()()(((()(()())))())", "()()(((()(()()))))()", "()()(((()(())(()))))", "()()(((()(())()())))", "()()(((()(())())()))", "()()(((()(())()))())", "()()(((()(())())))()", "()()(((()(()))(())))", "()()(((()(()))()()))", "()()(((()(()))())())", "()()(((()(()))()))()", "()()(((()(())))(()))", "()()(((()(())))()())", "()()(((()(())))())()", "()()(((()(()))))(())", "()()(((()(()))))()()", "()()(((()()((())))))", "()()(((()()(()()))))", "()()(((()()(())())))", "()()(((()()(()))()))", "()()(((()()(())))())", "()()(((()()(()))))()", "()()(((()()()(()))))", "()()(((()()()()())))", "()()(((()()()())()))", "()()(((()()()()))())", "()()(((()()()())))()", "()()(((()()())(())))", "()()(((()()())()()))", "()()(((()()())())())", "()()(((()()())()))()", "()()(((()()()))(()))", "()()(((()()()))()())", "()()(((()()()))())()", "()()(((()()())))(())", "()()(((()()())))()()", "()()(((()())((()))))", "()()(((()())(()())))", "()()(((()())(())()))", "()()(((()())(()))())", "()()(((()())(())))()", "()()(((()())()(())))", "()()(((()())()()()))", "()()(((()())()())())", "()()(((()())()()))()", "()()(((()())())(()))", "()()(((()())())()())", "()()(((()())())())()", "()()(((()())()))(())", "()()(((()())()))()()", "()()(((()()))((())))", "()()(((()()))(()()))", "()()(((()()))(())())", "()()(((()()))(()))()", "()()(((()()))()(()))", "()()(((()()))()()())", "()()(((()()))()())()", "()()(((()()))())(())", "()()(((()()))())()()", "()()(((()())))((()))", "()()(((()())))(()())", "()()(((()())))(())()", "()()(((()())))()(())", "()()(((()())))()()()", "()()(((())(((())))))", "()()(((())((()()))))", "()()(((())((())())))", "()()(((())((()))()))", "()()(((())((())))())", "()()(((())((()))))()", "()()(((())(()(()))))", "()()(((())(()()())))", "()()(((())(()())()))", "()()(((())(()()))())", "()()(((())(()())))()", "()()(((())(())(())))", "()()(((())(())()()))", "()()(((())(())())())", "()()(((())(())()))()", "()()(((())(()))(()))", "()()(((())(()))()())", "()()(((())(()))())()", "()()(((())(())))(())", "()()(((())(())))()()", "()()(((())()((()))))", "()()(((())()(()())))", "()()(((())()(())()))", "()()(((())()(()))())", "()()(((())()(())))()", "()()(((())()()(())))", "()()(((())()()()()))", "()()(((())()()())())", "()()(((())()()()))()", "()()(((())()())(()))", "()()(((())()())()())", "()()(((())()())())()", "()()(((())()()))(())", "()()(((())()()))()()", "()()(((())())((())))", "()()(((())())(()()))", "()()(((())())(())())", "()()(((())())(()))()", "()()(((())())()(()))", "()()(((())())()()())", "()()(((())())()())()", "()()(((())())())(())", "()()(((())())())()()", "()()(((())()))((()))", "()()(((())()))(()())", "()()(((())()))(())()", "()()(((())()))()(())", "()()(((())()))()()()", "()()(((()))(((()))))", "()()(((()))((()())))", "()()(((()))((())()))", "()()(((()))((()))())", "()()(((()))((())))()", "()()(((()))(()(())))", "()()(((()))(()()()))", "()()(((()))(()())())", "()()(((()))(()()))()", "()()(((()))(())(()))", "()()(((()))(())()())", "()()(((()))(())())()", "()()(((()))(()))(())", "()()(((()))(()))()()", "()()(((()))()((())))", "()()(((()))()(()()))", "()()(((()))()(())())", "()()(((()))()(()))()", "()()(((()))()()(()))", "()()(((()))()()()())", "()()(((()))()()())()", "()()(((()))()())(())", "()()(((()))()())()()", "()()(((()))())((()))", "()()(((()))())(()())", "()()(((()))())(())()", "()()(((()))())()(())", "()()(((()))())()()()", "()()(((())))(((())))", "()()(((())))((()()))", "()()(((())))((())())", "()()(((())))((()))()", "()()(((())))(()(()))", "()()(((())))(()()())", "()()(((())))(()())()", "()()(((())))(())(())", "()()(((())))(())()()", "()()(((())))()((()))", "()()(((())))()(()())", "()()(((())))()(())()", "()()(((())))()()(())", "()()(((())))()()()()", "()()((()((((()))))))", "()()((()(((()())))))", "()()((()(((())()))))", "()()((()(((()))())))", "()()((()(((())))()))", "()()((()(((()))))())", "()()((()(((())))))()", "()()((()((()(())))))", "()()((()((()()()))))", "()()((()((()())())))", "()()((()((()()))()))", "()()((()((()())))())", "()()((()((()()))))()", "()()((()((())(()))))", "()()((()((())()())))", "()()((()((())())()))", "()()((()((())()))())", "()()((()((())())))()", "()()((()((()))(())))", "()()((()((()))()()))", "()()((()((()))())())", "()()((()((()))()))()", "()()((()((())))(()))", "()()((()((())))()())", "()()((()((())))())()", "()()((()((()))))(())", "()()((()((()))))()()", "()()((()(()((())))))", "()()((()(()(()()))))", "()()((()(()(())())))", "()()((()(()(()))()))", "()()((()(()(())))())", "()()((()(()(()))))()", "()()((()(()()(()))))", "()()((()(()()()())))", "()()((()(()()())()))", "()()((()(()()()))())", "()()((()(()()())))()", "()()((()(()())(())))", "()()((()(()())()()))", "()()((()(()())())())", "()()((()(()())()))()", "()()((()(()()))(()))", "()()((()(()()))()())", "()()((()(()()))())()", "()()((()(()())))(())", "()()((()(()())))()()", "()()((()(())((()))))", "()()((()(())(()())))", "()()((()(())(())()))", "()()((()(())(()))())", "()()((()(())(())))()", "()()((()(())()(())))", "()()((()(())()()()))", "()()((()(())()())())", "()()((()(())()()))()", "()()((()(())())(()))", "()()((()(())())()())", "()()((()(())())())()", "()()((()(())()))(())", "()()((()(())()))()()", "()()((()(()))((())))", "()()((()(()))(()()))", "()()((()(()))(())())", "()()((()(()))(()))()", "()()((()(()))()(()))", "()()((()(()))()()())", "()()((()(()))()())()", "()()((()(()))())(())", "()()((()(()))())()()", "()()((()(())))((()))", "()()((()(())))(()())", "()()((()(())))(())()", "()()((()(())))()(())", "()()((()(())))()()()", "()()((()()(((())))))", "()()((()()((()()))))", "()()((()()((())())))", "()()((()()((()))()))", "()()((()()((())))())", "()()((()()((()))))()", "()()((()()(()(()))))", "()()((()()(()()())))", "()()((()()(()())()))", "()()((()()(()()))())", "()()((()()(()())))()", "()()((()()(())(())))", "()()((()()(())()()))", "()()((()()(())())())", "()()((()()(())()))()", "()()((()()(()))(()))", "()()((()()(()))()())", "()()((()()(()))())()", "()()((()()(())))(())", "()()((()()(())))()()", "()()((()()()((()))))", "()()((()()()(()())))", "()()((()()()(())()))", "()()((()()()(()))())", "()()((()()()(())))()", "()()((()()()()(())))", "()()((()()()()()()))", "()()((()()()()())())", "()()((()()()()()))()", "()()((()()()())(()))", "()()((()()()())()())", "()()((()()()())())()", "()()((()()()()))(())", "()()((()()()()))()()", "()()((()()())((())))", "()()((()()())(()()))", "()()((()()())(())())", "()()((()()())(()))()", "()()((()()())()(()))", "()()((()()())()()())", "()()((()()())()())()", "()()((()()())())(())", "()()((()()())())()()", "()()((()()()))((()))", "()()((()()()))(()())", "()()((()()()))(())()", "()()((()()()))()(())", "()()((()()()))()()()", "()()((()())(((()))))", "()()((()())((()())))", "()()((()())((())()))", "()()((()())((()))())", "()()((()())((())))()", "()()((()())(()(())))", "()()((()())(()()()))", "()()((()())(()())())", "()()((()())(()()))()", "()()((()())(())(()))", "()()((()())(())()())", "()()((()())(())())()", "()()((()())(()))(())", "()()((()())(()))()()", "()()((()())()((())))", "()()((()())()(()()))", "()()((()())()(())())", "()()((()())()(()))()", "()()((()())()()(()))", "()()((()())()()()())", "()()((()())()()())()", "()()((()())()())(())", "()()((()())()())()()", "()()((()())())((()))", "()()((()())())(()())", "()()((()())())(())()", "()()((()())())()(())", "()()((()())())()()()", "()()((()()))(((())))", "()()((()()))((()()))", "()()((()()))((())())", "()()((()()))((()))()", "()()((()()))(()(()))", "()()((()()))(()()())", "()()((()()))(()())()", "()()((()()))(())(())", "()()((()()))(())()()", "()()((()()))()((()))", "()()((()()))()(()())", "()()((()()))()(())()", "()()((()()))()()(())", "()()((()()))()()()()", "()()((())((((())))))", "()()((())(((()()))))", "()()((())(((())())))", "()()((())(((()))()))", "()()((())(((())))())", "()()((())(((()))))()", "()()((())((()(()))))", "()()((())((()()())))", "()()((())((()())()))", "()()((())((()()))())", "()()((())((()())))()", "()()((())((())(())))", "()()((())((())()()))", "()()((())((())())())", "()()((())((())()))()", "()()((())((()))(()))", "()()((())((()))()())", "()()((())((()))())()", "()()((())((())))(())", "()()((())((())))()()", "()()((())(()((()))))", "()()((())(()(()())))", "()()((())(()(())()))", "()()((())(()(()))())", "()()((())(()(())))()", "()()((())(()()(())))", "()()((())(()()()()))", "()()((())(()()())())", "()()((())(()()()))()", "()()((())(()())(()))", "()()((())(()())()())", "()()((())(()())())()", "()()((())(()()))(())", "()()((())(()()))()()", "()()((())(())((())))", "()()((())(())(()()))", "()()((())(())(())())", "()()((())(())(()))()", "()()((())(())()(()))", "()()((())(())()()())", "()()((())(())()())()", "()()((())(())())(())", "()()((())(())())()()", "()()((())(()))((()))", "()()((())(()))(()())", "()()((())(()))(())()", "()()((())(()))()(())", "()()((())(()))()()()", "()()((())()(((()))))", "()()((())()((()())))", "()()((())()((())()))", "()()((())()((()))())", "()()((())()((())))()", "()()((())()(()(())))", "()()((())()(()()()))", "()()((())()(()())())", "()()((())()(()()))()", "()()((())()(())(()))", "()()((())()(())()())", "()()((())()(())())()", "()()((())()(()))(())", "()()((())()(()))()()", "()()((())()()((())))", "()()((())()()(()()))", "()()((())()()(())())", "()()((())()()(()))()", "()()((())()()()(()))", "()()((())()()()()())", "()()((())()()()())()", "()()((())()()())(())", "()()((())()()())()()", "()()((())()())((()))", "()()((())()())(()())", "()()((())()())(())()", "()()((())()())()(())", "()()((())()())()()()", "()()((())())(((())))", "()()((())())((()()))", "()()((())())((())())", "()()((())())((()))()", "()()((())())(()(()))", "()()((())())(()()())", "()()((())())(()())()", "()()((())())(())(())", "()()((())())(())()()", "()()((())())()((()))", "()()((())())()(()())", "()()((())())()(())()", "()()((())())()()(())", "()()((())())()()()()", "()()((()))((((()))))", "()()((()))(((()())))", "()()((()))(((())()))", "()()((()))(((()))())", "()()((()))(((())))()", "()()((()))((()(())))", "()()((()))((()()()))", "()()((()))((()())())", "()()((()))((()()))()", "()()((()))((())(()))", "()()((()))((())()())", "()()((()))((())())()", "()()((()))((()))(())", "()()((()))((()))()()", "()()((()))(()((())))", "()()((()))(()(()()))", "()()((()))(()(())())", "()()((()))(()(()))()", "()()((()))(()()(()))", "()()((()))(()()()())", "()()((()))(()()())()", "()()((()))(()())(())", "()()((()))(()())()()", "()()((()))(())((()))", "()()((()))(())(()())", "()()((()))(())(())()", "()()((()))(())()(())", "()()((()))(())()()()", "()()((()))()(((())))", "()()((()))()((()()))", "()()((()))()((())())", "()()((()))()((()))()", "()()((()))()(()(()))", "()()((()))()(()()())", "()()((()))()(()())()", "()()((()))()(())(())", "()()((()))()(())()()", "()()((()))()()((()))", "()()((()))()()(()())", "()()((()))()()(())()", "()()((()))()()()(())", "()()((()))()()()()()", "()()(()(((((()))))))", "()()(()((((()())))))", "()()(()((((())()))))", "()()(()((((()))())))", "()()(()((((())))()))", "()()(()((((()))))())", "()()(()((((())))))()", "()()(()(((()(())))))", "()()(()(((()()()))))", "()()(()(((()())())))", "()()(()(((()()))()))", "()()(()(((()())))())", "()()(()(((()()))))()", "()()(()(((())(()))))", "()()(()(((())()())))", "()()(()(((())())()))", "()()(()(((())()))())", "()()(()(((())())))()", "()()(()(((()))(())))", "()()(()(((()))()()))", "()()(()(((()))())())", "()()(()(((()))()))()", "()()(()(((())))(()))", "()()(()(((())))()())", "()()(()(((())))())()", "()()(()(((()))))(())", "()()(()(((()))))()()", "()()(()((()((())))))", "()()(()((()(()()))))", "()()(()((()(())())))", "()()(()((()(()))()))", "()()(()((()(())))())", "()()(()((()(()))))()", "()()(()((()()(()))))", "()()(()((()()()())))", "()()(()((()()())()))", "()()(()((()()()))())", "()()(()((()()())))()", "()()(()((()())(())))", "()()(()((()())()()))", "()()(()((()())())())", "()()(()((()())()))()", "()()(()((()()))(()))", "()()(()((()()))()())", "()()(()((()()))())()", "()()(()((()())))(())", "()()(()((()())))()()", "()()(()((())((()))))", "()()(()((())(()())))", "()()(()((())(())()))", "()()(()((())(()))())", "()()(()((())(())))()", "()()(()((())()(())))", "()()(()((())()()()))", "()()(()((())()())())", "()()(()((())()()))()", "()()(()((())())(()))", "()()(()((())())()())", "()()(()((())())())()", "()()(()((())()))(())", "()()(()((())()))()()", "()()(()((()))((())))", "()()(()((()))(()()))", "()()(()((()))(())())", "()()(()((()))(()))()", "()()(()((()))()(()))", "()()(()((()))()()())", "()()(()((()))()())()", "()()(()((()))())(())", "()()(()((()))())()()", "()()(()((())))((()))", "()()(()((())))(()())", "()()(()((())))(())()", "()()(()((())))()(())", "()()(()((())))()()()", "()()(()(()(((())))))", "()()(()(()((()()))))", "()()(()(()((())())))", "()()(()(()((()))()))", "()()(()(()((())))())", "()()(()(()((()))))()", "()()(()(()(()(()))))", "()()(()(()(()()())))", "()()(()(()(()())()))", "()()(()(()(()()))())", "()()(()(()(()())))()", "()()(()(()(())(())))", "()()(()(()(())()()))", "()()(()(()(())())())", "()()(()(()(())()))()", "()()(()(()(()))(()))", "()()(()(()(()))()())", "()()(()(()(()))())()", "()()(()(()(())))(())", "()()(()(()(())))()()", "()()(()(()()((()))))", "()()(()(()()(()())))", "()()(()(()()(())()))", "()()(()(()()(()))())", "()()(()(()()(())))()", "()()(()(()()()(())))", "()()(()(()()()()()))", "()()(()(()()()())())", "()()(()(()()()()))()", "()()(()(()()())(()))", "()()(()(()()())()())", "()()(()(()()())())()", "()()(()(()()()))(())", "()()(()(()()()))()()", "()()(()(()())((())))", "()()(()(()())(()()))", "()()(()(()())(())())", "()()(()(()())(()))()", "()()(()(()())()(()))", "()()(()(()())()()())", "()()(()(()())()())()", "()()(()(()())())(())", "()()(()(()())())()()", "()()(()(()()))((()))", "()()(()(()()))(()())", "()()(()(()()))(())()", "()()(()(()()))()(())", "()()(()(()()))()()()", "()()(()(())(((()))))", "()()(()(())((()())))", "()()(()(())((())()))", "()()(()(())((()))())", "()()(()(())((())))()", "()()(()(())(()(())))", "()()(()(())(()()()))", "()()(()(())(()())())", "()()(()(())(()()))()", "()()(()(())(())(()))", "()()(()(())(())()())", "()()(()(())(())())()", "()()(()(())(()))(())", "()()(()(())(()))()()", "()()(()(())()((())))", "()()(()(())()(()()))", "()()(()(())()(())())", "()()(()(())()(()))()", "()()(()(())()()(()))", "()()(()(())()()()())", "()()(()(())()()())()", "()()(()(())()())(())", "()()(()(())()())()()", "()()(()(())())((()))", "()()(()(())())(()())", "()()(()(())())(())()", "()()(()(())())()(())", "()()(()(())())()()()", "()()(()(()))(((())))", "()()(()(()))((()()))", "()()(()(()))((())())", "()()(()(()))((()))()", "()()(()(()))(()(()))", "()()(()(()))(()()())", "()()(()(()))(()())()", "()()(()(()))(())(())", "()()(()(()))(())()()", "()()(()(()))()((()))", "()()(()(()))()(()())", "()()(()(()))()(())()", "()()(()(()))()()(())", "()()(()(()))()()()()", "()()(()()((((())))))", "()()(()()(((()()))))", "()()(()()(((())())))", "()()(()()(((()))()))", "()()(()()(((())))())", "()()(()()(((()))))()", "()()(()()((()(()))))", "()()(()()((()()())))", "()()(()()((()())()))", "()()(()()((()()))())", "()()(()()((()())))()", "()()(()()((())(())))", "()()(()()((())()()))", "()()(()()((())())())", "()()(()()((())()))()", "()()(()()((()))(()))", "()()(()()((()))()())", "()()(()()((()))())()", "()()(()()((())))(())", "()()(()()((())))()()", "()()(()()(()((()))))", "()()(()()(()(()())))", "()()(()()(()(())()))", "()()(()()(()(()))())", "()()(()()(()(())))()", "()()(()()(()()(())))", "()()(()()(()()()()))", "()()(()()(()()())())", "()()(()()(()()()))()", "()()(()()(()())(()))", "()()(()()(()())()())", "()()(()()(()())())()", "()()(()()(()()))(())", "()()(()()(()()))()()", "()()(()()(())((())))", "()()(()()(())(()()))", "()()(()()(())(())())", "()()(()()(())(()))()", "()()(()()(())()(()))", "()()(()()(())()()())", "()()(()()(())()())()", "()()(()()(())())(())", "()()(()()(())())()()", "()()(()()(()))((()))", "()()(()()(()))(()())", "()()(()()(()))(())()", "()()(()()(()))()(())", "()()(()()(()))()()()", "()()(()()()(((()))))", "()()(()()()((()())))", "()()(()()()((())()))", "()()(()()()((()))())", "()()(()()()((())))()", "()()(()()()(()(())))", "()()(()()()(()()()))", "()()(()()()(()())())", "()()(()()()(()()))()", "()()(()()()(())(()))", "()()(()()()(())()())", "()()(()()()(())())()", "()()(()()()(()))(())", "()()(()()()(()))()()", "()()(()()()()((())))", "()()(()()()()(()()))", "()()(()()()()(())())", "()()(()()()()(()))()", "()()(()()()()()(()))", "()()(()()()()()()())", "()()(()()()()()())()", "()()(()()()()())(())", "()()(()()()()())()()", "()()(()()()())((()))", "()()(()()()())(()())", "()()(()()()())(())()", "()()(()()()())()(())", "()()(()()()())()()()", "()()(()()())(((())))", "()()(()()())((()()))", "()()(()()())((())())", "()()(()()())((()))()", "()()(()()())(()(()))", "()()(()()())(()()())", "()()(()()())(()())()", "()()(()()())(())(())", "()()(()()())(())()()", "()()(()()())()((()))", "()()(()()())()(()())", "()()(()()())()(())()", "()()(()()())()()(())", "()()(()()())()()()()", "()()(()())((((()))))", "()()(()())(((()())))", "()()(()())(((())()))", "()()(()())(((()))())", "()()(()())(((())))()", "()()(()())((()(())))", "()()(()())((()()()))", "()()(()())((()())())", "()()(()())((()()))()", "()()(()())((())(()))", "()()(()())((())()())", "()()(()())((())())()", "()()(()())((()))(())", "()()(()())((()))()()", "()()(()())(()((())))", "()()(()())(()(()()))", "()()(()())(()(())())", "()()(()())(()(()))()", "()()(()())(()()(()))", "()()(()())(()()()())", "()()(()())(()()())()", "()()(()())(()())(())", "()()(()())(()())()()", "()()(()())(())((()))", "()()(()())(())(()())", "()()(()())(())(())()", "()()(()())(())()(())", "()()(()())(())()()()", "()()(()())()(((())))", "()()(()())()((()()))", "()()(()())()((())())", "()()(()())()((()))()", "()()(()())()(()(()))", "()()(()())()(()()())", "()()(()())()(()())()", "()()(()())()(())(())", "()()(()())()(())()()", "()()(()())()()((()))", "()()(()())()()(()())", "()()(()())()()(())()", "()()(()())()()()(())", "()()(()())()()()()()", "()()(())(((((())))))", "()()(())((((()()))))", "()()(())((((())())))", "()()(())((((()))()))", "()()(())((((())))())", "()()(())((((()))))()", "()()(())(((()(()))))", "()()(())(((()()())))", "()()(())(((()())()))", "()()(())(((()()))())", "()()(())(((()())))()", "()()(())(((())(())))", "()()(())(((())()()))", "()()(())(((())())())", "()()(())(((())()))()", "()()(())(((()))(()))", "()()(())(((()))()())", "()()(())(((()))())()", "()()(())(((())))(())", "()()(())(((())))()()", "()()(())((()((()))))", "()()(())((()(()())))", "()()(())((()(())()))", "()()(())((()(()))())", "()()(())((()(())))()", "()()(())((()()(())))", "()()(())((()()()()))", "()()(())((()()())())", "()()(())((()()()))()", "()()(())((()())(()))", "()()(())((()())()())", "()()(())((()())())()", "()()(())((()()))(())", "()()(())((()()))()()", "()()(())((())((())))", "()()(())((())(()()))", "()()(())((())(())())", "()()(())((())(()))()", "()()(())((())()(()))", "()()(())((())()()())", "()()(())((())()())()", "()()(())((())())(())", "()()(())((())())()()", "()()(())((()))((()))", "()()(())((()))(()())", "()()(())((()))(())()", "()()(())((()))()(())", "()()(())((()))()()()", "()()(())(()(((()))))", "()()(())(()((()())))", "()()(())(()((())()))", "()()(())(()((()))())", "()()(())(()((())))()", "()()(())(()(()(())))", "()()(())(()(()()()))", "()()(())(()(()())())", "()()(())(()(()()))()", "()()(())(()(())(()))", "()()(())(()(())()())", "()()(())(()(())())()", "()()(())(()(()))(())", "()()(())(()(()))()()", "()()(())(()()((())))", "()()(())(()()(()()))", "()()(())(()()(())())", "()()(())(()()(()))()", "()()(())(()()()(()))", "()()(())(()()()()())", "()()(())(()()()())()", "()()(())(()()())(())", "()()(())(()()())()()", "()()(())(()())((()))", "()()(())(()())(()())", "()()(())(()())(())()", "()()(())(()())()(())", "()()(())(()())()()()", "()()(())(())(((())))", "()()(())(())((()()))", "()()(())(())((())())", "()()(())(())((()))()", "()()(())(())(()(()))", "()()(())(())(()()())", "()()(())(())(()())()", "()()(())(())(())(())", "()()(())(())(())()()", "()()(())(())()((()))", "()()(())(())()(()())", "()()(())(())()(())()", "()()(())(())()()(())", "()()(())(())()()()()", "()()(())()((((()))))", "()()(())()(((()())))", "()()(())()(((())()))", "()()(())()(((()))())", "()()(())()(((())))()", "()()(())()((()(())))", "()()(())()((()()()))", "()()(())()((()())())", "()()(())()((()()))()", "()()(())()((())(()))", "()()(())()((())()())", "()()(())()((())())()", "()()(())()((()))(())", "()()(())()((()))()()", "()()(())()(()((())))", "()()(())()(()(()()))", "()()(())()(()(())())", "()()(())()(()(()))()", "()()(())()(()()(()))", "()()(())()(()()()())", "()()(())()(()()())()", "()()(())()(()())(())", "()()(())()(()())()()", "()()(())()(())((()))", "()()(())()(())(()())", "()()(())()(())(())()", "()()(())()(())()(())", "()()(())()(())()()()", "()()(())()()(((())))", "()()(())()()((()()))", "()()(())()()((())())", "()()(())()()((()))()", "()()(())()()(()(()))", "()()(())()()(()()())", "()()(())()()(()())()", "()()(())()()(())(())", "()()(())()()(())()()", "()()(())()()()((()))", "()()(())()()()(()())", "()()(())()()()(())()", "()()(())()()()()(())", "()()(())()()()()()()", "()()()((((((()))))))", "()()()(((((()())))))", "()()()(((((())()))))", "()()()(((((()))())))", "()()()(((((())))()))", "()()()(((((()))))())", "()()()(((((())))))()", "()()()((((()(())))))", "()()()((((()()()))))", "()()()((((()())())))", "()()()((((()()))()))", "()()()((((()())))())", "()()()((((()()))))()", "()()()((((())(()))))", "()()()((((())()())))", "()()()((((())())()))", "()()()((((())()))())", "()()()((((())())))()", "()()()((((()))(())))", "()()()((((()))()()))", "()()()((((()))())())", "()()()((((()))()))()", "()()()((((())))(()))", "()()()((((())))()())", "()()()((((())))())()", "()()()((((()))))(())", "()()()((((()))))()()", "()()()(((()((())))))", "()()()(((()(()()))))", "()()()(((()(())())))", "()()()(((()(()))()))", "()()()(((()(())))())", "()()()(((()(()))))()", "()()()(((()()(()))))", "()()()(((()()()())))", "()()()(((()()())()))", "()()()(((()()()))())", "()()()(((()()())))()", "()()()(((()())(())))", "()()()(((()())()()))", "()()()(((()())())())", "()()()(((()())()))()", "()()()(((()()))(()))", "()()()(((()()))()())", "()()()(((()()))())()", "()()()(((()())))(())", "()()()(((()())))()()", "()()()(((())((()))))", "()()()(((())(()())))", "()()()(((())(())()))", "()()()(((())(()))())", "()()()(((())(())))()", "()()()(((())()(())))", "()()()(((())()()()))", "()()()(((())()())())", "()()()(((())()()))()", "()()()(((())())(()))", "()()()(((())())()())", "()()()(((())())())()", "()()()(((())()))(())", "()()()(((())()))()()", "()()()(((()))((())))", "()()()(((()))(()()))", "()()()(((()))(())())", "()()()(((()))(()))()", "()()()(((()))()(()))", "()()()(((()))()()())", "()()()(((()))()())()", "()()()(((()))())(())", "()()()(((()))())()()", "()()()(((())))((()))", "()()()(((())))(()())", "()()()(((())))(())()", "()()()(((())))()(())", "()()()(((())))()()()", "()()()((()(((())))))", "()()()((()((()()))))", "()()()((()((())())))", "()()()((()((()))()))", "()()()((()((())))())", "()()()((()((()))))()", "()()()((()(()(()))))", "()()()((()(()()())))", "()()()((()(()())()))", "()()()((()(()()))())", "()()()((()(()())))()", "()()()((()(())(())))", "()()()((()(())()()))", "()()()((()(())())())", "()()()((()(())()))()", "()()()((()(()))(()))", "()()()((()(()))()())", "()()()((()(()))())()", "()()()((()(())))(())", "()()()((()(())))()()", "()()()((()()((()))))", "()()()((()()(()())))", "()()()((()()(())()))", "()()()((()()(()))())", "()()()((()()(())))()", "()()()((()()()(())))", "()()()((()()()()()))", "()()()((()()()())())", "()()()((()()()()))()", "()()()((()()())(()))", "()()()((()()())()())", "()()()((()()())())()", "()()()((()()()))(())", "()()()((()()()))()()", "()()()((()())((())))", "()()()((()())(()()))", "()()()((()())(())())", "()()()((()())(()))()", "()()()((()())()(()))", "()()()((()())()()())", "()()()((()())()())()", "()()()((()())())(())", "()()()((()())())()()", "()()()((()()))((()))", "()()()((()()))(()())", "()()()((()()))(())()", "()()()((()()))()(())", "()()()((()()))()()()", "()()()((())(((()))))", "()()()((())((()())))", "()()()((())((())()))", "()()()((())((()))())", "()()()((())((())))()", "()()()((())(()(())))", "()()()((())(()()()))", "()()()((())(()())())", "()()()((())(()()))()", "()()()((())(())(()))", "()()()((())(())()())", "()()()((())(())())()", "()()()((())(()))(())", "()()()((())(()))()()", "()()()((())()((())))", "()()()((())()(()()))", "()()()((())()(())())", "()()()((())()(()))()", "()()()((())()()(()))", "()()()((())()()()())", "()()()((())()()())()", "()()()((())()())(())", "()()()((())()())()()", "()()()((())())((()))", "()()()((())())(()())", "()()()((())())(())()", "()()()((())())()(())", "()()()((())())()()()", "()()()((()))(((())))", "()()()((()))((()()))", "()()()((()))((())())", "()()()((()))((()))()", "()()()((()))(()(()))", "()()()((()))(()()())", "()()()((()))(()())()", "()()()((()))(())(())", "()()()((()))(())()()", "()()()((()))()((()))", "()()()((()))()(()())", "()()()((()))()(())()", "()()()((()))()()(())", "()()()((()))()()()()", "()()()(()((((())))))", "()()()(()(((()()))))", "()()()(()(((())())))", "()()()(()(((()))()))", "()()()(()(((())))())", "()()()(()(((()))))()", "()()()(()((()(()))))", "()()()(()((()()())))", "()()()(()((()())()))", "()()()(()((()()))())", "()()()(()((()())))()", "()()()(()((())(())))", "()()()(()((())()()))", "()()()(()((())())())", "()()()(()((())()))()", "()()()(()((()))(()))", "()()()(()((()))()())", "()()()(()((()))())()", "()()()(()((())))(())", "()()()(()((())))()()", "()()()(()(()((()))))", "()()()(()(()(()())))", "()()()(()(()(())()))", "()()()(()(()(()))())", "()()()(()(()(())))()", "()()()(()(()()(())))", "()()()(()(()()()()))", "()()()(()(()()())())", "()()()(()(()()()))()", "()()()(()(()())(()))", "()()()(()(()())()())", "()()()(()(()())())()", "()()()(()(()()))(())", "()()()(()(()()))()()", "()()()(()(())((())))", "()()()(()(())(()()))", "()()()(()(())(())())", "()()()(()(())(()))()", "()()()(()(())()(()))", "()()()(()(())()()())", "()()()(()(())()())()", "()()()(()(())())(())", "()()()(()(())())()()", "()()()(()(()))((()))", "()()()(()(()))(()())", "()()()(()(()))(())()", "()()()(()(()))()(())", "()()()(()(()))()()()", "()()()(()()(((()))))", "()()()(()()((()())))", "()()()(()()((())()))", "()()()(()()((()))())", "()()()(()()((())))()", "()()()(()()(()(())))", "()()()(()()(()()()))", "()()()(()()(()())())", "()()()(()()(()()))()", "()()()(()()(())(()))", "()()()(()()(())()())", "()()()(()()(())())()", "()()()(()()(()))(())", "()()()(()()(()))()()", "()()()(()()()((())))", "()()()(()()()(()()))", "()()()(()()()(())())", "()()()(()()()(()))()", "()()()(()()()()(()))", "()()()(()()()()()())", "()()()(()()()()())()", "()()()(()()()())(())", "()()()(()()()())()()", "()()()(()()())((()))", "()()()(()()())(()())", "()()()(()()())(())()", "()()()(()()())()(())", "()()()(()()())()()()", "()()()(()())(((())))", "()()()(()())((()()))", "()()()(()())((())())", "()()()(()())((()))()", "()()()(()())(()(()))", "()()()(()())(()()())", "()()()(()())(()())()", "()()()(()())(())(())", "()()()(()())(())()()", "()()()(()())()((()))", "()()()(()())()(()())", "()()()(()())()(())()", "()()()(()())()()(())", "()()()(()())()()()()", "()()()(())((((()))))", "()()()(())(((()())))", "()()()(())(((())()))", "()()()(())(((()))())", "()()()(())(((())))()", "()()()(())((()(())))", "()()()(())((()()()))", "()()()(())((()())())", "()()()(())((()()))()", "()()()(())((())(()))", "()()()(())((())()())", "()()()(())((())())()", "()()()(())((()))(())", "()()()(())((()))()()", "()()()(())(()((())))", "()()()(())(()(()()))", "()()()(())(()(())())", "()()()(())(()(()))()", "()()()(())(()()(()))", "()()()(())(()()()())", "()()()(())(()()())()", "()()()(())(()())(())", "()()()(())(()())()()", "()()()(())(())((()))", "()()()(())(())(()())", "()()()(())(())(())()", "()()()(())(())()(())", "()()()(())(())()()()", "()()()(())()(((())))", "()()()(())()((()()))", "()()()(())()((())())", "()()()(())()((()))()", "()()()(())()(()(()))", "()()()(())()(()()())", "()()()(())()(()())()", "()()()(())()(())(())", "()()()(())()(())()()", "()()()(())()()((()))", "()()()(())()()(()())", "()()()(())()()(())()", "()()()(())()()()(())", "()()()(())()()()()()", "()()()()(((((())))))", "()()()()((((()()))))", "()()()()((((())())))", "()()()()((((()))()))", "()()()()((((())))())", "()()()()((((()))))()", "()()()()(((()(()))))", "()()()()(((()()())))", "()()()()(((()())()))", "()()()()(((()()))())", "()()()()(((()())))()", "()()()()(((())(())))", "()()()()(((())()()))", "()()()()(((())())())", "()()()()(((())()))()", "()()()()(((()))(()))", "()()()()(((()))()())", "()()()()(((()))())()", "()()()()(((())))(())", "()()()()(((())))()()", "()()()()((()((()))))", "()()()()((()(()())))", "()()()()((()(())()))", "()()()()((()(()))())", "()()()()((()(())))()", "()()()()((()()(())))", "()()()()((()()()()))", "()()()()((()()())())", "()()()()((()()()))()", "()()()()((()())(()))", "()()()()((()())()())", "()()()()((()())())()", "()()()()((()()))(())", "()()()()((()()))()()", "()()()()((())((())))", "()()()()((())(()()))", "()()()()((())(())())", "()()()()((())(()))()", "()()()()((())()(()))", "()()()()((())()()())", "()()()()((())()())()", "()()()()((())())(())", "()()()()((())())()()", "()()()()((()))((()))", "()()()()((()))(()())", "()()()()((()))(())()", "()()()()((()))()(())", "()()()()((()))()()()", "()()()()(()(((()))))", "()()()()(()((()())))", "()()()()(()((())()))", "()()()()(()((()))())", "()()()()(()((())))()", "()()()()(()(()(())))", "()()()()(()(()()()))", "()()()()(()(()())())", "()()()()(()(()()))()", "()()()()(()(())(()))", "()()()()(()(())()())", "()()()()(()(())())()", "()()()()(()(()))(())", "()()()()(()(()))()()", "()()()()(()()((())))", "()()()()(()()(()()))", "()()()()(()()(())())", "()()()()(()()(()))()", "()()()()(()()()(()))", "()()()()(()()()()())", "()()()()(()()()())()", "()()()()(()()())(())", "()()()()(()()())()()", "()()()()(()())((()))", "()()()()(()())(()())", "()()()()(()())(())()", "()()()()(()())()(())", "()()()()(()())()()()", "()()()()(())(((())))", "()()()()(())((()()))", "()()()()(())((())())", "()()()()(())((()))()", "()()()()(())(()(()))", "()()()()(())(()()())", "()()()()(())(()())()", "()()()()(())(())(())", "()()()()(())(())()()", "()()()()(())()((()))", "()()()()(())()(()())", "()()()()(())()(())()", "()()()()(())()()(())", "()()()()(())()()()()", "()()()()()((((()))))", "()()()()()(((()())))", "()()()()()(((())()))", "()()()()()(((()))())", "()()()()()(((())))()", "()()()()()((()(())))", "()()()()()((()()()))", "()()()()()((()())())", "()()()()()((()()))()", "()()()()()((())(()))", "()()()()()((())()())", "()()()()()((())())()", "()()()()()((()))(())", "()()()()()((()))()()", "()()()()()(()((())))", "()()()()()(()(()()))", "()()()()()(()(())())", "()()()()()(()(()))()", "()()()()()(()()(()))", "()()()()()(()()()())", "()()()()()(()()())()", "()()()()()(()())(())", "()()()()()(()())()()", "()()()()()(())((()))", "()()()()()(())(()())", "()()()()()(())(())()", "()()()()()(())()(())", "()()()()()(())()()()", "()()()()()()(((())))", "()()()()()()((()()))", "()()()()()()((())())", "()()()()()()((()))()", "()()()()()()(()(()))", "()()()()()()(()()())", "()()()()()()(()())()", "()()()()()()(())(())", "()()()()()()(())()()", "()()()()()()()((()))", "()()()()()()()(()())", "()()()()()()()(())()", "()()()()()()()()(())", "()()()()()()()()()()"] TODO