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Given an integer n, your task is to count how many strings of length n can be formed under the following rules:
- Each character is a lower case vowel (
'a','e','i','o','u') - Each vowel
'a'may only be followed by an'e'. - Each vowel
'e'may only be followed by an'a'or an'i'. - Each vowel
'i'may not be followed by another'i'. - Each vowel
'o'may only be followed by an'i'or a'u'. - Each vowel
'u'may only be followed by an'a'.
Since the answer may be too large, return it modulo 10^9 + 7.
Example 1:
Input: n = 1
Output: 5
Explanation: All possible strings are: "a", "e", "i" , "o" and "u".
Example 2:
Input: n = 2
Output: 10
Explanation: All possible strings are: "ae", "ea", "ei", "ia", "ie", "io", "iu", "oi", "ou" and "ua".
Example 3:
Input: n = 5
Output: 68
Constraints:
1 <= n <= 2 * 10^4