1220 - Count Vowels Permutation.

Hard

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