- Since from the end char of prev permutation, we can get next permutation. It looks like a
dp[i][j]be the number of permutations of a string with length
iand ending with
- From the rules, we can deduct that
e, i, u.
- For example, if the vowel is
a, then it must appear after
e, i, u, so we can just add the number of permutations that end with
e, i, u. Then what we get would be the number of permutations ending with
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.
Input: n = 2