<p>Given an integer <code>n</code>, your task is to count how many strings of length <code>n</code> can be formed under the following rules:</p>

<ul>
	<li>Each character is a lower case vowel&nbsp;(<code>&#39;a&#39;</code>, <code>&#39;e&#39;</code>, <code>&#39;i&#39;</code>, <code>&#39;o&#39;</code>, <code>&#39;u&#39;</code>)</li>
	<li>Each vowel&nbsp;<code>&#39;a&#39;</code> may only be followed by an <code>&#39;e&#39;</code>.</li>
	<li>Each vowel&nbsp;<code>&#39;e&#39;</code> may only be followed by an <code>&#39;a&#39;</code>&nbsp;or an <code>&#39;i&#39;</code>.</li>
	<li>Each vowel&nbsp;<code>&#39;i&#39;</code> <strong>may not</strong> be followed by another <code>&#39;i&#39;</code>.</li>
	<li>Each vowel&nbsp;<code>&#39;o&#39;</code> may only be followed by an <code>&#39;i&#39;</code> or a&nbsp;<code>&#39;u&#39;</code>.</li>
	<li>Each vowel&nbsp;<code>&#39;u&#39;</code> may only be followed by an <code>&#39;a&#39;</code>.</li>
</ul>

<p>Since the answer&nbsp;may be too large,&nbsp;return it modulo&nbsp;<code>10^9 + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 5
<strong>Explanation:</strong> All possible strings are: &quot;a&quot;, &quot;e&quot;, &quot;i&quot; , &quot;o&quot; and &quot;u&quot;.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> 10
<strong>Explanation:</strong> All possible strings are: &quot;ae&quot;, &quot;ea&quot;, &quot;ei&quot;, &quot;ia&quot;, &quot;ie&quot;, &quot;io&quot;, &quot;iu&quot;, &quot;oi&quot;, &quot;ou&quot; and &quot;ua&quot;.
</pre>

<p><strong class="example">Example 3:&nbsp;</strong></p>

<pre>
<strong>Input:</strong> n = 5
<strong>Output:</strong> 68</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 2 * 10^4</code></li>
</ul>

class Solution {
public:
    long long dp(int curChar, int strLenSoFar, int maxStrLen, vector<vector<long long>>& memo) {
        if (strLenSoFar == maxStrLen) {
            return 1;
        }

        if (memo[curChar][strLenSoFar] != -1) {
            return memo[curChar][strLenSoFar];
        }

        long long methods = 0;
        if (curChar == 1) {
            // current char is 'a', next char can be 'e'
            methods += dp(2, strLenSoFar + 1, maxStrLen, memo) % MOD;
        } else if (curChar == 2) {
            // current char is 'e', next char can be 'a', 'i'
            methods += dp(1, strLenSoFar + 1, maxStrLen, memo) % MOD;
            methods += dp(3, strLenSoFar + 1, maxStrLen, memo) % MOD;
        } else if (curChar == 3) {
            // current char is 'i', next char can be 'a', 'e', 'o', 'u'
            methods += dp(1, strLenSoFar + 1, maxStrLen, memo) % MOD;
            methods += dp(2, strLenSoFar + 1, maxStrLen, memo) % MOD;
            methods += dp(4, strLenSoFar + 1, maxStrLen, memo) % MOD;
            methods += dp(5, strLenSoFar + 1, maxStrLen, memo) % MOD;
        } else if (curChar == 4) {
            // current char is 'o', next char can be 'i', 'u'
            methods += dp(3, strLenSoFar + 1, maxStrLen, memo) % MOD;
            methods += dp(5, strLenSoFar + 1, maxStrLen, memo) % MOD;
        } else if (curChar == 5) {
            // current char is 'u', next char can be 'a'
            methods += dp(1, strLenSoFar + 1, maxStrLen, memo) % MOD;
        }

        return memo[curChar][strLenSoFar] = methods % MOD;
    }

    int countVowelPermutation(int n) {
        long long methods = 0;
        vector<vector<long long>> memo(6, vector<long long>(n + 1, -1));

        // 'a', 'e', 'i', 'o', 'u' mapping to 1, 2, 3, 4, 5
        for (int i = 1; i <= 5; i++) {
            methods += dp(i, 1, n, memo) % MOD;
        }

        return methods % MOD;
    }

private:
    int MOD = 1000000007;
};
35174