<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 {
    vector<vector<int>> memo;
    const int MOD = 1000000007;
    
    int countAll(int n, int pChar){
        if( n == 0){ return 1;}
        if(memo[n][pChar] == -1){
            int count = 0;
            if( pChar == 0){
                count = ((countAll(n-1, 1) + countAll(n-1, 2))% MOD + countAll(n-1, 4)) % MOD;}
            else if( pChar == 1){
                count = (countAll(n-1, 0) + countAll(n-1, 2)) % MOD;}
            else if( pChar == 2){
                count = (countAll(n-1, 1) + countAll(n-1, 3)) % MOD ;}
            else if( pChar == 3){
                count = countAll(n-1, 2) % MOD;}
            else if( pChar == 4){
                count = (countAll(n-1, 2) + countAll(n-1, 3)) % MOD ;}
            memo[n][pChar] = count;
        }
        return memo[n][pChar];
    }
public:
    int countVowelPermutation(int n) {
        // a = 0, e = 1, i = 2, o = 3, u = 4, ' ' = 5
        vector<vector<int>> memo(n+1, vector<int>(6,-1));
        this->memo = memo;
        int res = 0;
        for(int i=0; i<5; i++){
            res = (res + countAll(n-1, i)) % MOD;
        }
        return res;
    }
};
65965