<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 {
    int mod=1e9+7 ;
private:
    int count(const string &s, int i, int n, char prev, vector<vector<int>> &dp) {
        if (i == n) return 1; 
        int prev_index = abs(prev-'a') ;
        
        if (dp[i][prev_index] != -1) return dp[i][prev_index]%mod;
        
        int inc = 0;
        for (char next : s) {
            if (prev == ']') {
                inc = (inc+count(s, i + 1, n, next, dp)%mod)%mod;
            } else if (prev == 'a' && next == 'e') {
               inc = (inc+count(s, i + 1, n, next, dp)%mod)%mod;
            } else if (prev == 'e' && (next == 'a' || next == 'i')) {
                 inc = (inc+count(s, i + 1, n, next, dp)%mod)%mod;
            } else if (prev == 'i' && (next != 'i')) {
                    inc = (inc+count(s, i + 1, n, next, dp)%mod)%mod;
            } else if (prev == 'o' && (next == 'i' || next == 'u')) {
                 inc = (inc+count(s, i + 1, n, next, dp)%mod)%mod;
            } else if (prev == 'u' && next == 'a') {
                 inc = (inc+count(s, i + 1, n, next, dp)%mod)%mod;
            }
        }
        
        return dp[i][prev_index] = ((inc)%mod)%mod;
    }

public:
    int countVowelPermutation(int n) {
        vector<vector<int>> dp(n, vector<int>(27, -1)); // Use 27 to include the initial state index
        string s = "aeiou";
        return count(s, 0, n, ']', dp)%mod;
    }
};

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