<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:

    int solve(int i, char flag, int n, vector<vector<int>>& dp){
        if(i==n) return 1;
        int mod=1000000007;
        if(flag=='0'){
            int ans=0;
            vector<char> vowels{'a','e','i','o','u'};
            for(int j=0;j<5;j++){
                ans=((ans%mod)+(solve(i+1,vowels[j],n,dp)%mod))%mod;
            }
            return ans;
        }
        if(dp[i][flag-'a']!=-1) return dp[i][flag-'a'];
        int ans=0;
        if(flag=='a'){
            ans=((ans%mod)+(solve(i+1,'e',n,dp))%mod)%mod;
        }
        else if(flag=='e'){
            ans=((ans%mod)+(solve(i+1,'a',n,dp))%mod)%mod;
            ans=((ans%mod)+(solve(i+1,'i',n,dp))%mod)%mod;
        }
        else if(flag=='i'){
            ans=((ans%mod)+(solve(i+1,'a',n,dp))%mod)%mod;
            ans=((ans%mod)+(solve(i+1,'e',n,dp))%mod)%mod;
            ans=((ans%mod)+(solve(i+1,'o',n,dp))%mod)%mod;
            ans=((ans%mod)+(solve(i+1,'u',n,dp))%mod)%mod;

        }
        else if(flag=='o'){
            ans=((ans%mod)+(solve(i+1,'i',n,dp))%mod)%mod;
            ans=((ans%mod)+(solve(i+1,'u',n,dp))%mod)%mod;
        }
        else{
            ans=((ans%mod)+(solve(i+1,'a',n,dp))%mod)%mod;
        }
        dp[i][flag-'a']=ans;
        return dp[i][flag-'a'];
    }

    int countVowelPermutation(int n) {
        vector<vector<int>> dp(n,vector<int>(26,-1));
        return solve(0,'0',n,dp);
    }
};
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