<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 prev, int n, vector<char>&v, vector<vector<int>>&mem){
    if(n==0){
        return mem[n][prev+1]= 1;
    }
    if(mem[n][prev+1] != -1){
        return mem[n][prev+1];
    }
    int ans =0;
    for(int i=0; i<5; i++){
        if(prev ==-1){
           ans +=solve( i, n-1, v, mem);
        }
        else{
            if(v[i]=='e' && v[prev]=='a'){
                 ans +=solve( i, n-1, v, mem);
            }
            else if((v[prev]=='e') && (v[i]=='a' || v[i]=='i')){
               ans +=solve( i, n-1, v, mem);
            }
            else if(v[i]!='i' && v[prev]=='i'){
               ans +=solve( i, n-1, v, mem);
            }
            else if((v[prev]=='o') && (v[i]=='u' || v[i]=='i')){
              ans +=solve( i, n-1, v, mem);
            }
            else if(v[prev]=='u' && v[i]=='a'){
                ans +=solve( i, n-1, v, mem);
            }
        }
    }
    return mem[n][prev+1]= ans%1000000007;
}
int solve2(int n,  vector<char>v ){
    vector<vector<int>>dp(n+1, vector<int>(6, 0));
    for(int i=0; i<=5; i++){
        dp[0][i]=1;
    }
    for(int k=1; k<=n; k++){
    for(int j=0; j<=5; j++){
        int ans =0;
        for(int i=0; i<5; i++){
          // int prev = j-1;
           
            if(j-1 ==-1){
           ans = (ans + dp[k-1][i+1])%1000000007;
        }
        else{
            if(v[i]=='e' && v[j-1]=='a'){
                 ans = (ans + dp[k-1][i+1])%1000000007;
            }
            else if((v[j-1]=='e') && (v[i]=='a' || v[i]=='i')){
               ans = (ans + dp[k-1][i+1])%1000000007;
            }
            else if(v[i]!='i' && v[j-1]=='i'){
            ans = (ans + dp[k-1][i+1])%1000000007;
            }
            else if((v[j-1]=='o') && (v[i]=='u' || v[i]=='i')){
             ans = (ans + dp[k-1][i+1])%1000000007;
            }
            else if(v[j-1]=='u' && v[i]=='a'){
             ans = (ans + dp[k-1][i+1])%1000000007;
            }
        }
        
        
        }
        dp[k][j]= ans%1000000007;
    }}
    return dp[n][0];
}
    int countVowelPermutation(int n) {
        vector<char>v = {'a', 'e', 'i', 'o', 'u'};
        vector<vector<int>>mem(n+1, vector<int>(6, -1));
   // return solve( -1, n, v, mem);
   return solve2(n, v);
    }
};
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