<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 m=1e9+7;
    int solve(int prev,int n,vector<vector<int>> &dp){
        if(n==0){
            return 1;
        }
        if(dp[prev][n]!=-1){
            return dp[prev][n];
        }
        int ans=0;
        if(prev==0){
            ans=ans%m+solve(1,n-1,dp)%m;
        }
        else if(prev==1){
            ans=ans%m+solve(0,n-1,dp)%m;
            ans=ans%m+solve(2,n-1,dp)%m;
        }
        else if(prev==2){
            for(int i=0;i<5;i++){
                if(i!=2){
                     ans=ans%m+solve(i,n-1,dp)%m;
                }
            }
        }
        else if(prev==3){
            ans=ans%m+solve(2,n-1,dp)%m;
            ans=ans%m+solve(4,n-1,dp)%m;
        }
        else if(prev==4){
            ans=ans%m+solve(0,n-1,dp)%m;
        }
        return dp[prev][n]=ans%m;
    }
    int countVowelPermutation(int n) {
       int ans=0;
       vector<vector<int>> dp(5,vector<int>(n,-1));
       for(int i=0;i<5;i++){
            dp[i][0]=1;
       }
       for(int j=1;j<n;j++){
            dp[0][j] = dp[1][j-1]%m;
            dp[1][j] = (dp[0][j-1]%m+dp[2][j-1]%m)%m;
            dp[2][j] = ((dp[0][j-1]%m+dp[1][j-1]%m)%m + (dp[3][j-1]%m+dp[4][j-1]%m)%m)%m;
            dp[3][j] = (dp[4][j-1]%m+dp[2][j-1]%m)%m;
            dp[4][j] = dp[0][j-1]%m;
       }
       for(int j=0;j<5;j++){
        ans=ans%m+dp[j][n-1]%m;
       }
       return ans%m;
    }
};
18873