<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>

const int mod=1e9+7;
class Solution {
private:
    int func(int n, int x,vector <vector <int>> &dp ){
        if(n==1){
            return 1;
        }
        if(dp[x][n]!=-1){
            return dp[x][n]%mod;
        }
        if(x==0){
            return dp[x][n]=func(n-1, 1,dp)%mod;
        }
        if(x==1){
            return dp[x][n]=(func(n-1, 0,dp)+func(n-1, 2, dp))%mod;
        }
        if(x==2){
            return dp[x][n]=((func(n-1, 0,dp)+func(n-1, 1,dp))%mod+(func(n-1, 3,dp)+func(n-1, 4,dp))%mod)%mod;
        }
        if(x==3){
            return dp[x][n]=(func(n-1, 2,dp)+func(n-1, 4,dp))%mod;
        }
        if(x==4){
            return dp[x][n]=func(n-1, 0,dp)%mod;
        }
        return dp[x][n]%mod;
    }
public:
    int countVowelPermutation(int n) {
        vector <vector <int>> dp(5, vector <int> (n+1, -1));
        int ans=0;
        for(int i=0 ;i<5;i++){
            ans+= func(n, i,dp);
            ans%=mod;
        }
        return ans%mod;
    }
};
20684