<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 mod=1000000007;
    long long func (int i,int prev,int n,vector <vector <long long > >& dp){
        if (i==n)return 1;
        if (dp[i][prev]!=-1)return dp[i][prev];
        if (prev==0){
            return  dp[i][prev]=func(i+1,1,n,dp)%mod;
        }
        if (prev==1){
            return  dp[i][prev]=(func(i+1,0,n,dp)%mod+func(i+1,2,n,dp)%mod)%mod;
        }
        if (prev==2){
            long long ans=0;
            for (int j=0;j<5;j++){
                if (j==2)continue;
                ans+=func(i+1,j,n,dp)%mod;
            }
            return  dp[i][prev]=ans%mod;

        }
        if (prev==3){
            long long ans=0;
            ans+=func(i+1,2,n,dp)%mod;
            ans+=func(i+1,4,n,dp)%mod;
            return  dp[i][prev]=ans%mod;
        }
        if (prev==4){
            return  dp[i][prev]=func(i+1,0,n,dp)%mod;
        }
        return 0;
    }
    int countVowelPermutation(int n) {
        vector <vector <long long > > dp (n,vector <long long > (5,-1));
        long long ans=0;
        for (int i=0;i<5;i++){
            ans+=func(1,i,n,dp)%mod;
        }
        return ans%mod;
    }
};
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