<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:
   long long int dp[200001][26];
   int mod=1e9+7;
    vector<char> v = {'a','e','i','o','u'};
    long long int f(int i,char pre,int n){
        if(i==n){
            return 1;
        }
        if(dp[i][pre-'a']!=-1){
            return dp[i][pre-'a'];
        }
        if(pre=='a'){
            return dp[i][pre-'a']=f(i+1,'e',n)%mod;
        }
        if(pre=='e'){
            return dp[i][pre-'a']= (f(i+1,'a',n)+f(i+1,'i',n))%mod;
        }
        if(pre=='i'){
            long long int sum=0;
            for(char x:v){
                if(x!='i'){
                   sum+=f(i+1,x,n);
                }
            }
            return dp[i][pre-'a']= sum%mod;
        }
        if(pre=='o'){
            return dp[i][pre-'a']=(f(i+1,'i',n)+f(i+1,'u',n))%mod;
        }
        if(pre=='u'){
             long long int sum=0;
             sum+=f(i+1,'a',n);
            return dp[i][pre-'a']=sum%mod;
        }
        return 0;
    }
    int countVowelPermutation(int n) {
       long long int sum=0;
       memset(dp,-1,sizeof(dp));
        for(char x:v){
             sum+=f(1,x,n)%mod;
            //  cout<<f(1,x,n)<<" ";
        }
        return sum%mod;
    }
};
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