<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=1e9+7;
    int help(int i,int prev,vector<char> &vowels,int n, vector<vector<int>> &dp){
        if(i>=n) {
            return  1;
        }
        if(dp[i][prev+1]!=-1) return dp[i][prev+1];
        long long  ans=0;
        for(int c=0;c<5;c++){
            if(vowels[c]=='a'){
                if(prev==-1 || char(prev+97)=='u' || char(prev+97)=='e' || char(prev+97)=='i'){
                    ans+=help(i+1,vowels[c]-'a',vowels,n,dp)%mod;
                }
            }
            if(vowels[c]=='e'){
                if(prev==-1 || char(prev+97)=='a'|| char(prev+97)=='i'){
                    ans+=help(i+1,vowels[c]-'a',vowels,n,dp)%mod;
                }
            }
            if(vowels[c]=='i'){
                if(prev==-1 || char(prev+97)=='o' || char(prev+97)=='e'  ){
                    ans+=help(i+1,vowels[c]-'a',vowels,n,dp)%mod;
                }
            }
            if(vowels[c]=='u'){
                if(prev==-1 || char(prev+97)=='o' || char(prev+97)=='i'){
                    ans+=help(i+1,vowels[c]-'a',vowels,n,dp)%mod;
                }
            }
            if(vowels[c]=='o' ){
                if(prev==-1 || char(prev+97)=='i')
                    ans+=help(i+1,vowels[c]-'a',vowels,n,dp)%mod;
            }
        }
        return dp[i][prev+1]=ans%mod;
    }
    int countVowelPermutation(int n) {
        vector<char> vowels={'a','e','i','o','u'};
        vector<vector<int>> dp(n+1,vector<int>(27,-1));
        return help(0,-1,vowels,n,dp);

    }
};
82266