<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:
    vector<char>v={'a','e','i','o','u'};
    map<char,int>index;

    int mod=1e9+7;

    vector<vector<int>>dp;
    int solution(map<char,vector<char>>&mpp,int pi,int n){

        if(n==0){
            return 1;
        }
        if(pi==-1){
            int ans=0;
            for(int i=0;i<v.size();i++){
                 ans=(ans%mod+ solution(mpp,index[v[i]],n-1)%mod)%mod;
            }
            return ans;
        }
        if(pi!=-1 && dp[pi][n]!=-1){
            return dp[pi][n];
        }
        else{
            int ans=0;
            
            for(auto it:mpp[v[pi]]){
                ans=(ans%mod+solution(mpp,index[it],n-1)%mod)%mod;
            }

            return dp[pi][n]=ans;
        }

        return 0;

    }
    int countVowelPermutation(int n) {


        map<char,vector<char>>mpp;
        mpp['a'].push_back('e');

        mpp['e'].push_back('a');
        mpp['e'].push_back('i');
        
        mpp['i'].push_back('a');
        mpp['i'].push_back('e');
        mpp['i'].push_back('o');
        mpp['i'].push_back('u');

        mpp['o'].push_back('i');
        mpp['o'].push_back('u');

        mpp['u'].push_back('a');

        dp.assign(6,vector<int>(n+1,-1));

        index['a']=0;
        index['e']=1;
        index['i']=2;
        index['o']=3;
        index['u']=4;


        return solution(mpp,-1,n);
    }
};
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