<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;
    // int dfs(int n,char prev, unordered_map<char,vector<char>>& allowed,vector<vector<int>>& dp)
    // {
    //     if(n==0)
    //         return 1;
    //     if(n<0)
    //         return 0;
    //     if(dp[n][prev-'a']==-1)
    //     {
    //         int ans=0;
    //         for(char c: allowed[prev])
    //             ans= (ans+dfs(n-1,c,allowed,dp))%m;
    //         dp[n][prev-'a']=ans%m;
    //     }
    //     return dp[n][prev-'a'];
    // }
    int countVowelPermutation(int n) {
        // vector<vector<int>> dp(n+1,vector<int> (26,-1));
        // unordered_map<char,vector<char>> allowed={
        //     {'z',{'a','e','i','o','u'}},
        //     {'a',{'e'}},
        //     {'e',{'a','i'}},
        //     {'i',{'a','e','o','u'}},
        //     {'o',{'i','u'}},
        //     {'u',{'a'}}
        // };
        // char prev='z';
        // return dfs(n,prev,allowed,dp);
        
        // int chars[5]={'a','e','i','o','u'};
        vector<vector<int>> dp(n+1,vector<int> (5,0));
        unordered_map<int,vector<int>> allowed={
            {0,{1}},
            {1,{0,2}},
            {2,{0,1,3,4}},
            {3,{2,4}},
            {4,{0}}
        };
        for(int i=0;i<5;i++)
            dp[1][i]=1;
        for(int m=2;m<=n;m++)
            for(int j=0;j<5;j++)
            {
                for(int a:allowed[j])
                    dp[m][j]=(dp[m][j]+dp[m-1][a])%mod;
            }
        int ans=0;
        for(int i=0;i<5;i++)
            ans=(ans+dp[n][i])%mod;
        return ans;
    }
};

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