<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 countVowelPermutation(int n) {
        if(n==1)
            return 5;

        vector<vector<long long>> dp(5,vector<long long>(n,0));
        long long sum = 0;

        for(int i=0;i<5;i++){
            dp[i][0] = 1;
        }

        for(int j=1;j<n;j++){
            dp[0][j] = (dp[1][j-1] + dp[2][j-1] + dp[4][j-1])%mod;
            dp[1][j] = (dp[0][j-1] + dp[2][j-1])%mod;
            dp[2][j] = (dp[1][j-1] + dp[3][j-1])%mod;
            dp[3][j] = (dp[2][j-1])%mod;
            dp[4][j] = (dp[2][j-1] + dp[3][j-1])%mod;
            
            if(j==n-1){
                sum =0;
                sum += (dp[0][j] + dp[1][j] + dp[2][j] + dp[3][j] + dp[4][j])%mod;
            }
        }

        return sum%mod;       

    }

/*
    int mod = 1e9+7;

    int f(int ind, int n, string temp,unordered_map<char,vector<char>>& mp){
        if(ind == n){
            return 1;
        }

        long long ans =0;

        if(ind == 0){
            for(int i=0;i<mp['x'].size();i++){
                temp.push_back(mp['x'][i]);
                ans += f(ind+1,n,temp,mp)%mod;
                temp.pop_back();
            }
        } else{
            char c = temp[temp.size()-1];

            for(int i=0;i<mp[c].size();i++){
                temp.push_back(mp[c][i]);
                ans += f(ind+1,n,temp,mp)%mod;
                temp.pop_back();
            }
        }

        return ans%mod;
    }
    int countVowelPermutation(int n) {
        unordered_map<char,vector<char>> mp;
        mp['x'] = {'a','e','i','o','u'};
        mp['a'] = {'e'};
        mp['e'] = {'a','i'};
        mp['i'] = {'a','e','o','u'};
        mp['o'] = {'i','u'};
        mp['u'] = {'a'};

        string temp = "";
        return f(0,n,temp,mp);
    }
*/
};
27929