<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 recurse(char x, int n, vector<vector<int>>& dp) {
        
        if(n == 1) return 1;
        if(dp[x-'a'][n] != -1) return dp[x-'a'][n];
        
        int temp = 0;
        if(x == 'a') {
            temp = (temp % MOD + recurse('e', n-1, dp)) % MOD;
        } else if(x == 'e') {
            temp = (temp % MOD + recurse('a', n-1, dp)) % MOD;
            temp = (temp % MOD + recurse('i', n-1, dp)) % MOD;
        } else if(x == 'i') {
            temp = (temp % MOD + recurse('a', n-1, dp)) % MOD;
            temp = (temp % MOD + recurse('e', n-1, dp)) % MOD;
            temp = (temp % MOD + recurse('o', n-1, dp)) % MOD;
            temp = (temp % MOD + recurse('u', n-1, dp)) % MOD;
        } else if(x == 'o') {
            temp = (temp % MOD + recurse('u', n-1, dp)) % MOD;
            temp = (temp % MOD + recurse('i', n-1, dp)) % MOD;
        } else {
            temp = (temp % MOD + recurse('a', n-1, dp)) % MOD;
        }
        return dp[x-'a'][n] = temp;
    }
    
    int countVowelPermutation(int n) {
        
        vector<char> ch = {'a','e','i','o','u'};
        vector<vector<int>> dp(26, vector<int>(n+1, -1));
        int ans = 0;
        for(auto x: ch) {
            ans = (ans % MOD + recurse(x, n, dp) % MOD) % MOD;
        }
        return ans;
    }
};
55098