<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:
    const long long MOD = (long long) 1e9 + 7;
    
    
  
    long long countVowelPermutation(long long n) {
        long long dp[n + 3][30];
        memset(dp, 0, sizeof dp);
       
        string s = "aeiou";
        
        for(auto i : s) {
            dp[1][i - 'a'] = 1;
        }
        
        
        for(long long i = 2; i <= n; i++) {
            for(auto j : s) {
                if(j == 'a') { //curr
                    dp[i][j - 'a'] = dp[i - 1]['u' - 'a']%MOD + dp[i - 1]['e' - 'a']%MOD + dp[i - 1]['i' - 'a']%MOD;
                    dp[i][j  - 'a'] %= MOD;
                    
                    
                }
                else if(j == 'e') {
                    dp[i][j - 'a'] = dp[i - 1]['a' - 'a']%MOD + dp[i - 1]['i' - 'a']%MOD;
                    dp[i][j  - 'a'] %= MOD;
                    
                }
                else if(j == 'i') {
                    dp[i][j - 'a'] = dp[i - 1]['e' - 'a']%MOD + dp[i - 1]['o' - 'a']%MOD;
                    dp[i][j  - 'a'] %= MOD;
                }
                else if(j == 'o') {
                    dp[i][j - 'a'] =  dp[i - 1]['i' - 'a']%MOD;
                    dp[i][j  - 'a'] %= MOD;
                }
                else if(j == 'u') {
                    dp[i][j - 'a']= dp[i - 1]['i' - 'a']%MOD + dp[i - 1]['o' - 'a']%MOD;
                    dp[i][j  - 'a'] %= MOD;
                }
            }
        }
        

        long long ans = 0;
        for(auto j : s) {
            ans += dp[n][j - 'a']%MOD;
            ans %= MOD;
        }
        return ans;
        
        
    }
};
13439