<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:
    Solution() {
        ios_base :: sync_with_stdio( false );
        cin.tie( nullptr ) , cout.tie( nullptr );
    }
    int countVowelPermutation(int n) {
        vector< vector< int>> dp( n , vector< int >(5 , 0) );
        for(int i=0 ; i<5 ; i++) {
            dp[0][i] = 1;
        }
        long long mod = 1e9 + 7 ;
        for(int i=1 ; i<n ; i++) {
            dp[i][0] = ( dp[i-1][1]%mod + dp[i-1][2]%mod + dp[i-1][4]%mod ) %mod;
            dp[i][1] = ( dp[i-1][0]%mod + dp[i-1][2]%mod ) %mod;
            dp[i][2] = ( dp[i-1][1]%mod + dp[i-1][3]%mod ) %mod;
            dp[i][3] = ( dp[i-1][2] ) %mod;
            dp[i][4] = ( dp[i-1][2]%mod + dp[i-1][3]%mod ) %mod;
        }
        int res = 0 ;
        for(int i=0 ; i<5 ; i++){
            res = ( res + dp[n-1][i]) % mod;
        }
        return res ;
    }
};
40608