<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 countVowelPermutation(int n) {
        vector<vector<int>> DP(5,vector<int>(n,0));
        int mod = pow(10,9) + 7;
        for(int i=0;i<5;i++)
            DP[i][0] =1;
        //DP[i][k] is the number of permutations of length k-1 , starting with i(0-a,1-e..)
        //if we know DP[i][k-1] , then DP[j][k] can only be followed by DP[j][k].. use above rules
        for(int k=1;k<n;k++)
        {
            DP[0][k] = DP[1][k-1]; //a -> e
            DP[1][k] = (DP[0][k-1] + DP[2][k-1])%mod; //e -> a,i
            DP[2][k] = ( (DP[0][k-1] + DP[1][k-1])%mod + (DP[3][k-1] + DP[4][k-1])%mod )%mod; //i->a,e,o,u
            DP[3][k] = (DP[2][k-1] + DP[4][k-1])%mod; //o->i,u
            DP[4][k] = DP[0][k-1]; //u->a
        }
        int ans = 0;
        for(int i=0;i<5;i++)
        {
            ans = (ans + DP[i][n-1])%mod;
        }
        return ans;
    }
};
18873