<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>


int mod=1e9+7;
int solve(int i,int mask,vector<vector<int>>&dp)
{
    if(i==dp.size()-10)
    return 1;
    if(dp[i][mask]!=-1)return dp[i][mask];
    long long ways=0;
    for(int j=0;j<5;j++)
    {
        if(((mask>>j)&1))
        {
            
            if(j==0)
            {
                ways=((ways%mod)+(solve(i+1,2,dp)%mod))%mod;
            }
            if(j==1)
            {
                ways=((ways%mod)+(solve(i+1,5,dp)%mod))%mod;
            }
            if(j==2)
            {
                ways=((ways%mod)+(solve(i+1,27,dp)%mod))%mod;
            }
            if(j==3)
            {
                ways=((ways%mod)+(solve(i+1,20,dp)%mod))%mod;
            }
            if(j==4)
            {
                ways=((ways%mod)+(solve(i+1,1,dp)%mod))%mod;
            }
        }
    }
    return dp[i][mask]=ways;
}

class Solution {
public:
    int countVowelPermutation(int n) {
        vector<vector<int>>dp(n+10,vector<int>(33,-1));
        return solve(0,31,dp);
        
    }
};
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