<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 = 1e9 + 7;
    long long int f(int i, int n, int prev, vector<vector<long long int>> &dp)
    {
        if(i >= n) return 1 % mod;
        if(dp[i][prev+1] != -1) return dp[i][prev+1] % mod;
        long long int ans = 0;
        if(prev == -1) for(int ind = 0; ind < 5; ind++) ans += (f(i+1, n, ind, dp) % mod);
        else if(prev == 0) ans += (f(i+1, n, 1, dp) % mod);
        else if(prev == 1) ans += ((f(i+1, n, 0, dp) % mod + f(i+1, n, 2, dp) % mod) % mod);
        else if(prev == 2) ans += ((f(i+1, n, 0, dp) % mod + f(i+1, n, 1, dp) % mod + f(i+1, n, 3, dp) % mod + f(i+1, n, 4, dp) % mod) % mod);
        else if(prev == 3) ans += ((f(i+1, n, 2, dp) % mod + f(i+1, n, 4, dp) % mod) % mod);
        else if(prev == 4) ans += f(i+1, n, 0, dp) % mod;
        return dp[i][prev+1] = ans % mod;
    }
    int countVowelPermutation(int n) 
    {
        vector<vector<long long int>> dp(n+1, vector<long long int>(6, -1));
        return f(0, n, -1, dp) % mod;
    }
};
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