<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 {
private:
    int mod = pow(10, 9)+7;
    void solve(int n, int last, long long& count, vector<vector<int>>& dp){
        if(n==0){
            count = (count+1)%mod;
            return;
        }
        if(dp[n][last] != -1){
            count = (count+dp[n][last])%mod;
            return;
        }
        long long tempCount = 0;
        if(last == 0){
            solve(n-1, 1, tempCount, dp);
        }
        if(last == 1){
            solve(n-1, 0, tempCount, dp);
            solve(n-1, 2, tempCount, dp);
        }
        if(last == 2){
            solve(n-1, 0, tempCount, dp);
            solve(n-1, 1, tempCount, dp);
            solve(n-1, 3, tempCount, dp);
            solve(n-1, 4, tempCount, dp);
        }
        if(last == 3){
            solve(n-1, 2, tempCount, dp);
            solve(n-1, 4, tempCount, dp);
        }
        if(last == 4){
            solve(n-1, 0, tempCount, dp);
        }
        dp[n][last] = tempCount;
        count = (count+tempCount)%mod;
    }
public:
    // vector<int> vect = {'a','e','i','o','u'};
    int countVowelPermutation(int n) {
        long long count = 0;
        vector<vector<int>> dp(n+1, vector<int>(6, -1));
        for(int i=0;i<5;i++){
            solve(n-1, i, count, dp);
        }
        return count%mod;
    }
};
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