<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 = 1000000007;
    int func(int index, char pre, int n, vector<vector<int>> &dp) {
        if(index == n) return 1;
        else if(index > n) return 0;
        if(dp[index][pre - '`'] != -1) return dp[index][pre - '`'];
        int op1 = 0, op2 = 0, op3 = 0, op4 = 0, op5 = 0;
        if(pre == '`') {
            op1 = func(index + 1, 'a', n, dp);
            op2 = func(index + 1, 'e', n, dp);
            op3 = func(index + 1, 'i', n, dp);
            op4 = func(index + 1, 'o', n, dp);
            op5 = func(index + 1, 'u', n, dp);
        }
        else {
            if(pre == 'e') op1 = func(index + 1, 'a', n, dp);
            if(pre == 'a' || pre == 'i') op2 = func(index + 1, 'e', n, dp);
            if(pre != 'i') op3 = func(index + 1, 'i', n, dp);
            if(pre == 'i' || pre == 'u') op4 = func(index + 1, 'o', n, dp);
            if(pre == 'a') op5 = func(index + 1, 'u', n, dp);
        }
        return dp[index][pre - '`'] = (((((op1 + op2) % mod) + ((op3 + op4) % mod)) % mod) + op5) % mod;
    }
public:
    int countVowelPermutation(int n) {
        vector<vector<int>> dp(n, vector<int> (27, -1));
        return func(0, '`', n, dp);
    }
};
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