<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) {
        const int MOD = 1e9 + 7;  // Modulo value

        // dp arrays for each vowel: a, e, i, o, u
        vector<long long> dp(5, 1);  // Base case: for length 1, there's exactly one way to end with each vowel.

        // Iterate through lengths from 2 to n
        for (int len = 2; len <= n; ++len) {
            vector<long long> new_dp(5, 0);

            // Update counts based on the transitions
            new_dp[0] = dp[1] % MOD;                                  // 'a' can be followed by 'e'
            new_dp[1] = (dp[0] + dp[2]) % MOD;                        // 'e' can be followed by 'a' or 'i'
            new_dp[2] = (dp[0] + dp[1] + dp[3] + dp[4]) % MOD;        // 'i' can be followed by 'a', 'e', 'o', 'u'
            new_dp[3] = (dp[2] + dp[4]) % MOD;                        // 'o' can be followed by 'i' or 'u'
            new_dp[4] = dp[0] % MOD;                                  // 'u' can be followed by 'a'

            dp = new_dp;  // Move to the next length
        }

        // Sum the counts of all strings of length n and return result modulo MOD
        return (dp[0] + dp[1] + dp[2] + dp[3] + dp[4]) % MOD;
    
    }
};
36985