<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:
    def countVowelPermutation(self, n: int) -> int:
        # Recurrence relations:
        # countA(n) = countE(n-1)
        # countE(n) = countA(n-1) + countI(n-1)
        # countI(n) = countA(n-1) + countE(n-1) + countO(n-1) + countU(n-1)
        # countO(n) = countI(n-1) + countU(n-1)
        # countU(n) = countA(n-1)
        # TotalCount(n) = countA(n) + ... + countU(n)

        # dp table
        # inner lists are for each vowel
        # dp[i][0] -> 'a', dp[i][1] -> 'e', dp[i][2] -> 'i', 
        # dp[i][3] -> 'o', dp[i][4] -> 'u'
        # outer list is for string of length n
        mod = 10**9 + 7
        dp = [[1 for _ in range(5)] for _ in range(n+1)]
        for i in range(1, n):
            dp[i][0] = dp[i-1][1] # countE(n-1)
            dp[i][1] = dp[i-1][0] + dp[i-1][2] # countA(n-1) + countI(n-1)
            dp[i][2] = dp[i-1][0] + dp[i-1][1] + dp[i-1][3] + dp[i-1][4]
            dp[i][3] = dp[i-1][2] + dp[i-1][4]
            dp[i][4] = dp[i-1][0] 
        return sum(dp[n-1]) % mod
94407