<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:
    MOD = 10 ** 9 + 7

    def dfs(self, n: int, i: int, string: str, memory: dict) -> int:
        count = 0

        if i == 0:
            for char in ['a', 'e', 'i', 'o', 'u']:
                count += self.dfs(n, i + 1, string + char, memory)
        elif i < n:
            if (i, string[-1]) in memory:
                count = memory[(i, string[-1])]
            elif string[i - 1] == 'a':
                count += self.dfs(n, i + 1, string + 'e', memory)
            elif string[i - 1] == 'e':
                count += self.dfs(n, i + 1, string + 'a', memory)
                count += self.dfs(n, i + 1, string + 'i', memory)
            elif string[i - 1] == 'i':
                for char in ['a', 'e', 'o', 'u']:
                    count += self.dfs(n, i + 1, string + char, memory)
            elif string[i - 1] == 'o':
                count += self.dfs(n, i + 1, string + 'i', memory)
                count += self.dfs(n, i + 1, string + 'u', memory)
            elif string[i - 1] == 'u':
                count += self.dfs(n, i + 1, string + 'a', memory)

            memory[(i, string[-1])] = count
        elif i == n:
            count += 1

        return count

    def countVowelPermutation(self, n: int) -> int:
        string = ""
        memory = {}
        ans = self.dfs(n, 0, string, memory)
        return ans % self.MOD

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