<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:
        vowels = ["a", "e", "i", "o", "u"]
        follow_dict = {
            "a": ["e"],
            "e": ["a", "i"],
            "i": ["a", "e", "o", "u"],
            "o": ["i", "u"],
            "u": ["a"],
            "x": ["a", "e", "i", "o", "u"],
        }

        followed_dict = {
            "a" : ["e", "i", "u"],
            "e" : ["a", "i"],
            "i" : ["e", "o"],
            "o" : ["i"],
            "u" : ["i", "o"]
        }

        dp = [[0] * (n) for _ in range(5)]

        for i in range(5):
            dp[i][n-1] = 1
        
        for i in range(n-2,-1,-1):
            for j in range(5):
                last_char = vowels[j]
                ans = 0
                for char in followed_dict[last_char]:
                    ans +=  dp[vowels.index(char)][i+1]
                dp[j][i] = ans % (10**9 + 7)
        
        res = 0
        for i in range(5):
            res += dp[i][0]
        return res  % (10**9 + 7)

        
        @lru_cache(None)
        def helper(num, last_char):
            if num == n:
                return 1
            
            ans = 0
            for char in follow_dict[last_char]:
                ans +=  helper(num+1, char)
            return ans % (10**9 + 7)
        
        return helper(0, "x")
21922