<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:
        def f(s,n,dp,d):
            if(n==0):
                return 1
            elif(s==''):
                return f('a',n-1,dp,d)+f('e',n-1,dp,d)+f('i',n-1,dp,d)+f('o',n-1,dp,d)+f('u',n-1,dp,d)                
            elif(dp[d[s]][n]!=-1):
                return dp[d[s]][n]
            else:
                if(s=='a'):
                    dp[d[s]][n]=f('e',n-1,dp,d)
                elif(s=='e'):
                    dp[d[s]][n]=f('a',n-1,dp,d)+f('i',n-1,dp,d)
                elif(s=='i'):
                    dp[d[s]][n]=f('a',n-1,dp,d)+f('e',n-1,dp,d)+f('o',n-1,dp,d)+f('u',n-1,dp,d)
                elif(s=='o'):
                    dp[d[s]][n]=f('i',n-1,dp,d)+f('u',n-1,dp,d)
                else:
                    dp[d[s]][n]=f('a',n-1,dp,d)
                return dp[d[s]][n]
        from collections import defaultdict
        dp=[[-1 for j in range(n)] for i in range(5)]
        d=defaultdict(int)
        d['a']=0
        d['e']=1
        d['i']=2
        d['o']=3
        d['u']=4
        return f('',n,dp,d)%((10**9)+7)
82962