<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:
        """
        a -> e : a -> (e)
        e -> a or e -> i : e -> (a,i)
        i -> a, i -> e, i -> o, i -> u: i -> (a,e,o,u)
        o -> i, o -> u : o -> (i, u)
        u -> a : u -> (a)

        a <- (e, i, u) 0 => 1 + 2 + 4
        e <- (a, i)    1 => 0 + 2
        i <- (e, o)    2 => 1 + 3
        o <- (i)       3 => 2
        u <- (i, o)    4 => 2 + 3

              0    1    2    3    4   Total
              a    e    i    o    u   
        n=1   1    1    1    1    1     5
        n=2   3    2    2    1    2     10 
        """
        m = 5
        dp = [[0]*m for _ in range(n)]
        if n == 1:
            return 5
        for j in range(m):
            dp[0][j] = 1
        res = 0
        MOD = 10**9 + 7
        #print(dp)
        for i in range(1, n):
            dp[i][0] = dp[i-1][1] + dp[i-1][2] + dp[i-1][4] # For 'a'
            dp[i][1] = dp[i-1][0] + dp[i-1][2] # For 'e'
            dp[i][2] = dp[i-1][1] + dp[i-1][3] # For 'i'
            dp[i][3] = dp[i-1][2] # For 'o'
            dp[i][4] = dp[i-1][2] + dp[i-1][3] # For 'u'
            #print(dp)
            if i == n-1:
                for j in range(m):
                    res += dp[i][j] 

        return res % MOD




        
109667