<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:

    # dp of (char, vowel)
    # thus dp has length: (n, 5)
    # a followed only by e
    # e only followed by a or i
    # i cannot follow another i
    # o can only be followed by i or u
    # u only followed by a
    vowels = ['a', 'e', 'i', 'o', 'u']
    dp = [[0 for _ in range(5)] for _ in range(n)]
    for j in range(5):
      dp[0][j] = 1

    for i in range(1, n):
      # print(dp)
      for j, vowel in enumerate(vowels):
        if j == 0:
          # a
          dp[i][j] = dp[i-1][1] + dp[i-1][4] + dp[i-1][2]
        elif j == 1:
          # e
          dp[i][j] = dp[i-1][0] + dp[i-1][2]
        elif j == 2:
          # i # e, o
          dp[i][j] = dp[i-1][1] + dp[i-1][3]
        elif j == 3:
          # o
          dp[i][j] = dp[i-1][2]
        elif j == 4:
          # u # i, o
          dp[i][j] = dp[i-1][3] + dp[i-1][2]

    # print(dp)
    total = 0
    for j in range(5):
      total += dp[-1][j]
    return total % 1000000007
121112