<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 {
public:
    long long dp[20000][5];
    int n;
    const int MOD = 1000000007;
    
    unordered_map<char, int> ind;
    
    long long recurse(int i, char c) {
        if (i == n-1) return 1;
        int d = ind[c];
        if (dp[i][d]) return dp[i][d];
        
        if (c == 'a') {
            dp[i][d] = recurse(i+1, 'e');
        } else if (c == 'e') {
            dp[i][d] = recurse(i+1, 'a') + recurse(i+1, 'i');
        } else if (c == 'i') {
            dp[i][d] = recurse(i+1, 'a') + recurse(i+1, 'e') + recurse(i+1, 'o') + recurse(i+1, 'u');
        } else if (c == 'o') {
            dp[i][d] = recurse(i+1, 'i') + recurse(i+1, 'u');
        } else {
            dp[i][d] = recurse(i+1, 'a');
        }
        dp[i][d] %= MOD;
        return dp[i][d];
    }
    
    int countVowelPermutation(int n2) {
        n = n2;
        ind['a'] = 0;
        ind['e'] = 1;
        ind['i'] = 2;
        ind['o'] = 3;
        ind['u'] = 4;
        long long ans = 0;
        for (int i = 0; i<n; i++) {
            for (int j = 0; j<5; j++) dp[i][j] = 0;
        }
        
        ans += recurse(0, 'a') + recurse(0, 'e') + recurse(0, 'i') + recurse(0, 'o') + recurse(0, 'u');
        
        return ans%MOD;
    }
};
13439