<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:
    int dp[26][20001];
    map<char, vector<char>> m;
    vector<char> &next(char c) {
        return m[c];
    }

    int find(char c, int n) {
        if (n == 1) {
            return 1;
        }
        if (dp[c - 'a'][n] != -1) {
            return dp[c - 'a'][n];
        }
        vector<char> &v = next(c);
        int ans = 0;
        for (int i = 0; i < v.size(); i++) {
            ans = (ans % 1000000007 + find(v[i], n - 1) % 1000000007) % 1000000007;
        }
        return dp[c - 'a'][n] = ans;
    }

    int countVowelPermutation(int n) {
        vector<char> v1, v2, v3, v4, v5;
        v1.push_back('e');
        m['a'] = v1;

        v2.push_back('a');
        v2.push_back('i');
        m['e'] = v2;

        v3.push_back('a');
        v3.push_back('e');
        v3.push_back('o');
        v3.push_back('u');
        m['i'] = v3;

        v4.push_back('i');
        v4.push_back('u');
        m['o'] = v4;

        v5.push_back('a');
        m['u'] = v5;
        for (int i = 0; i < 26; i++) {
            for (int j = 0; j < 20001; j++) {
                dp[i][j] = -1;
            }
        }
        return ((((find('a', n) % 1000000007 + find('e', n) % 1000000007) % 1000000007 + find('i', n) % 1000000007) % 1000000007 + find('o', n) % 1000000007) % 1000000007 + find('u', n) % 1000000007) % 1000000007;
    }
};
17061