<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 {
    const int mod = 1e9 + 7;
    int solve(char ch, int n, map<char, vector<char>> &mp, vector<vector<int>> &dp) {
        if(n == 0) {
            return 1;
        }
        
        if(dp[n][ch - 'a'] != -1) return dp[n][ch - 'a'];
        
        int ans = 0;
        for(char it: mp[ch]) {
            ans = (ans + solve(it, n-1, mp, dp))%mod;
        }
        
        return dp[n][ch - 'a'] = ans;
    }
public:
    int countVowelPermutation(int n) {
        map<char, vector<char>> mp;
        
        mp['u'].push_back('a');
        mp['o'].push_back('i'); 
        mp['o'].push_back('u'); 
        mp['e'].push_back('a'); 
        mp['e'].push_back('i'); 
        mp['a'].push_back('e'); 
        mp['i'].push_back('a');
        mp['i'].push_back('e');
        mp['i'].push_back('o');
        mp['i'].push_back('u'); 
        
        vector<char> v = {'a', 'e', 'i', 'o', 'u'};
        int ans = 0;
        
        vector<vector<int>> dp(n+1, vector<int> (26, -1));
        for(char ch : v) {
            int temp  = solve(ch, n-1, mp, dp);
            ans = (ans + temp) % mod;
        }
        
        return ans;
    }
};
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