<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:
    vector<vector<long>> memo;

    int countVowelPermutation(int n) {
        unordered_map<char, vector<char>> adj;
        memo.resize(26, vector<long>(n + 1, -1));
        

        adj['a'].push_back('e');
        adj['e'].push_back('a');
        adj['e'].push_back('i');
        adj['i'].push_back('a');
        adj['i'].push_back('e');
        adj['i'].push_back('o');
        adj['i'].push_back('u');
        adj['o'].push_back('i');
        adj['o'].push_back('u');
        adj['u'].push_back('a');
        
        long res = (dfs('a', n - 1) % 1000000007) + 
                   (dfs('e', n - 1) % 1000000007) + 
                   (dfs('i', n - 1) % 1000000007) + 
                   (dfs('o', n - 1) % 1000000007) + 
                   (dfs('u', n - 1) % 1000000007);

        return res % 1000000007;

    }

private:
    long dfs(char curr, int length) {
        if (length == 0) {
            return 1;
        }
        if (memo[curr - 'a'][length] != -1) {
            return memo[curr - 'a'][length];
        }

        // long total = 0;
        // vector<char> neighbors = adj[curr];

        // for (char nei : neighbors) {
        //     total += dfs(nei, length - 1, adj);
        // }

        // memo[curr - 'a'][length] = total % 1000000007; 
        // return memo[curr - 'a'][length];


        if(curr == 'a') {
            return memo[curr - 'a'][length] = dfs('e', length-1) % 1000000007;
        } else if(curr == 'e') {
            return memo[curr - 'a'][length] = (dfs('a', length-1) + dfs('i', length-1)) % 1000000007;
        } else if(curr == 'i') {
            return memo[curr - 'a'][length] = (dfs('a', length-1) + dfs('e', length-1) + dfs('o', length-1) + dfs('u', length-1)) % 1000000007;
        } else if(curr == 'o') {
            return memo[curr - 'a'][length] = (dfs('i', length-1) + dfs('u', length-1)) % 1000000007;
        } else { //curr == u
            return memo[curr - 'a'][length] = dfs('a', length-1);
        }
    }
};


//ae
//ea
//ei
//ia
//ie
//io
//iu
//oi
//ou
//ua
100379