<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 to implement the Top-down approach:
class Solution {
    vector<char> vowels = {'a','e','i','o','u'};
    const int MOD = 1e9+7;

public:
    // Method to count how many such strings of length n that can be formed, using recursion with memoization - O(N) & O(N)
    int countVowelPermutation(int n) {
        vector<vector<int>> memory(n + 1, vector<int>(26, -1));
        return solveWithMemo(memory, n, 'w');
    }

private:
    // O(5*N*26) & O(N*26 + N)
    int solveWithMemo(vector<vector<int>>& memory, int n, char prevLetter) {
        // Edge case: If you've created such string of length n then return 1
        if(n == 0)
            return 1;

        // Memoization table: If the current state is already computed then return the computed value
        if(memory[n][prevLetter - 'a'] != -1)
            return memory[n][prevLetter - 'a'];

        // Stores the result value 
        int count = 0;
        
        // Explore all the ways of creating such string from the vowels
        for(char v : vowels) 
            if(prevLetter == 'w' || (prevLetter == 'a' && v == 'e') || (prevLetter == 'e' && (v == 'a' || v == 'i')) || (prevLetter == 'i' && v != 'i') || (prevLetter == 'o' && (v == 'i' || v == 'u')) || (prevLetter == 'u' && v == 'a')) 
                count = count % MOD + solveWithMemo(memory, n - 1, v) % MOD;

        // Store the result value to the memoization table and then return it
        return memory[n][prevLetter - 'a'] = count % MOD;
    }

    // O(5^N) & O(N)
    int solveWithoutMemo(int n, char prevLetter) {
        // Edge case: If you've created such string of length n then return 1
        if(n == 0)
            return 1;

        // Stores the result value
        int count = 0;
        
        // Explore all the ways of creating such string from the vowels
        for(char v : vowels) 
            if(prevLetter == 'w' || (prevLetter == 'a' && v == 'e') || (prevLetter == 'e' && (v == 'a' || v == 'i')) || (prevLetter == 'i' && v != 'i') || (prevLetter == 'o' && (v == 'i' || v == 'u')) || (prevLetter == 'u' && v == 'a')) 
                count = count % MOD + solveWithoutMemo(n - 1, v) % MOD;

        // Return the result value
        return count % MOD;
    }
};

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