<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 {
private:

unordered_map<char, int> intFromChar;
int modulo;

public:
    int countVowelPermutation(int n) {
        intFromChar['a'] = 0;
        intFromChar['e'] = 1;
        intFromChar['i'] = 2;
        intFromChar['o'] = 3;
        intFromChar['u'] = 4;
        modulo = 1e9 + 7;

        // create dp array where dp[i][j] is number is strings of length i and ending with 'j'
        vector<vector<int>> dp(n+1, vector<int>(5, -1));

        dp[1][0] = dp[1][1] = dp[1][2] = dp[1][3] = dp[1][4] = 1;

        int result = 0;

        result+=getDp(dp, n, 'a');
        result%=modulo;
        result+=getDp(dp, n, 'e');
        result%=modulo;
        result+=getDp(dp, n, 'i');
        result%=modulo;
        result+=getDp(dp, n, 'o');
        result%=modulo;
        result+=getDp(dp, n, 'u');
        result%=modulo;

        return result;
    }

    int getDp(vector<vector<int>>& dp, int n, char letter) {
        // cout<<"Finding for length "<<n<<" and letter "<<letter<<endl;
        int currentLetter = intFromChar[letter];

        if(dp[n][currentLetter] != -1) {
            ;
        }
        else {
            if(letter == 'a') {
                dp[n][currentLetter] = (getDp(dp, n-1, 'i') + getDp(dp, n-1, 'u'))%modulo + getDp(dp, n-1, 'e');
            }
            else if(letter == 'e') {
                dp[n][currentLetter] = getDp(dp, n-1, 'a') + getDp(dp, n-1, 'i');
            }
            else if(letter == 'i') {
                dp[n][currentLetter] = getDp(dp, n-1, 'o') + getDp(dp, n-1, 'e');
            }
            else if(letter == 'o') {
                dp[n][currentLetter] = getDp(dp, n-1, 'i');
            }
            else if(letter == 'u') {
                dp[n][currentLetter] = getDp(dp, n-1, 'o') + getDp(dp, n-1, 'i');
            }
        }

        return dp[n][currentLetter]%modulo;
    }
};
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