<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:
    const int MOD = 1e9 + 7;

    int charToIndex(char c) {
        switch(c) {
            case 'a': return 0;
            case 'e': return 1;
            case 'i': return 2;
            case 'o': return 3;
            case 'u': return 4;
            default: return -1;
        }
    }

    int solve(int n, char prev, unordered_map<char, vector<char>> &mpp, vector<vector<int>> &dp){
        if(n == 0) return 1;

        int prevIdx = charToIndex(prev);
        if(dp[n][prevIdx] != -1){
            return dp[n][prevIdx];
        }

        int ans = 0;
        for(auto it: mpp[prev]){
            ans = (ans + solve(n-1, it, mpp, dp) % MOD) % MOD;
        }

        return dp[n][prevIdx] = ans;
    }

    int countVowelPermutation(int n) {
        unordered_map<char, vector<char>> mpp;
        mpp['a'] = {'e'};
        mpp['e'] = {'a', 'i'};
        mpp['i'] = {'a', 'e', 'o', 'u'};
        mpp['o'] = {'i', 'u'};
        mpp['u'] = {'a'};

        vector<vector<int>> dp(n + 1, vector<int>(5, -1));
        int ans = 0;
        ans = (ans + solve(n-1, 'a', mpp, dp) % MOD) % MOD;
        ans = (ans + solve(n-1, 'e', mpp, dp) % MOD) % MOD;
        ans = (ans + solve(n-1, 'i', mpp, dp) % MOD) % MOD;
        ans = (ans + solve(n-1, 'o', mpp, dp) % MOD) % MOD;
        ans = (ans + solve(n-1, 'u', mpp, dp) % MOD) % MOD;

        return ans;
    }
};

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