<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:
    int mod = 1000000007;
    int getStrCount(vector<vector<int>> &dp, int pos, char ch, int n,  unordered_map<char, vector<char>> &vowelMap){
        if(pos == n)return 1;
        int charIdx = ch -'a';
        if(dp[pos][charIdx] != -1)return dp[pos][charIdx];

        dp[pos][charIdx] = 0;
        for(int i=0;i<vowelMap[ch].size(); i++){
            dp[pos][charIdx]+=getStrCount(dp, pos+1,vowelMap[ch][i] ,n, vowelMap);
            dp[pos][charIdx]%=mod;
        }
        return dp[pos][charIdx];
    }

    int countVowelPermutation(int n) {
       vector<vector<int>> dp(n, vector<int>(26, -1));
       int answer = 0;
       vector<char> vowels = {'a', 'e', 'i', 'o', 'u'};
    //    vector<vector<char>> vowelMap = { {'e'},  {'a', 'i'}, {'a', 'e', 'o', 'u'}, {'i', 'u'}, {'a'}};
       unordered_map<char, vector<char>> vowelMap;
       vowelMap['a'] = {'e'}, vowelMap['e'] = {'a', 'i'}, vowelMap['i'] = {'a', 'e', 'o', 'u'}, vowelMap['o']={'i', 'u'}, vowelMap['u'] = {'a'};
        for(int i=0;i<5;i++){
            answer+=getStrCount(dp,1, vowels[i], n, vowelMap);
            answer = answer % mod;
        }
        return answer;
    }
};
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