<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 = 1e9 + 7;
    int addMod(int a, int b) { return (a % mod + b % mod) % mod; }
    int countWow(vector<vector<int>>& dp, map<char, vector<char>>& mp, int n,
                 char prv) {
        if (n == 0) {
            return 1;
        }

        if (dp[n][prv - 'a'] != -1) {
            return dp[n][prv - 'a'];
        }

        int ans = 0;

        for (char c : mp[prv]) {
            ans = addMod(ans, countWow(dp, mp, n - 1, c));
        }

        return dp[n][prv - 'a'] = ans;
    }
    int countVowelPermutation(int n) {
        vector<vector<int>> dp(n + 1, vector<int>(26, -1));
        map<char, vector<char>> mp;
        mp['a'] = vector<char>{'e'};
        mp['e'] = vector<char>{'a', 'i'};
        mp['i'] = vector<char>{'a', 'e', 'o', 'u'};
        mp['o'] = vector<char>{'i', 'u'};
        mp['u'] = vector<char>{'a'};

        int ans = 0;
        for (auto [k, v] : mp) {
            ans = addMod(ans, countWow(dp, mp, n - 1, k));
        }

        return ans;
    }
};
98568