<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 m = 1e9+7; 
    vector<char> vec = {'a', 'e', 'i', 'o', 'u'};
    vector<vector<int>> memo;
    int a = 0, e = 1, i = 2, o = 3, u = 4;

    int solve(int idx, int n) {
        if (memo[idx][n] != -1)
            return memo[idx][n];
        
        if (n == 1)
            return 1;

        if (idx == a) {
            return memo[a][n] = solve(e, n-1);
        } else if (idx == e) {
            return memo[e][n] = (solve(a, n-1) + solve(i, n-1)) % m;
        } else if (idx == i) {
            int ans = 0;
            for (int k = 0; k < 5; ++k) {
                if (k != i)
                    ans = (ans + solve(k, n-1)) % m;
            }
            return memo[i][n] = ans;
        } else if (idx == o) {
            return memo[o][n] = (solve(i, n-1) + solve(u, n-1)) % m;
        } else if (idx == u) {
            return memo[u][n] = solve(a, n-1);
        }
        return 0;
    }

    int countVowelPermutation(int n) {
        memo.resize(5, vector<int>(n + 1, -1));
        int res = 0;
        for (int k = 0; k < 5; ++k) {
            res = (res + solve(k, n)) % m;
        }
        return res;
    }
};

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