<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>

#define mod 1000000007
class Solution {
public:
    // int f(int i, int last, int n, unordered_map<int, vector<int>>& mp, vector<vector<int>>& dp) {
    //     if (i == n) return 1;
    //     if (dp[i][last] != -1) return dp[i][last];
    //     vector<int> nexts = mp[last];
    //     long long ways = 0;
    //     for (auto x: nexts) {
    //         ways = ((ways + f(i + 1, x, n, mp, dp)) % mod);
    //     }
    //     return dp[i][last] = ways;
    // }
    int countVowelPermutation(int n) {
        unordered_map<int, vector<int>> mp = {
            {0, {1}},
            {1, {0, 2}},
            {2, {0, 1, 3, 4}},
            {3, {2, 4}},
            {4, {0}}
        };
        vector<vector<int>> dp(n + 1, vector<int>(5, 0));
        for (int last = 0; last < 5; last++) dp[n][last] = 1;
        for (int i = n - 1; i >= 0; i--) {
            for (int last = 0; last < 5; last++) {
                vector<int> nexts = mp[last];
                long long ways = 0;
                for (auto x: nexts) {
                    ways = ((ways + dp[i + 1][x]) % mod);
                }
                dp[i][last] = ways;
            }
        }
        long long ans = 0;
        for (int i = 0; i < 5; i++) {
            ans = ((ans + dp[1][i]) % mod);
        }
        return ans;

    }
};

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