<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 {
    // 0 --> a
    // 1 --> e
    // 2 --> i
    // 3 --> o
    // 4 --> u

    int mod = 1e9 + 7;
    long long solve(int prev, int n, vector<vector<int>>& dp)
    {
        if(n == 0)
        {
            return 1;
        }

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

        long long zero = 0;
        long long one = 0;
        long long two = 0;
        long long three = 0;
        long long four = 0;

        if(prev == -1)
        {
            zero =  solve(0,n-1,dp);
            one =  solve(1,n-1,dp);
            two =  solve(2,n-1,dp);
            three =  solve(3,n-1,dp);
            four =  solve(4,n-1,dp);
        }

        if(prev == 0)
        {
            one =  solve(1,n-1,dp);
            four =  solve(4,n-1,dp);
            two =  solve(2,n-1,dp);
        }
        if(prev == 1)
        {
            zero = solve(0,n-1,dp);
            two = solve(2,n-1,dp);
        }

        if(prev == 2)
        {
            one = solve(1,n-1,dp);
            three = solve(3,n-1,dp);
        }

        if(prev == 3)
        {
            two = solve(2,n-1,dp);
        }

        if(prev == 4)
        {
            two = solve(2,n-1,dp);
            three = solve(3,n-1,dp);
        }

        return dp[prev+1][n] = ((one + two + three + four + zero)%mod);
    }
public:
    int countVowelPermutation(int ne) {
        vector<vector<long long >> dp(6,vector<long long>(ne+1,0));
        // return solve(-1,n,dp);

        for (int i = 0; i < 5; i++) {
            dp[i][1] = 1;
        }

        for (int n = 2; n <= ne; n++) {
            dp[0][n] = (dp[1][n-1] + dp[2][n-1] + dp[4][n-1]) % mod; 
            dp[1][n] = (dp[0][n-1] + dp[2][n-1]) % mod;            
            dp[2][n] = (dp[1][n-1] + dp[3][n-1]) % mod;            
            dp[3][n] = dp[2][n-1] % mod;                        
            dp[4][n] = (dp[2][n-1] + dp[3][n-1]) % mod;            
        }
        long long result = 0;
        for (int i = 0; i < 5; i++) {
            result = (result + dp[i][ne]) % mod;
        }

        return result%mod;
    }
};
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