<p>You are given several <code>boxes</code> with different colors represented by different positive numbers.</p>

<p>You may experience several rounds to remove boxes until there is no box left. Each time you can choose some continuous boxes with the same color (i.e., composed of <code>k</code> boxes, <code>k &gt;= 1</code>), remove them and get <code>k * k</code> points.</p>

<p>Return <em>the maximum points you can get</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> boxes = [1,3,2,2,2,3,4,3,1]
<strong>Output:</strong> 23
<strong>Explanation:</strong>
[1, 3, 2, 2, 2, 3, 4, 3, 1] 
----&gt; [1, 3, 3, 4, 3, 1] (3*3=9 points) 
----&gt; [1, 3, 3, 3, 1] (1*1=1 points) 
----&gt; [1, 1] (3*3=9 points) 
----&gt; [] (2*2=4 points)
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> boxes = [1,1,1]
<strong>Output:</strong> 9
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> boxes = [1]
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= boxes.length &lt;= 100</code></li>
	<li><code>1 &lt;= boxes[i]&nbsp;&lt;= 100</code></li>
</ul>

class Solution {

public:
    int solve(vector<int>&boxes, int s, int e, int cnt, vector<vector<vector<int>>>&dp)
    {
        if (s>e)
        return 0;

        if (dp[s][e][cnt]!=-1)
        return dp[s][e][cnt];

        int int_i = s;
        int ini_cnt = cnt;

        while(s+1 <= e && boxes[int_i]==boxes[s+1])
        {
            cnt++;
            s++;
        }

        int ans = (cnt+1)*(cnt+1) + solve(boxes,s+1,e,0,dp);

        for (int i = s+1;i<=e;i++)
        {
            if (boxes[int_i]==boxes[i])
            ans = max(ans, solve(boxes,s+1,i-1,0,dp) + solve(boxes,i,e,cnt+1,dp));
        }
        return dp[int_i][e][ini_cnt] = ans;
    }
    int removeBoxes(vector<int>& boxes) {
        int n = boxes.size();
        vector<vector<vector<int>>> dp(n+1,vector<vector<int>>(n+1,vector<int>(n+1,-1)));
        return solve(boxes, 0, n-1, 0,dp);
    }
};
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