<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 dp_fun(vector<vector<vector<int>>>&dp, vector<vector<int>>&grp, int l, int r, int ext)
    {
        if(l > r)   return 0;
        if(dp[l][r][ext] == -1)
        {
            int maxm=0;
            maxm = (grp[l][0]+ext)*(grp[l][0]+ext) + dp_fun(dp, grp, l+1, r, 0);
            for(int i=l+1; i <= r; i++)
            {
                if(grp[l][1] == grp[i][1])
                {
                    maxm = max(maxm, dp_fun(dp, grp, l+1, i-1, 0)+dp_fun(dp, grp, i, r, ext+grp[l][0]));
                }
            }
            dp[l][r][ext] = maxm;
        }
        return dp[l][r][ext];
    }

    int removeBoxes(vector<int>& boxes) 
    {
        int n=boxes.size(), cnt=1;
        vector<vector<int>> grp;
        for(int i=1; i < boxes.size(); i++)
        {
            if(boxes[i] != boxes[i-1])
            {
                grp.push_back({cnt, boxes[i-1]});
                cnt=0;
            }
            cnt++;
        }
        grp.push_back({cnt, boxes[n-1]});
        int sz = grp.size();
        vector<vector<vector<int>>> dp(sz, vector<vector<int>>(sz, vector<int>(101, -1)));     
        return dp_fun(dp, grp, 0, sz-1, 0);   
    }
};
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