<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 func(int i,int j,int ext,vector<vector<int>> &grp, vector<vector<vector<int>>>&dp){
        if(i>=j) return 0;
        if(dp[i][j][ext]!=-1) return dp[i][j][ext];
        int ans=((ext+grp[i][0])*(ext+grp[i][0]))+func(i+1,j,0,grp,dp);
        for(int p=i+2; p<j; p++){
            if(grp[i][1]==grp[p][1]){
                ans=max(ans,func(i+1,p,0,grp,dp)+func(p,j,ext+grp[i][0],grp,dp));
            }
        }
        return dp[i][j][ext]=ans;
    }
    
    int removeBoxes(vector<int>& a) {
        int n=a.size();
        vector<vector<int>> grp;
        int ct=1;
        for(int i=1; i<n; i++){
            if(a[i]==a[i-1]) ct++;
            else{
                grp.push_back({ct,a[i-1]});
                ct=1;
            }
        }
        grp.push_back({ct,a[n-1]});
        vector<vector<vector<int>>> dp(grp.size()+1,vector<vector<int>>(grp.size()+1,vector<int>(101,-1)));
        int ans=func(0,grp.size(),0,grp,dp);
        return ans;
    }
};
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