<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[200][200][200] = {};
    int helper(vector<int>&boxes,int i,int j,int k){
        if(i>j)
         return 0;

        if(dp[i][j][k]>0)
         return dp[i][j][k]; 
         int lOrg = i, kOrg = k;

        while(i+1<=j && boxes[i]==boxes[i+1]){
            i+=1;
            k+=1;
        } 

        int ans=(k+1)*(k+1)+helper(boxes,i+1,j,0);

        for(int l=i+1;l<=j;l++)
            if(boxes[l]==boxes[i])
            ans=max(ans,(helper(boxes,i+1,l-1,0)+helper(boxes,l,j,k+1)));
        
        return dp[lOrg][j][kOrg]=ans;
    }
    int removeBoxes(vector<int>& boxes) {

        
        memset(dp, 0, sizeof(dp));
        return helper(boxes,0,boxes.size()-1,0);
        
    }
};
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