<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 maxValue(vector<int>& boxes,int i,int j,int count,vector<vector<vector<int>>>& dp){

        if(i > j){
            return 0;
        }

        if(dp[i][j][count] != -1){
            return dp[i][j][count];
        }

        int io = i,jo = j,counto = count;

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

        int ans = (count+1)*(count+1) + maxValue(boxes,i+1,j,0,dp);

        for(int k = i+1;k <= j;k++){
            if(boxes[k] == boxes[i]){
                ans = max(ans,maxValue(boxes,i+1,k-1,0,dp) + maxValue(boxes,k,j,count+1,dp));
            }
        }

        return dp[io][jo][counto] = ans;

    }

    int removeBoxes(vector<int>& boxes) {
        // Testcase -> [2,2,3,3,2]
        int n = boxes.size();
        vector<vector<vector<int>>> dp(n,vector<vector<int>>(n,vector<int>(n,-1)));
        return maxValue(boxes,0,n-1,0,dp);
    }
};
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