<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 {

private:
    int solve(int i, int j, int k, vector<int>& boxes, vector<vector<vector<int>>>& dp){
        if(i > j) return 0;
        if(i == j) return (k+1)*(k+1);

        if(dp[i][j][k] != -1) return dp[i][j][k];

        int i_org = i;
        int k_org = k;

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

        // case 1 : merge the prev k boxes and move to i+1
        int ans = (k+1)*(k+1) + solve(i+1, j, 0, boxes, dp);

        // case 2 : merge any simliar element with the prev k boxes
        for(int ind = i+1; ind <= j; ind++) {
            if(boxes[ind] == boxes[i]) {
                int points = solve(i+1, ind-1, 0, boxes, dp) + solve(ind, j, k+1, boxes, dp);

                ans = max(ans, points);
            }
        }

        return dp[i_org][j][k_org] = ans;
    }

public:
    int removeBoxes(vector<int>& boxes) {
        int n = boxes.size();

        vector<vector<vector<int>>> dp(n, vector<vector<int>>(n, vector<int>(101, -1)));

        // k is # of prev boxes of same color as boxes[i]
        return solve(0, n-1, 0, boxes, dp);
    }
};
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