<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:
    
    vector<vector<vector<int>>> dp;

    int rec(vector<int> &boxes, int start, int end, int leftBoxes)
    {
        if (start > end) return 0;
        else if (start == end) return (leftBoxes + 1) * (leftBoxes + 1);
        else if (dp[start][end][leftBoxes]) return dp[start][end][leftBoxes]; 
        else
        {//either we merge all left boxes with start, or with some i: [start , left];
            int ans = (leftBoxes + 1) * (leftBoxes + 1) + rec(boxes, start + 1, end, 0);
            for (int i = start + 1; i <= end; i++) if (boxes[i] == boxes[start]) ans = max(ans, rec(boxes, start + 1, i-1, 0) + rec(boxes, i, end, leftBoxes + 1));

            return dp[start][end][leftBoxes] = ans;
        }
    }

    int removeBoxes(vector<int>& boxes)
    {
        int const n = boxes.size(); //dp[i][j][k] = ans for subarray i -> j where k = num boxes before i w/ color == boxes[i]
        dp = vector<vector<vector<int>>>(n, vector<vector<int>>(n, vector<int>(n, 0)));     

        return rec(boxes, 0, n-1, 0);
    }
};
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