<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(101, vector<vector<int>>(101, vector<int>(101, -1)));
    int dp[201][201][201] = {};

    int retAns(vector<int>& boxes, int l, int r, int streak){
        if(l>r)
            return 0;
        if(l==r)
            return (streak+1)*(streak+1);

        if(dp[l][r][streak] != 0)
            return dp[l][r][streak];
    
        int maxi = (streak+1)*(streak+1) + retAns(boxes, l+1, r, 0);

        for(int i = l+1; i<=r; i++){
            if(boxes[i] == boxes[l])
                maxi = max(maxi, retAns(boxes, l+1, i-1, 0) + retAns(boxes, i, r, streak+1));
        }

        dp[l][r][streak] = maxi;
        return maxi;
    }

    int removeBoxes(vector<int>& boxes) {
        return retAns(boxes, 0, boxes.size() - 1, 0);
    }
};
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