<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 go(int l, int r, int k, vector<int>& boxes) {
        if(l > r) return 0;
        if(l == r) return k*k;
        int &ans = dp[l][r][k];
        if(ans != -1) return ans;
        ans = 0;
        for(int i = l+1; i <= r; ++i) {
            if(boxes[i] == boxes[l]) {
                ans = max(ans, go(l+1, i-1, 1, boxes) + go(i, r, k+1, boxes));
            }
        }
        ans = max(ans, k*k + go(l+1, r, 1, boxes));
        return ans;
    }
    int removeBoxes(vector<int>& boxes) {
        int n = boxes.size();
        dp.assign(n, vector <vector<int>> (n, vector <int>(n, -1)));
        return go(0, n-1, 1, boxes);
    }
};
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