<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 memo[200][200][200] = {};
    int removeBoxes(vector<int>& boxes) {
        return dp(boxes, 0, boxes.size() - 1, 0);
    }
    int dp(vector<int>& boxes, int l, int r, int k) {
        if (l > r) return 0;
        if (memo[l][r][k] > 0) return memo[l][r][k];
        int lOrg = l, kOrg = k;

        while (l+1 <= r && boxes[l] == boxes[l+1]) { // Increase both `l` and `k` if they have consecutive colors with `boxes[l]`
            l += 1;
            k += 1;
        }
        int ans = (k+1) * (k+1) + dp(boxes, l+1, r, 0); // Remove all boxes which has the same with `boxes[l]`
        for (int m = l + 1; m <= r; ++m) // Try to merge non-contiguous boxes of the same color together
            if (boxes[m] == boxes[l])
                ans = max(ans, dp(boxes, m, r, k+1) + dp(boxes, l+1, m-1, 0));
        return memo[lOrg][r][kOrg] = ans;
    }
};
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