<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 removeBoxes(vector<int>& boxes) {
        int n = boxes.size();
        vector<vector<vector<int>>> dp(n, vector<vector<int>>(n, vector<int>(n, 0)));
        
        // Helper function to calculate dp[l][r][k]
        function<int(int, int, int)> dfs = [&](int l, int r, int k) -> int {
            if (l > r) return 0;
            if (dp[l][r][k] > 0) return dp[l][r][k];
            
            int maxPoints = (k + 1) * (k + 1) + dfs(l, r - 1, 0);
            for (int i = l; i < r; ++i) {
                if (boxes[i] == boxes[r]) {
                    maxPoints = max(maxPoints, dfs(l, i, k + 1) + dfs(i + 1, r - 1, 0));
                }
            }
            
            dp[l][r][k] = maxPoints;
            return maxPoints;
        };
        
        return dfs(0, n - 1, 0);
    }
};

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