<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>

from typing import List

class Solution:
    def removeBoxes(self, boxes: List[int]) -> int:
        def dp(l, r, k):
            if l > r: 
                return 0
            if memo[l][r][k] != -1:
                return memo[l][r][k]
            
            # When removing the leftmost box and any additional boxes of the same color
            orig_l, orig_k = l, k
            while l+1 <= r and boxes[l+1] == boxes[orig_l]: 
                l += 1  # Skip all boxes with the same color
                k += 1
            result = (k + 1) ** 2 + dp(l + 1, r, 0)

            # Try to merge non-contiguous blocks with the same color
            for i in range(l + 1, r + 1):
                if boxes[i] == boxes[orig_l]:
                    result = max(result, dp(l + 1, i - 1, 0) + dp(i, r, k + 1))
            
            memo[orig_l][r][orig_k] = result
            return result
        
        n = len(boxes)
        memo = [[[-1] * (n+1) for _ in range(n)] for _ in range(n)]
        return dp(0, n - 1, 0)

# Example usage: 
# solution = Solution()
# print(solution.removeBoxes([1,3,2,2,2,3,4,3,1]))
97300