<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:
        n = len(boxes)
        
        # Initialize the 3D DP array
        dp = [[[0] * n for _ in range(n)] for _ in range(n)]
        
        def calculatePoints(i, j, k):
            if i > j:
                return 0
            if dp[i][j][k] != 0:
                return dp[i][j][k]
            
            # Start with the current best: removing the current box with the appended boxes
            points = (k + 1) ** 2 + calculatePoints(i, j - 1, 0)
            
            # Try all possible ways to merge the current box with other boxes of the same color
            for m in range(i, j):
                if boxes[m] == boxes[j]:
                    points = max(points, calculatePoints(i, m, k + 1) + calculatePoints(m + 1, j - 1, 0))
            
            dp[i][j][k] = points
            return dp[i][j][k]
        
        return calculatePoints(0, n - 1, 0)

# Example usage:
solution = Solution()
print(solution.removeBoxes([1, 3, 2, 2, 2, 3, 4, 3, 1]))  # Output: 23
print(solution.removeBoxes([1, 1, 1]))  # Output: 9
print(solution.removeBoxes([1]))  # Output: 1
101900