<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:
    def removeBoxes(self, boxes: List[int]) -> int:
        # return self.max_points_memoize(boxes)
        return self.max_points_bottom_up(boxes)

    

    def max_points_bottom_up(self, boxes):
        n = len(boxes)
        dp = [[[0 for _ in range(n)] for _ in range(n)] for _ in range(n)]

        for i in range(n - 1, -1, -1):
            for j in range(i, n):
                # k can go in this range, if our left range is i and k means the same boxes seen BEFORE index i
                # so we can count from 0,1,2,...i. So eg if i = 4, we count 0,1,2,3 = 4 count. This is before counting index 4
                # so basically k can go from 0 to i (inclusive)
                for k in range(i + 1): 
                    # if i == j:
                    #     dp[i][j][k] = (k + 1) * (k + 1)
                    #     continue

                    # max_points = 0
                    # if i + 1 <= j:
                    max_points = (k + 1) * (k + 1) + dp[i + 1][j][0] if i + 1 <= j else (k + 1) * (k + 1)
                    # else:
                    #     max_points = (k + 1) * (k + 1)

                    for partition in range(i + 1, j + 1):
                        if boxes[i] == boxes[partition]:
                            # print(i, j, k+1)
                            max_points = max(max_points, dp[partition][j][k + 1] + dp[i + 1][partition - 1][0])

                    dp[i][j][k] = max_points

        # print(dp)
        return dp[0][n - 1][0]
30500