<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 functools import cache

class Solution:
    def removeBoxes(self, boxes: List[int]) -> int:
        @cache
        def calc(lo: int, hi: int, prev_lo_s: int) -> int:
            if lo > hi:
                return 0
            lo1 = lo + 1
            lo_col = cols[lo]
            return max(
                (new_lo_s := prev_lo_s + sizes[lo]) ** 2 +
                calc(lo1, hi, 0),  # without merge
                max((calc(lo1, j - 1, 0) + calc(j, hi, new_lo_s)
                     for j in range(lo1, hi + 1)
                     if cols[j] == lo_col), default=0))  # best merge

        nb = len(boxes)
        cols = []  # colors of consecutive same-color box groups
        sizes = []  # sizes of consecutive same-color box groups
        cur = boxes[0]
        cur_start = 0
        i = 1
        while True:
            while i < nb and boxes[i] == cur:
                i += 1
            cols.append(cur)
            sizes.append(i - cur_start)
            if i == nb:
                break
            cur = boxes[i]
            cur_start = i
        return calc(0, len(cols) - 1, 0)
26700