<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
from itertools import groupby

class Solution:
    def removeBoxes(self, boxes: List[int]) -> int:
        n = len(boxes)
        gp = tuple((k, len(tuple(v))) for k, v in groupby(boxes))
        ngp = len(gp)
        @cache
        def dp(i, j, k):
            if i > j:
                return 0
            p = (k + gp[i][1]) ** 2 + dp(i + 1, j, 0)
            for m in range(i + 1, j + 1):
                if gp[m][0] == gp[i][0]:
                    p = max(
                        p,
                        dp(i + 1, m - 1, 0) + dp(m, j, k + gp[i][1])
                    )
            return p
        return dp(0, ngp - 1, 0)
26900