<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:
        rle = []
        for num in boxes:
            if rle and rle[-1][0] == num:
                rle[-1][1] += 1
            else:
                rle.append([num, 1])

        @cache
        # := max points you can get between boxes[start:end] 
        # where k boxes before have the same color as start
        def dp(start, end, k): 
            if start >= end: 
                return 0

            num, cnt = rle[start]
            split1 = start + 1
            # remove streak at the beginning and recurse the suffix
            res = dp(split1, end, 0) + (k+cnt)**2 
            for split2 in range(split1, end):
                if rle[split2][0] == num: # find another streak
                    res = max(res, 
                        # try to conjoin the two streaks, but removing everything in between
                        # and dealing with the now combined streak
                        dp(split1, split2, 0) + dp(split2, end, k+cnt)
                    )
            return res

        return dp(0, len(rle), 0)
27000