<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 __init__(self):
        self.colors = []
        self.counts = []

    def removeBoxes(self, boxes: List[int]) -> int:
        pre_color = boxes[0]
        pre_count = 1

        for box in boxes[1:]:
            if box == pre_color:
                pre_count += 1
            else:
                self.colors.append(pre_color)
                self.counts.append(pre_count)
                pre_color = box
                pre_count = 1
        self.colors.append(pre_color)
        self.counts.append(pre_count)

        return self.dfs(0, len(self.colors) - 1, 0)

    @lru_cache(None)
    def dfs(self, start, end, pre_sum) -> int:
        if start == end:
            return (self.counts[start] + pre_sum) * (self.counts[start] + pre_sum)

        cur_pre_sum = self.counts[start] + pre_sum
        res = cur_pre_sum * cur_pre_sum + self.dfs(start + 1, end, 0)

        for i in range(start + 2, end + 1):
            if self.colors[i] != self.colors[start]:
                continue

            cur_res = self.dfs(start + 1, i - 1, 0) + self.dfs(i, end, cur_pre_sum)
            res = max(res, cur_res)

        return res
33900