<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:
        self.counts = []
        self.colors = []
        tcol = boxes[0]
        tcnt = 0
        for c in boxes:
            if tcol == c:
                tcnt += 1
            else:
                self.proc(tcol,tcnt)
                tcol = c
                tcnt = 1
        self.proc(tcol,tcnt)
        @cache
        def search(i,j,k):
            if i > j:
                return 0
            if i == j:
                return (k + self.counts[i])**2
            opts = []
            opts.append(search(i+1, j, 0) + (self.counts[i] + k)**2)
            for m in range(i+2, j+1):
                if self.colors[m] == self.colors[i]:
                    opts.append(search(i+1, m-1, 0) + search(m, j, k+self.counts[i]))
            return max(opts)
        return search(0,len(self.colors)-1,0)
    def proc(self,col,cnt):
        self.counts.append(cnt)
        self.colors.append(col)
        return
26600