<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) -> None:
        self.freq: list[int] = list() 
        self.boxes: list[int] = list()

    def __removeDuplicates(self, boxes: list[int]) -> None:
        i = 0
        while i < len(boxes):
            self.boxes.append(boxes[i])
            self.freq.append(1)
            while i+1 < len(boxes) and boxes[i] == boxes[i+1]:
                self.freq[-1] += 1
                i += 1
            i += 1
        return 

    def __removeIt(self, left: int, right: int, count: int, dp:dict[tuple[int, int, int], int]) -> int:
        if left >= right: return 0
        if (left, right, count) in dp: return dp[(left, right, count)]
                
        maxPoints = (count+self.freq[left])**2 + self.__removeIt(left+1, right, 0, dp)
        for i in range(left+1, right):
            if self.boxes[left] == self.boxes[i]:
                maxPoints = max(maxPoints, self.__removeIt(left+1, i, 0, dp) + self.__removeIt(i, right, count+self.freq[left], dp))
        
        dp[(left, right, count)] = maxPoints
        return maxPoints

    def removeBoxes(self, boxes: List[int]) -> int:
        self.__removeDuplicates(boxes)
        return self.__removeIt(0, len(self.boxes), 0, {})
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