<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:
        # 2, 1, 3, 2
        # 1, 3, 2 --> 1
        # 3, 2 --> 1
        # 2 --> 1
        # '' --> 1

        # 2, 3, 2 -> 1
        # 3, 2 --> 1
        # 2 --> 1
        # '' --> 1
        # 1 3 3 1 3

        # f(n) = f(n - k) + k * k
        
        # 1 1 2 3 1 3 2


        def dfs(left, right, k ,boxes, memo):
            if left == right:
                return 0

            left_box = boxes[left]

            while left < right and left_box == boxes[left]:
                left += 1
                k += 1
            
            if memo[left][right][k] != -1:
                return memo[left][right][k]
            
            ans = k*k + dfs(left, right, 0, boxes, memo)
            for index in range(left, right):
                if boxes[index] == left_box:
                    ans = max(ans, dfs(left, index, 0, boxes, memo) + dfs(index, right, k, boxes, memo))
            
            memo[left][right][k] = ans
            return ans
        
        memo =[[[-1 for _ in range(len(boxes) + 1)] for _ in range(len(boxes) + 1)] for _ in range(len(boxes) + 1)]
        return dfs(0, len(boxes), 0, boxes, memo)
        



        

27900