<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>

def solve(i, j, k, dp, boxes):
    if i > j: return 0
    if dp[i][j][k] > 0: return dp[i][j][k]

    _i, _k = i, k
    while i + 1 <= j and boxes[i+1] == boxes[i]:
        i += 1 
        k += 1
    
    result = (k+1)**2 + solve(i+1, j, 0, dp, boxes)

    for m in range(i+1, j+1):
        if boxes[i] == boxes[m]:
            result = max(result, solve(i+1, m-1, 0, dp, boxes) + solve(m, j, k+1, dp, boxes))
    
    dp[_i][j][_k] = result
    return result


class Solution:
    def removeBoxes(self, boxes: List[int]) -> int:
        n = len(boxes)
        dp = [[[0] * n for _ in range(n)] for _ in range(n)]

        return solve(0, n-1, 0, dp, boxes)
27100