<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:
        n = len(boxes)
        # dp[start][end][sameCount] 表示在区间 [start, end]，前面有 sameCount 个和 boxes[start] 颜色相同的盒子的情况下能获得的最大分数
        dp = [[[0] * n for _ in range(n)] for _ in range(n)]

        # 初始化单个盒子的分数
        for end in range(n):
            for sameCount in range(end + 1):
                dp[end][end][sameCount] = (sameCount + 1) * (sameCount + 1)

        # 开始动态规划的填充过程
        for length in range(1, n):  # 区间长度
            for end in range(length, n):
                start = end - length  # 区间起始点

                for sameCount in range(start + 1):  # sameCount 是表示有多少个相同的盒子在 start 的左边
                    # 先假设直接移除 start 位置的盒子及其前面的相同颜色的盒子
                    maxScore = (sameCount + 1) * (sameCount + 1) + dp[start + 1][end][0]

                    # 尝试将和 start 颜色相同的盒子合并在一起，提高分数
                    for mid in range(start + 1, end + 1):
                        if boxes[mid] == boxes[start]:
                            maxScore = max(maxScore, dp[start + 1][mid - 1][0] + dp[mid][end][sameCount + 1])

                    dp[start][end][sameCount] = maxScore

        # 返回移除整个序列的最大得分
        return dp[0][n - 1][0] if n > 0 else 0
30000