<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 {
public:
    int removeBoxes(vector<int>& boxes) {
        unordered_map<int, int> pos;
        int n = boxes.size();
        vector<int> right(n, n);
        for(int i = n - 1; i >= 0; --i) {
            if (pos.find(boxes[i]) != pos.end()) {
                right[i] = pos[boxes[i]];
            }
            pos[boxes[i]] = i;
        }
        vector<vector<vector<int>>> memo(n+1, vector<vector<int>>(n+1, vector<int>(n+1, -1)));
        auto dfs = [&] (auto& dfs, int l, int r, int presame) {
            if (l > r) return presame * presame;
            if (memo[presame][l][r] != -1) return memo[presame][l][r];

            int res = presame * presame;
            int i = l;
            while(i + 1 <= r && boxes[i] == boxes[i+1]) i++;
            res = max(res, (presame + i-l+1) * (presame + i - l + 1) + dfs(dfs, i+1, r, 0));
            int nexti = right[i];
            while(nexti <= r) {
                res = max(res, dfs(dfs, i+1, nexti-1, 0) + dfs(dfs, nexti, r, presame+i-l+1));
                nexti = right[nexti];
            }
            return memo[presame][l][r] = res;
        };
        return dfs(dfs, 0, n-1, 0);
    }
};
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