<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 
{
private:
    int solve(int l, int r, int size, vector<vector<int>> &groups, vector<vector<vector<int>>> &dp)
    {
        if(l > r)
            return 0;
        if(dp[l][r][size] != -1)
            return dp[l][r][size];
        int curr = groups[l][0], curr_size = groups[l][1];
        dp[l][r][size] = (size + curr_size) * (size + curr_size) + solve(l + 1, r, 0, groups, dp);
        for(int i = l + 1; i <= r; i++)
            if(groups[i][0] == curr)
                dp[l][r][size] = max(dp[l][r][size], solve(l + 1, i - 1, 0, groups, dp) + solve(i, r, curr_size + size, groups, dp));
        return dp[l][r][size];
    }
public:
    int removeBoxes(vector<int>& boxes) 
    {
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
        cout.tie(nullptr);

        vector<vector<int>> groups;
        int curr = boxes[0], size = 0, m = boxes.size();
        for(int i = 0; i < m; i++)
        {
            if(curr == boxes[i])
                size++;
            else
                groups.push_back({boxes[i - 1], size}), size = 1, curr = boxes[i];
        }
        groups.push_back({curr, size});

        int n = groups.size();
        vector<vector<vector<int>>> dp(n, vector<vector<int>> (n, vector<int> (m + 1, -1)));
        return solve(0, n - 1, 0, groups, dp);
    }
};
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