<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 fun(int l, int r, int extra, vector<pair<int, int>>& groups, vector<vector<vector<int>>> &dp){
        if(l>r){
            return 0;
        }
        if(dp[l][r][extra] != -1){
            return dp[l][r][extra];
        }

        int ans= pow(groups[l].first + extra, 2) + fun(l+1, r, 0, groups, dp);
        for(int i=l+1; i<=r; i++){
            if(groups[i].second == groups[l].second){
                ans = max(ans, fun(l+1, i-1, 0, groups, dp) + fun(i, r, extra + groups[l].first, groups, dp));
            }
        }
        return dp[l][r][extra]= ans;
    }

    int removeBoxes(vector<int>& boxes) {
        int i=0, j=0, n=boxes.size();
        vector<pair<int, int>> groups;

        while (j < n){
            i = j;
            while (j < n && boxes[j] == boxes[i]) {
                j++;
            }
            groups.push_back({j - i, boxes[i]});
        }
        int m= groups.size();
        
        vector<vector<vector<int>>> dp(m, vector<vector<int>>(m, vector<int>(101, -1)));
        return fun(0, m-1, 0, groups, dp);

    }
};
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