<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 f(int i,int j,int aage,vector<pair<int,int>> &nums,vector<vector<vector<int>>> &dp){
        if(i>j){
            return 0;
        }
        if(dp[i][j][aage]!=-1){
            return dp[i][j][aage];
        }
        int count = (aage + nums[i].second)*1LL*(aage + nums[i].second);
        int ans = count + f(i+1,j,0,nums,dp);
        for(int ind = i+1 ;ind<=j;ind++){
            if(nums[ind].first == nums[i].first){
                ans = max(ans,f(i+1,ind-1,0,nums,dp) + f(ind,j,aage+nums[i].second,nums,dp));
            }
        }
        return dp[i][j][aage] = ans;
    }
    int removeBoxes(vector<int>& boxes) {
       int n = boxes.size();
       vector<pair<int,int>> nums;
       int i=0;
       while(i<n){
            int  x = boxes[i];
            int c=0;
            while(i<n && boxes[i]==x){
                i++;
                c++;
            }
            nums.push_back({x,c});
        } 
        vector<vector<vector<int>>> dp(nums.size()+1,vector<vector<int>>(nums.size()+1,vector<int>(102,-1)));
        return f(0,nums.size()-1,0,nums,dp);
    }
};
53436