<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:
    typedef long long ll;
    map<int,int> mp;
    ll t[101][101][101];
    ll solve(vector<int> &groups,int i,int j,int extra){
        if(i > j) return 0;

        if(t[i][j][extra] != -1)
        return t[i][j][extra];

        ll ans =  (groups[i]+extra)*(groups[i]+extra) + solve(groups,i+1,j,0); 

        for(int k = i+1;k<=j;k++){
            if(mp[k] == mp[i]){
                ans = max(ans,solve(groups,i+1,k-1,0)+ solve(groups,k,j,extra+groups[i]));
            }
        }
        return t[i][j][extra] =  ans;
    }

    int removeBoxes(vector<int>& boxes) {
        int n = boxes.size();
        vector<int> groups;
        memset(t,-1,sizeof(t));
        mp.clear();
        int j = 0;
        for(int i = 0;i<n;i++){
            if(i == 0)
            j++;
            else{
                if(boxes[i] == boxes[i-1]){
                    j++;
                }
                else{
                    groups.push_back(j);
                    mp[groups.size()-1] = boxes[i-1];
                    j = 1;
                }
            }
        }
         groups.push_back(j);
         mp[groups.size()-1] = boxes[n-1];
        for(int i = 0;i<groups.size();i++){
            // cout << mp[i] << " " << groups[i];
             cout << groups[i] << " ";
        }
        cout << endl;
        for(int i = 0;i<groups.size();i++){
            // cout << mp[i] << " " << groups[i];
             cout << mp[i] << " ";
        }

        return solve(groups,0,groups.size()-1,0);

    }
};
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