<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:
    long long dp[101][101][101];
    long long solve(int i, int j,int cnt,  vector<pair<int, int>>&vec)
    {
        if(i>j) return 0;
        if(i==j) return (vec[i].second+cnt)*1ll*(vec[i].second+cnt);
        if(dp[i][j][cnt]!=-1) return dp[i][j][cnt];
        
       
        long long ans2=(vec[i].second+cnt)*(vec[i].second+cnt)+solve(i+1, j,0,  vec);
        // long long ans3=(vec[j].second)*1ll*(vec[j].second)+solve(i, j-1,0, vec);
        long long ans1=INT_MIN;
        for(int ind=i+1;ind<=j;ind++)
        {
            if(vec[ind].first==vec[i].first)
            {
                    ans1=max(ans1, solve(i+1, ind-1, 0, vec)+solve(ind, j , vec[i].second+cnt, vec));
            }
        }




        return dp[i][j][cnt]= max(ans1, ans2);
    }
    int removeBoxes(vector<int>& boxes) {
       vector<pair<int, int>> vec;
       vec.push_back({boxes[0], 1});
       for(int i=1;i<boxes.size();i++)
       {
        if(vec.back().first==boxes[i]){
            vec.back().second++;

        }
        else{
            vec.push_back({boxes[i], 1});
        }
       }
       memset(dp,-1, sizeof(dp));

       return solve(0, vec.size()-1,0, vec);
        
    }
};
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