<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:
    unordered_map<string,int> mp;

    int f(int l,int r,int extra,vector<int>& boxes){
        if(l>r) return 0;
        string s=to_string(l)+" "+to_string(r)+" "+to_string(extra);
        if(mp.find(s)!=mp.end()) return mp[s];
        while(l<r && boxes[l]==boxes[l+1]){
            l++;
            extra++;
        }
        int res=(extra+1)*(extra+1)+f(l+1,r,0,boxes);
        for(int i=l+1;i<=r;i++){
            if(boxes[i]==boxes[l]){
                res=max(res,f(l+1,i-1,0,boxes)+f(i,r,extra+1,boxes));
            }
        }
        return mp[s]=res;
    }

    int removeBoxes(vector<int>& boxes) {
        mp.clear();
        int n=boxes.size()-1;
        return f(0,n,0,boxes);
    }
};
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