<p>There is a pizza with <code>3n</code> slices of varying size, you and your friends will take slices of pizza as follows:</p>

<ul>
	<li>You will pick <strong>any</strong> pizza slice.</li>
	<li>Your friend Alice will pick the next slice in the anti-clockwise direction of your pick.</li>
	<li>Your friend Bob will pick the next slice in the clockwise direction of your pick.</li>
	<li>Repeat until there are no more slices of pizzas.</li>
</ul>

<p>Given an integer array <code>slices</code> that represent the sizes of the pizza slices in a clockwise direction, return <em>the maximum possible sum of slice sizes that you can pick</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/02/18/sample_3_1723.png" style="width: 500px; height: 266px;" />
<pre>
<strong>Input:</strong> slices = [1,2,3,4,5,6]
<strong>Output:</strong> 10
<strong>Explanation:</strong> Pick pizza slice of size 4, Alice and Bob will pick slices with size 3 and 5 respectively. Then Pick slices with size 6, finally Alice and Bob will pick slice of size 2 and 1 respectively. Total = 4 + 6.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/02/18/sample_4_1723.png" style="width: 500px; height: 299px;" />
<pre>
<strong>Input:</strong> slices = [8,9,8,6,1,1]
<strong>Output:</strong> 16
<strong>Explanation:</strong> Pick pizza slice of size 8 in each turn. If you pick slice with size 9 your partners will pick slices of size 8.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>3 * n == slices.length</code></li>
	<li><code>1 &lt;= slices.length &lt;= 500</code></li>
	<li><code>1 &lt;= slices[i] &lt;= 1000</code></li>
</ul>

class Solution {
public:
    int dp[501][501];
    int give(int i,int curr,vector<int> &s,int req){
        if(i>=s.size()){
            if(curr==req){
                return 0;
            }
            return -1e5;

        }
        if(dp[i][curr]!=-1){
            return dp[i][curr];
        }
        int no_take=give(i+1,curr,s,req);
        int take=-1e5;
        if(curr<req){

            take=s[i]+give(i+2,curr+1,s,req);

        }
        return dp[i][curr]=max(take,no_take);
        
    }
    int maxSizeSlices(vector<int>& slices) {
        int n=slices.size();
        vector<int> s1; vector<int> s2;
        for(int i=0;i<n-1;i++){
            s1.push_back(slices[i]);
        }
         for(int i=1;i<n;i++){
            s2.push_back(slices[i]);
        }
        memset(dp,-1,sizeof(dp));
        int maxi1=give(0,0,s1,n/3);
         memset(dp,-1,sizeof(dp));
        int maxi2=give(0,0,s2,n/3);
        return max(maxi1,maxi2);

        
    }
};
11800