<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 fun(int ind, int left , vector<int>&nums){
        if(ind >=  nums.size() ) return  0 ; 
        if(dp[ind][left]!=-1) return dp[ind][left] ; 
        if(left == 0 ) return  0 ; 
        int take = nums[ind] +  fun(ind+2 , left-1,  nums) ; 
        int notake =  fun(ind+1 ,  left ,  nums)  ;
            return dp[ind][left] =  max(take,  notake) ; 
    }
    int maxSizeSlices(vector<int>& nums) {
       /*
       take alternate wise then all of them will arrange and would be taken by rest of them 
       */  
       vector<int>temp1, temp2  ;
       for(int  i = 0 ; i <nums.size() ; i ++ ) { 
        if(i!=0)  temp1.push_back(nums[i]) ; 
        if(i!= nums.size()-1)  temp2.push_back(nums[i]) ; 
       }
       memset(dp,-1,sizeof dp) ; 
       int ans =  fun(0 ,  nums.size()/3 ,  temp1) ;
       memset(dp,-1,sizeof dp) ; 
        ans =  max(ans, fun(0 , nums.size()/3 ,  temp2)) ; 
       return ans ; 

       
    }
};
11700