<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 {
    int dp[1502][502];
    int helper(int i,int size,int slice,vector<int>& slices)
    {
        //base case
        if(i>=size) return 0;
        //pruning
        if(slice<=0) return 0;
        //cache check
        if(dp[i][slice]!=-1) return dp[i][slice];
        //variable
        int take=0,not_take=0;
        //case
        not_take=helper(i+1,size,slice,slices);
        take=slices[i]+helper(i+2,size,slice-1,slices);
        
        //return possible ans and save cache
        return dp[i][slice]=max(take,not_take);
    }
public:
    int maxSizeSlices(vector<int>& slices) 
    {
        int size=slices.size();
        memset(dp,-1,sizeof(dp));
        int lastremove=helper(0,size-1,(size/3),slices);
        memset(dp,-1,sizeof(dp));
        int lasttaken=helper(1,size,(size/3),slices);
        //return helper(0,size-1,size/3,slices);
        return max(lastremove,lasttaken);

    }
};
13700