<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 maxSizeSlices(vector<int>& slices) 
    {
        #define ll long long
        ll n = slices.size();
        deque<int>dq;
        for(auto it:slices)
        dq.push_back(it);
        int dp[n+5][n/3+5][3];
        memset(dp,-1,sizeof(dp));
        auto f=[&](int idx,int cnt,int zer,auto &&f)->ll
        {
            ll ans=0;
            if(cnt>n/3)
            return -1e7;
            if(idx>=n)
            {
                if(cnt==n/3)
               return 0;

               return -1e7;
            }
            if(dp[idx][cnt][zer] != -1)
            return dp[idx][cnt][zer] ;
           int take =0,nottake=0;
            if(idx==0)
            {
                 take = slices[idx]+f(idx+2,cnt+1,1,f);
            }
            else if(idx==n-1)
            {
                if(zer==0)
                take = slices[idx]+f(idx+2,cnt+1,zer,f);
            }
            else
            {
           take = slices[idx]+f(idx+2,cnt+1,zer,f);
            }
             nottake = f(idx+1,cnt,zer,f);

            return dp[idx][cnt][zer] = max(take,nottake);
        };
        
        ll p = f(0,0,0,f);
       
        cout<<p<<endl;
        return p;
    }
};
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