<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) {
        int n = slices.size();
        vector<vector<int>> dp1(slices.size()-1,vector<int> ((n/3),INT_MIN));
        dp1[0][0] = slices[1];
        dp1[1][0] = slices[2];
        for(int i=3;i<n;i++){
            dp1[i-1][0] = slices[i];
            for(int j=1;j<n/3;j++){
                int ans = INT_MIN;
                for(int k=1;k<i-1;k++){
                    ans = max(dp1[k-1][j-1], ans);
                }
                if(ans==INT_MIN){
                    dp1[i-1][j] = INT_MIN;
                }
                else{
                    dp1[i-1][j] = ans + slices[i];
                }
            }
        }
        int res = INT_MIN;
        for(int i=0;i<n-1;i++){
            res = max(dp1[i][(n/3)-1], res);
        }

        vector<vector<int>> dp2(slices.size()-1,vector<int> ((n/3),INT_MIN));
        dp2[0][0] = slices[0];
        dp2[1][0] = slices[1];
        for(int i=2;i<n-1;i++){
            dp2[i][0] = slices[i];
            for(int j=1;j<n/3;j++){
                int ans = INT_MIN;
                for(int k=0;k<i-1;k++){
                    ans = max(dp2[k][j-1], ans);
                }
                if(ans==INT_MIN){
                    dp2[i][j] = INT_MIN;
                }
                else{
                    dp2[i][j] = ans + slices[i];
                }
            }
        }
        for(int i=0;i<n-1;i++){
            res = max(dp2[i][(n/3)-1], res);
        }
        return res;
    }
};
16400