<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>

long long int dp[501][501/3][2][2];
class Solution {
    long long int solve(int i ,int cnt, int prev ,int first , vector<int> &v) {
        int n = v.size();
        if(i == n) {
            return (cnt == n/3 ? 0 : INT_MIN);
        }
        if(cnt > n/3) return INT_MIN;
        if(dp[i][cnt][prev][first] != -1) return dp[i][cnt][prev][first];
        long long int ans = INT_MIN;
        if(!prev) {
            if(i < n - 1 or (i == n - 1 and first != 1))
                ans = solve(i + 1, cnt + 1 , 1, max(int(!i) , first) , v) + v[i];
        }

        ans = max(ans , solve(i + 1 , cnt , 0 , first , v));
        return dp[i][cnt][prev][first] = ans;
    }
public:
    int maxSizeSlices(vector<int>& slices) {
        memset(dp,-1,sizeof dp);
        return solve(0 ,0,  0 , 0 , slices);
    }
};
13000