# ---
# title: 1388. Pizza With 3n Slices
# id: problem1388
# author: Tian Jun
# date: 2020-10-31
# difficulty: Hard
# categories: Dynamic Programming
# link: <https://leetcode.com/problems/pizza-with-3n-slices/description/>
# hidden: true
# ---
# 
# There is a pizza with 3n slices of varying size, you and your friends will
# take slices of pizza as follows:
# 
#   * You will pick **any** pizza slice.
#   * Your friend Alice will pick next slice in anti clockwise direction of your pick. 
#   * Your friend Bob will pick next slice in clockwise direction of your pick.
#   * Repeat until there are no more slices of pizzas.
# 
# Sizes of Pizza slices is represented by circular array `slices` in clockwise
# direction.
# 
# Return the maximum possible sum of slice sizes which you can have.
# 
# 
# 
# **Example 1:**
# 
# ![](https://assets.leetcode.com/uploads/2020/02/18/sample_3_1723.png)
# 
#     
#     
#     Input: slices = [1,2,3,4,5,6]
#     Output: 10
#     Explanation: 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.
#     
# 
# **Example 2:**
# 
# **![](https://assets.leetcode.com/uploads/2020/02/18/sample_4_1723.png)**
# 
#     
#     
#     Input: slices = [8,9,8,6,1,1]
#     Output: 16
#     Output: Pick pizza slice of size 8 in each turn. If you pick slice with size 9 your partners will pick slices of size 8.
#     
# 
# **Example 3:**
# 
#     
#     
#     Input: slices = [4,1,2,5,8,3,1,9,7]
#     Output: 21
#     
# 
# **Example 4:**
# 
#     
#     
#     Input: slices = [3,1,2]
#     Output: 3
#     
# 
# 
# 
# **Constraints:**
# 
#   * `1 <= slices.length <= 500`
#   * `slices.length % 3 == 0`
#   * `1 <= slices[i] <= 1000`
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
