There are 3n piles of coins of varying size, you and your friends will take piles of coins as follows:

• In each step, you will choose any 3 piles of coins (not necessarily consecutive).
• Of your choice, Alice will pick the pile with the maximum number of coins.
• You will pick the next pile with maximum number of coins.
• Your friend Bob will pick the last pile.
• Repeat until there are no more piles of coins.

Given an array of integers piles where piles[i] is the number of coins in the ith pile.

Return the maximum number of coins which you can have.

Example 1:

Input: piles = [2,4,1,2,7,8]
Output: 9
Explanation: Choose the triplet (2, 7, 8), Alice Pick the pile with 8 coins, you the pile with 7 coins and Bob the last one.
Choose the triplet (1, 2, 4), Alice Pick the pile with 4 coins, you the pile with 2 coins and Bob the last one.
The maximum number of coins which you can have are: 7 + 2 = 9.
On the other hand if we choose this arrangement (1, 2, 8), (2, 4, 7) you only get 2 + 4 = 6 coins which is not optimal.


Example 2:

Input: piles = [2,4,5]
Output: 4


Example 3:

Input: piles = [9,8,7,6,5,1,2,3,4]
Output: 18


Constraints:

• 3 <= piles.length <= 10^5
• piles.length % 3 == 0
• 1 <= piles[i] <= 10^4

## Solution: Greedy

Always take the second largest element of a in the sorted array.
[1, 2, 3, 4, 5, 6, 7, 8, 9]
tuples: (1, 8, 9), (2, 6, 7), (3, 4, 5)
Alice: 9, 7, 5
You: 8, 6, 4
Bob: 1, 2, 3

Time complexity: O(nlogn) -> O(n + k)
Space complexity: O(1)

## C++ counting sort

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