You have an array of floating point numbers averages which is initially empty. You are given an array nums of n integers where n is even.

You repeat the following procedure n / 2 times:

Return the minimum element in averages.

 

Example 1:

Input: nums = [7,8,3,4,15,13,4,1]

Output: 5.5

Explanation:

step nums averages
0 [7,8,3,4,15,13,4,1] []
1 [7,8,3,4,13,4] [8]
2 [7,8,4,4] [8,8]
3 [7,4] [8,8,6]
4 [] [8,8,6,5.5]
The smallest element of averages, 5.5, is returned.

Example 2:

Input: nums = [1,9,8,3,10,5]

Output: 5.5

Explanation:

step nums averages
0 [1,9,8,3,10,5] []
1 [9,8,3,5] [5.5]
2 [8,5] [5.5,6]
3 [] [5.5,6,6.5]

Example 3:

Input: nums = [1,2,3,7,8,9]

Output: 5.0

Explanation:

step nums averages
0 [1,2,3,7,8,9] []
1 [2,3,7,8] [5]
2 [3,7] [5,5]
3 [] [5,5,5]

 

Constraints: