Problem:
Score : 400 points

Problem Statement

You are given N integers; the i-th of them is A_i.
Find the maximum possible sum of the absolute differences between the adjacent elements after arranging these integers in a row in any order you like.

Constraints

2 \leq N \leq 10^5

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the maximum possible sum of the absolute differences between the adjacent elements after arranging the given integers in a row in any order you like.

Sample Input 1

5
6
8
1
2
3

Sample Output 1

21

When the integers are arranged as 3,8,1,6,2, the sum of the absolute differences between the adjacent elements is |3 - 8| + |8 - 1| + |1 - 6| + |6 - 2| = 21. This is the maximum possible sum.

Sample Input 2

6
3
1
4
1
5
9

Sample Output 2

25

Sample Input 3

3
5
5
1

Sample Output 3

8

Solution in Go (1.6) (judge verdict: Accepted)

package main

import (
	"fmt"
	"sort"
)

const inf = 1 << 60

func intsSum(a []int) int {
	res := 0
	for _, v := range a {
		res += v
	}
	return res
}

func chmax(a *int, b int) {
	if *a < b {
		*a = b
	}
}

func main() {
	var n int
	fmt.Scan(&n)
	as := make([]int, n)
	for i := 0; i < n; i++ {
		fmt.Scan(&as[i])
	}
	sort.Ints(as)

	if n%2 == 0 {
		s := as[:n/2]
		l := as[n/2:]
		ans := (2*intsSum(l) - l[0]) - (2*intsSum(s) - s[len(s)-1])
		fmt.Println(ans)
	} else {
		ans := -inf
		{
			s := as[:n/2]
			l := as[n/2:]
			chmax(&ans, 2*intsSum(l)-l[0]-l[1]-2*intsSum(s))
		}
		{
			s := as[:(n+1)/2]
			l := as[(n+1)/2:]
			chmax(&ans, 2*intsSum(l)-(2*intsSum(s)-s[len(s)-1]-s[len(s)-2]))
		}
		fmt.Println(ans)
	}
}