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: Time Limit Exceeded)

package main

import (
	"fmt"
	"sort"
)

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

	b := make([]int, 2)
	b[0] = a[0]
	b[1] = a[n-1]
	a = a[1 : n-1]
	var x int
	for i := 1; i < n-1; i++ {
		if i%2 == 1 {
			x = a[0]
			a = a[1:]
		} else {
			x = a[len(a)-1]
			a = a[0 : len(a)-1]
		}

		if abs(b[0]-x) < abs(b[len(b)-1]-x) {
			b = append(b, x)
		} else {
			b = append([]int{x}, b...)
		}
	}

	ans := 0
	for i := 0; i < n-1; i++ {
		ans += abs(b[i] - b[i+1])
	}
	fmt.Println(ans)
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}