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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h> 

using namespace std; 
using ll = long long;
using ull = unsigned long long;
using pii = pair<int,int>; 

#define INF (INT_MAX)/2-1
#define MOD 1000000007
#define rng(a) a.begin(),a.end()
#define rrng(a) a.rbegin(),a.rend()

int main(){
  int N;
  cin>>N;
  vector<float>A(N);
  for(int i=0;i<N;i++)cin>>A[i];
  sort(rng(A));
  float ans=0;
  float ave;
  float sum=0;
  for(int i=0;i<N;i++)sum+=A[i];
  ave=1.*sum/N;
  for(int i=0;i<N;i++)A[i]=abs(A[i]-ave);
  sort(rng(A));
  ans+=A[0];
  ans+=A[1];
  for(int i=2;i<N;i++)ans+=2*A[i];
  cout<<ans<<endl;
  return 0;
}