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 <iostream>
#include <deque>
#include <map>
#include <algorithm>
#include <cmath>
#include <string>
using namespace std;


int main(){
  int N,a,ab,af,sb,sf;
  deque<int> A,S;
  multimap<int,string> list;
  cin >> N;
  for(int i=0;i<N;i++){
    cin >> a;
    A.push_back(a);
  }
  sort(A.begin(),A.end());
  S.push_back(A.back());
  A.pop_back();
  int ans=0;
  while(!A.empty()){
    list.clear();
    ab=A.back();
    af=A.front();
    sf=S.front();
    sb=S.back();
    list.emplace(abs(ab-sb),"back_back");
    list.emplace(abs(ab-sf),"back_front");
    list.emplace(abs(af-sb),"front_back");
    list.emplace(abs(af-sf),"front_front");
    auto itr = list.rbegin();
    ans += itr->first;
    if(itr->second=="back_back"){
      A.pop_back();
      S.push_back(ab);
    }else if(itr->second=="back_front"){
      A.pop_back();
      S.push_front(ab);
    }else if(itr->second=="front_back"){
      A.pop_front();
      S.push_back(af);
    }else if(itr->second=="front_front"){
      A.pop_front();
      S.push_front(af);
    }else{
      cout << "ouch" <<endl;
    }
  }
      

//  for(auto itr = S.begin();itr!=S.end();++itr)
//    cout << *itr << " ";
//  cout << endl;
  cout << ans << endl;
}