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++ (GCC 9.2.1) (judge verdict: Wrong Answer)


#include <stdio.h>
#include <string.h>
#include <limits.h>
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <map>
#include <set>
#include <stack>
#include <queue>

typedef unsigned long long ULLONG;
typedef long long LLONG;
static const LLONG MOD_NUM = 1000000007;

template<class _T> static void getint(_T& a) {
	std::cin >> a;
}
template<class _T> static void getint(_T& a, _T& b) {
	std::cin >> a >> b;
}
template<class _T> static void getint(_T& a, _T& b, _T& c) {
	std::cin >> a >> b >> c;
}
template <class _T> static _T tp_abs(_T a) {
	if (a < (_T)0) {
		a *= (_T)-1;
	}
	return a;
}

static void solve();

int main()
{
	solve();
	fflush(stdout);
	return 0;
}

static void solve()
{
	int N;
	getint(N);

	std::vector<LLONG> ai(N);
	for (int i = 0; i < N; i++) {
		getint(ai[i]);
	}
	std::sort(ai.begin(), ai.end());
	
	std::deque<LLONG> bi;
	bi.push_back(ai[0]);
	int start = 1;
	int end = N - 1;
	bool top = false;
	while (start <= end) {
		LLONG val = 0;
		if (top) {
			val = ai[start];
			start++;
			top = false;
		}
		else {
			val = ai[end];
			end--;
			top = true;
		}
		LLONG diff = tp_abs(bi.front() - val);
		if (diff < tp_abs(bi.back() - val)) {
			bi.push_back(val);
		}
		else {
			bi.push_front(val);
		}
	}

	LLONG ans = 0;
	LLONG bfr = bi.front(); bi.pop_front();
	for (int i = 1; i < N; i++) {
		ans += tp_abs(bi.front() - bfr);
		bfr = bi.front();
		bi.pop_front();
	}
	printf("%lld\n", ans);
}