Problem:
Score : 500 points

Problem Statement

There are N integers, A_1, A_2, ..., A_N, written on a blackboard.

We will repeat the following operation N-1 times so that we have only one integer on the blackboard.

Choose two integers x and y on the blackboard and erase these two integers. Then, write a new integer x-y.

Find the maximum possible value of the final integer on the blackboard and a sequence of operations that maximizes the final integer.

Constraints

2 \leq N \leq 10^5

-10^4 \leq A_i \leq 10^4

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible value M of the final integer on the blackboard, and a sequence of operations x_i, y_i that maximizes the final integer, in the format below.

Here x_i and y_i represent the integers x and y chosen in the i-th operation, respectively.

If there are multiple sequences of operations that maximize the final integer, any of them will be accepted.

M
x_1 y_1
:
x_{N-1} y_{N-1}

Sample Input 1

3
1 -1 2

Sample Output 1

4
-1 1
2 -2

If we choose x = -1 and y = 1 in the first operation, the set of integers written on the blackboard becomes (-2, 2).

Then, if we choose x = 2 and y = -2 in the second operation, the set of integers written on the blackboard becomes (4).

In this case, we have 4 as the final integer. We cannot end with a greater integer, so the answer is 4.

Sample Input 2

3
1 1 1

Sample Output 2

1
1 1
1 0

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		var A = new List<long>();
		string[] str = Console.ReadLine().Split();
		for(var i=0;i<N;i++){
			A.Add(long.Parse(str[i]));
		}
		A.Sort((x,y)=>x.CompareTo(y));
		long ans = 0;
		var list = new List<long[]>();
		while(N>=2){
			int f = 0;
			if(N>=3){
				if(N%2==0){
					if(Math.Abs(A[N/2])>Math.Abs(A[N/2+1])){
						if(A[N/2]>0){
							f = 1;
						} else {
							f = -1;
						}
					} else {
						if(A[N/2+1]>0){
							f = 1;
						} else {
							f = -1;
						}
					}
				} else if(A[N/2]>0){
					f = 1;
				} else {
					f = -1;
				}
				if(f==1){
					long a = A[0]-A[N-1];
	                list.Add(new long[2]{A[0],A[N-1]});
					A.RemoveAt(N-1);
					A[0] = a;
				} else {
					long a = A[N-1]-A[0];
	                list.Add(new long[2]{A[N-1],A[0]});
					A.RemoveAt(0);
					A[N-2] = a;
				}
				N--;
			} else {
				ans = A[1]-A[0];
				list.Add(new long[2]{A[1],A[0]});
				N--;
			}
		}
		Console.WriteLine(ans);
		for(var i=0;i<list.Count;i++){
			Console.WriteLine(list[i][0]+" "+list[i][1]);
		}
	}
}