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;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp4
{
	class Program
	{
		static void Main(string[] args)
		{
			string input1 = Console.ReadLine();
			int n = int.Parse(input1);

			string input2 = Console.ReadLine();
			var a = input2.Split(new char[] { ' ' }).Select(t => int.Parse(t)).OrderBy(t => t).ToArray();

			int minusN = n / 2;
			int plusN = n / 2;

			int minusSum = (-1) * (a.Take(minusN).Sum());
			int plusSum = a.Skip(minusN).Take(plusN).Concat(a.Skip(minusN + plusN)).Sum();

			int m = minusSum + plusSum;

			Console.WriteLine(m);

			var minusQ = new Queue<int>(a.Take(minusN));
			var plusQ = new Queue<int>(a.Skip(minusN).Take(plusN).Concat(a.Skip(minusN + plusN)));
			while (minusQ.Count + plusQ.Count > 1)
			{
				int minus = minusQ.Dequeue();
				int plus = plusQ.Dequeue();
				if ((minusQ.Count + plusQ.Count) % 2 == 0)
				{
					Console.WriteLine($"{plus} {minus}");
					plusQ.Enqueue(plus - minus);
				}
				else
				{
					Console.WriteLine($"{minus} {plus}");
					minusQ.Enqueue(minus - plus);
				}
			}
		}
	}
}