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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Linq;
using static MyIO;


public class C
{
	public static void Main()
	{
		int N = GetInt();
		int[] A = new int[N];
		for(int i = 0; i < N; i++)
			A[i] = GetInt();

		int min = A[0];
		int max = A[0];
		int iMin = 0;
		int iMax = 1;
		for(int i = 1; i < N; i++)
		{
			if(A[i] < min)
			{
				min = A[i];
				iMin = i;
			}
			if(A[i] > max)
			{
				max = A[i];
				iMax = i;
			}
		}

		StringBuilder sb = new StringBuilder();
		int num = min;
		for(int i = 0; i < N; i++)
		{
			if((i == iMin) || (i == iMax) || (A[i] < 0))
				continue;

			sb.AppendFormat($"{num} {A[i]}\n");
			num = num - A[i];
		}

		sb.AppendFormat($"{max} {num}\n");
		num = max - num;

		for(int i = 0; i < N; i++)
		{
			if((i == iMin) || (i == iMax) || (A[i] >= 0))
				continue;

			sb.AppendFormat($"{num} {A[i]}\n");
			num = num - A[i];
		}

		Console.WriteLine(num);
		Console.Write(sb);
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt(){ return int.Parse(getArg()); }
	public static long GetLong(){ return long.Parse(getArg()); }
	public static double GetDouble(){ return double.Parse(getArg()); }
	public static string GetString(){ return getArg(); }
}