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.Text;
using System.Collections.Generic;
using System.ComponentModel;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
class Program
{
    static void Main(string[] args)
    {
		int N = int.Parse(Console.ReadLine());
		int[] A = new int[N];
		string[] input = Console.ReadLine().Split(' ');
        for(int i = 0; i < N; i++)
		{
			A[i] = int.Parse(input[i]);
		}

		List<int> x = new List<int>();
		List<int> y = new List<int>();
		List<Tuple<int,int>> ans = new List<Tuple<int,int>>();
        for(int i = 0; i < N; i++)
		{
			if (A[i] >= 0)
			{
				x.Add(A[i]);
			}else { y.Add(A[i]); }
		}
		
		x.Sort();
		x.Reverse();
		y.Sort();
		int X;
		int Y;

		if (y.Count == 0)
		{
			int c = x.Count - 1;
			X = x[c];
			Y = x[0];
			while (x.Count > 0)
			{



				ans.Add(new Tuple<int, int>(Y, x[0]));
				Y = Y - x[0];
				x.RemoveAt(0);
			}
			int final = X - Y;
			ans.Add(new Tuple<int, int>(X, Y));

			Console.WriteLine(final);
			for (int i = 0; i < ans.Count; i++)
			{
				Console.WriteLine("{0}" + " " + "{1}", ans[i].Item1, ans[i].Item2);
			}
		}
		else if (x.Count == 0)
		{
			 X = y[0];
			y.RemoveAt(0);
			while (y.Count > 0)
			{
				ans.Add(new Tuple<int, int>(X, y[0]));
				X = X - y[0];
				y.RemoveAt(0);

			}
			int final = X;
			

			Console.WriteLine(final);
			for (int i = 0; i < ans.Count; i++)
			{
				Console.WriteLine("{0}" + " " + "{1}", ans[i].Item1, ans[i].Item2);
			}
		}
		else
		{

			X = x[0];
			Y = y[0];
			x.RemoveAt(0);
			y.RemoveAt(0);



			while (y.Count > 0)
			{
				int c = y.Count - 1;

				ans.Add(new Tuple<int, int>(X, y[c]));
				X = X - y[c];
				y.RemoveAt(c);

			}
			while (x.Count > 0)
			{
				int d = x.Count - 1;

				ans.Add(new Tuple<int, int>(Y, x[d]));
				Y = Y - x[d];
				x.RemoveAt(d);
			}

			int final = X - Y;
			ans.Add(new Tuple<int, int>(X, Y));

			Console.WriteLine(final);
			for (int i = 0; i < ans.Count; i++)
			{
				Console.WriteLine("{0}" + " " + "{1}", ans[i].Item1, ans[i].Item2);
			}
		}
	}
}