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;

public class Solution
{
    public static void Main()
    {
        var N = int.Parse(Console.ReadLine());
        var A = Console.ReadLine().Split(' ').Select(int.Parse).ToList();
        var B = A.ToList();
        var aList = new List<Tuple<int, int>>();
        var bList = new List<Tuple<int, int>>();
        while (A.Count > 1)
        {
            var max = A.Max();
            var min = A.Min();
            A.Remove(max);
            A.Remove(min);
            if (A.Count == 0)
            {
                aList.Add(Tuple.Create(max, min));
                A.Add(max - min);
            }
            else
            {
                aList.Add(Tuple.Create(min, max));
                A.Add(min - max);
            }
        }
        while (B.Count > 1)
        {
            var max = B.Max();
            var min = B.Min();
            B.Remove(max);
            B.Remove(min);
            bList.Add(Tuple.Create(max, min));
            B.Add(max - min);
        }

        var result = A.First();
        var list = aList;
        if (B.First() > A.First())
        {
            result = B.First();
            list = bList;
        }
        Console.WriteLine(result);
        Console.WriteLine(string.Join(Environment.NewLine, list.Select(t => $"{t.Item1} {t.Item2}")));
    }
}