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;

public class S
{
    private const char BLANK = '.';
    private const char ROCK = '#';
    public static void Main()
    {

        // diverta 2 C
        // 負数を1個作り(正数最小値-正数最大値)、ひたすら正数をそこに減算していく。
        // 負数は1個以外すべて最大値に対して減算する。
        var N = int.Parse(Console.ReadLine());

        var input = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);

        var list = new List<int>();
        foreach(var tgt in input){
            list.Add(tgt);
        }
        list.Sort();
        input = list.ToArray();

        int max = input[N-1];
        int hoge = 0;
        int focusIndex = -1;

        for(int i =0; i < N-1; i++){
            if(input[i] < 0){
                if(input[i + 1] >= 0 && i != N-2){
                    focusIndex = i;
                    hoge = input[i];
                }else{
                    max -= input[i];
                }
            }else{
                if(focusIndex == -1){
                    focusIndex = i;
                    hoge = input[i];
                }else{
                    hoge -= input[i];
                }
            }
        }


        Console.WriteLine(max - hoge);
        max = input[N-1];
        focusIndex = -1;
        hoge = 0;
        for(int i =0; i < N-1; i++){
            if(input[i] < 0){
                if(input[i + 1] >= 0 && i+1 != N-1){
                    focusIndex = i;
                    hoge = input[i];
                }else{
                    Console.WriteLine(max + " " + input[i]);
                    max -= input[i];
                }
            }else{
                if(focusIndex == -1){
                    focusIndex = i;
                    hoge = input[i];
                }else{
                    Console.WriteLine(hoge + " " + input[i]);
                    hoge -= input[i];
                }
            }

            
        }
        Console.WriteLine(max + " " + hoge);
    }
}