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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.util.stream.Collectors;

public class Main {

    private static final int INF = Integer.MAX_VALUE;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int m = sc.nextInt();
        List<Long> list = new ArrayList<>();
        boolean flagplus = false;
        boolean flagminus = false;

        long min = INF;
        for(int tmp=0;tmp<m;tmp++){
            long a = sc.nextLong();
            if(Math.abs(a) < min) min = a;

            if(a < 0) flagminus = true;
            if(a > 0) flagplus = true;
            list.add(a);
        }

        long result = 0;
        if(flagminus && flagplus){
            for(int tmp = 0; tmp < list.size(); tmp++){
                result += Math.abs(list.get(tmp));
            }
            System.out.println(result);

            long minus = Collections.min(list);
            list.remove(minus);

            List<Long> listPlus = list.stream().filter(s -> s >= 0).collect(Collectors.toList());
            List<Long> listMinus = list.stream().filter(s -> s<0).collect(Collectors.toList());
            System.out.println(minus + " " + listPlus.get(0));

            long number = minus - listPlus.get(0);
            listPlus.remove(0);
            for(long i: listPlus){
                System.out.println( i+" "+number);
                number = i - number;
            }
            for(long i: listMinus){
                System.out.println(number + " " + i);
                number = number - i;
            }



        }else{

            list.remove(min);
            for(int tmp = 0; tmp < list.size(); tmp++){
                result += Math.abs(list.get(tmp));
            }
            result -= Math.abs(min);
            System.out.println(result);
            long number;
            System.out.println(min + " " + list.get(0));
            number = min - list.get(0);
            for(int tmp = 1; tmp < list.size() - 1; tmp++){
                System.out.println(number + " " + list.get(tmp));
                number -= list.get(tmp);
            }
            if(flagplus){
                System.out.println(list.get(m - 2) + " " + number);
            } else {
                System.out.println(number + " " + list.get(m -2));
            }
        }


    }
}