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.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int num = sc.nextInt();
        List<Integer> minus = new ArrayList<Integer>();
        List<Integer> plus = new ArrayList<Integer>();
        List<String> result = new ArrayList<String>();
        int minusCount = 0;
        int plusCount = 0;
        int temp = 0;
        for(int i=0; i<num; i++){
  		  temp = sc.nextInt();
          if(temp >= 0) {
            //plus[plusCount] = temp;
            plus.add(temp);
            //plusCount++;
          }
          else{
            minus.add(temp);
            //minusCount++;
          }
        }
        if(minus.size() == 0){
          if(plus.size() == 2){
            int max = plus.get(0) >= plus.get(1) ? plus.get(0) : plus.get(1);
             int min = plus.get(0) >= plus.get(1) ? plus.get(1) : plus.get(0);
             temp = max- min;
             result.add(max + " " + min);
          }
          else{
             int max = plus.get(0) >= plus.get(1) ? plus.get(0) : plus.get(1);
             int min = plus.get(0) >= plus.get(1) ? plus.get(1) : plus.get(0);
             temp = min - max;
             result.add(min + " " + max);
             plus.remove(0);
             plus.remove(1);
             minus.add(temp);
          }
        }
        if(plus.size() == 0){
          if(minus.size() == 2){
            int max = plus.get(0) >= plus.get(1) ? plus.get(0) : plus.get(1);
             int min = plus.get(0) >= plus.get(1) ? plus.get(1) : plus.get(0);
             temp = min - max;
             result.add(min + " " + max);
          }
          else{
             int max = minus.get(0) >= minus.get(1) ? minus.get(0) : minus.get(1);
             int min = minus.get(0) >= minus.get(1) ? minus.get(1) : minus.get(0);
             temp = max - min;
             result.add(max + " " + min);
             minus.remove(0);
             minus.remove(1);
             plus.add(temp);
          }
        }
        while(minus.size() > 0 && plus.size() > 0){
          if(plus.size() > 1){
             temp = minus.get(0) - plus.get(0);
             result.add(minus.get(0) + " " + plus.get(0));
             minus.remove(0);
             plus.remove(0);
             minus.add(temp);
          }
          else{
             temp = plus.get(0) - minus.get(0);
             result.add(plus.get(0) + " " + minus.get(0));
             minus.remove(0);
             plus.remove(0);
             plus.add(temp);
          }
        }
		System.out.println(plus.get(0));
        //System.out.println(result.size());
        for(String item: result){
          System.out.println(item);           
        }
	}
}