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.*;
class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int ans = 0;
        int cnt = 0;
        int[] num = new int[n];
        int[] num1 = new int[n];
        int[] num2 = new int[2*n];
        List<Integer> map = new ArrayList<Integer>(); 
        for(int i = 0;i < n;i++){
            num[i] = sc.nextInt();
            num1[i] = num[i];
        }
        Arrays.sort(num);
        Arrays.sort(num1);
        

        for(int i = 0;i < n-1;i++){
                if(i < n-2){
                    map.add(num[i]);
                map.add(num[i+1]);
                }else{
                    map.add(num[n-1]);
                    map.add(num[i]);
                }
            cnt += 2;
            num1[i] = num[i]-num[i+1];
            num[i+1] = num1[i];
            if(i == n-2)
            ans = -1*(map.get(cnt-1) - map.get(cnt-2));
        }

        System.out.println(ans);
        for(int i = 0;i < map.size();i += 2){
            System.out.println(map.get(i)+"\t"+map.get(i+1));
        }
        
    }
}