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 in = new Scanner(System.in);
        int n = in.nextInt();
        int[] a = new int[n];
        for(int i=0; i<n; i++) {
            a[i] = in.nextInt();
        }
        Arrays.sort(a);
        List<Integer> l = new ArrayList<>(n);
        for(int i=0; i<n; i++) {
            l.add(a[i]);
        }

        List<Tuple> operations = new ArrayList<>();
        boolean isGoingToBeNegative = (n%2==1);
        while(l.size() > 1) {
            int min = l.get(0);
            int max = l.get(l.size()-1);
            l.remove(l.size()-1);
            l.remove(0);
            Tuple t = new Tuple();
            if(isGoingToBeNegative) {
                t.x = min;
                t.y = max;
            }
            else {
                t.x = max;
                t.y = min;
            }
            operations.add(t);
            int x_y = t.x-t.y;
            if(l.size()==0 || x_y >= l.get(l.size()-1)) {
                l.add(x_y);
            }
            else {
                for(int i=0; i<l.size(); i++) {
                    if(x_y <= l.get(i)) {
                        l.add(i, x_y);
                        break;
                    }
                }
            }
            isGoingToBeNegative ^= true;
        }
        System.out.println(l.get(0));
        for(int i=0; i<operations.size(); i++) {
            Tuple t = operations.get(i);
            System.out.print(t.x);
            System.out.print(" ");
            System.out.println(t.y);
        }
    }
}
class Tuple {
    int x;
    int y;
}