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.lang.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}
		Arrays.sort(a);
		long sum = 0;
		for (int i = 0; i < n / 2; i++) {
			sum -= a[i];
		}
		for (int i = n / 2; i < n; i++) {
			sum += a[i];
		}
		System.out.println(sum);
		if (n % 2 == 0) {
			int tmp = a[0];
			for (int i = 0; i < n - 1; i++) {
				if (i % 2 == 0) {
					System.out.println(a[n - i / 2 - 1] + " " + tmp);
					tmp = a[n - i / 2 - 1] - tmp;
				} else {
					System.out.println(a[i / 2 + 1] + " " + tmp);
					tmp = a[i / 2 + 1] - tmp;
				}
			}
		} else {
			int tmp = a[n - 1];
			for (int i = 0; i < n - 1; i++) {
				if (i % 2 != 0) {
					System.out.println(a[n - i / 2 - 2] + " " + tmp);
					tmp = a[n - i / 2 - 2] - tmp;
				} else {
					System.out.println(a[i / 2] + " " + tmp);
					tmp = a[i / 2] - tmp;
				}
			}
		}
	}
}