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 n = sc.nextInt();
		ArrayList<Integer> plus = new ArrayList<>();
		ArrayList<Integer> minus = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			int x = sc.nextInt();
			if (x < 0) {
				minus.add(x);
			} else {
				plus.add(x);
			}
		}
		Collections.sort(plus);
		Collections.sort(minus);
		int w;
		if (minus.size() > 0) {
			w = minus.remove(0);
		} else {
			w = plus.remove(0);
		}
		StringBuilder sb = new StringBuilder();
		while (plus.size() > 1) {
			int x = plus.remove(0);
			sb.append(w).append(" ").append(x).append("\n");
			w -= x;
		}
		minus.add(w);
		int ans;
		if (plus.size() > 0) {
			ans = plus.remove(0);
		} else {
			ans = minus.remove(minus.size() - 1);
		}
		for (int x : minus) {
			sb.append(ans).append(" ").append(x).append("\n");
			ans -= x;
		}
		System.out.println(ans);
		System.out.print(sb);
	}
}