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: Time Limit Exceeded)

import java.awt.TexturePaint;
import java.awt.event.ComponentAdapter;
import java.io.BufferedReader;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int first = Integer.parseInt(sc.next()); 
		ArrayList<Integer> minusList = new ArrayList<Integer>();
		ArrayList<Integer> list = new ArrayList<Integer>();
		
		for(int i=0; sc.hasNext(); i++) {
			int value = Integer.parseInt(sc.next());
			if(value<=0) {
				minusList.add(value);
			}else {
				list.add(value);
			}
		}
		Collections.sort(minusList);
		Collections.sort(list);
		
		ArrayList<String> textList = new ArrayList<String>();
		int minusLists = minusList.size();
		int lists = list.size();
		
		if(minusList.size() > 0) {
			if(list.size()>0) {
				for(int i=0; i<minusLists-1; i++) {
					textList.add((list.get(0) + " " + minusList.get(0)).toString());
					list.add(1, list.get(0)-minusList.get(0));
					minusList.remove(0);
					list.remove(0);
				}
				for(int i=0; i<lists-1;i++) {
					textList.add((minusList.get(0) + " " + list.get(0)).toString());
					minusList.add(minusList.get(0)-list.get(0));
					minusList.remove(0);
					list.remove(0);
				}
				textList.add((list.get(0) + " " + minusList.get(0)).toString());
				System.out.println(list.get(0)-minusList.get(0));
			}else {
				textList.add((minusList.get(minusList.size()-2)+" "+minusList.get(minusList.size()-1)).toString());
				list.add(minusList.get(0) - minusList.get(1));
				minusList.remove(minusList.size()-1);
				minusList.remove(minusList.size()-1);
				if(minusList.size()==0) {
					System.out.println(list.get(0));
				}else {
					for(int i=0; i<minusLists-3; i++) {
						textList.add((list.get(0) + " " + minusList.get(0)).toString());
						list.add(1, list.get(0)-minusList.get(0));
						minusList.remove(0);
						list.remove(0);
					}
					textList.add((list.get(0) + " " + minusList.get(0)).toString());
					System.out.println(list.get(0)-minusList.get(0));
				}
			}
		}else {
			textList.add((list.get(0)+" "+list.get(list.size()-1)).toString());
			minusList.add(list.get(0)-list.get(list.size()-1));
			list.remove(list.size()-1);
			list.remove(0);
			if(list.size()==0) {
				System.out.println(minusList.get(0));
			}else {
				for(int i=0; i<lists-3;i++) {
					textList.add((minusList.get(0) + " " + list.get(0)).toString());
					minusList.add(minusList.get(0)-list.get(0));
					minusList.remove(0);
					list.remove(0);
				}
				textList.add((list.get(0) + " " + minusList.get(0)).toString());
				System.out.println(list.get(0)-minusList.get(0));
			}
		}
		for(String s:textList) {
			System.out.println(s);
		}
	}
}