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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.StringTokenizer;

public class Main {
    private static class Pair{
        Long key;
        Long value;

        public Pair(Long a, Long b){
            key=a;
            value=b;
        }

    }
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        StringTokenizer st = new StringTokenizer(br.readLine());
        List<Integer> pos = new ArrayList<>();
        List<Integer> neg = new ArrayList<>();
        long sumPos;
        long sumNeg;
        ArrayList<Pair> pair = new ArrayList<>();
        for(int i=0;i<n;i++) {
            int temp = Integer.parseInt(st.nextToken());
            if (temp >= 0) {
                pos.add(temp);
            } else {
                neg.add(temp);
            }
        }
            Collections.sort(pos);
            Collections.sort(neg);
            Collections.reverse(neg);
            sumPos = (neg.size()==0)? pos.get(0):neg.get(0);
            sumNeg=(pos.size()==0)?neg.get(0):pos.get(0);
            if(pos.size()>0) {
                for (int i = 1; i < pos.size() - 1; i++) {
                    pair.add(new Pair(sumPos, (long) pos.get(i)));
                    sumPos -= pos.get(i);
                }
                if (neg.size() == 0) {
                    pair.add(new Pair((long) pos.get(pos.size() - 1), sumPos));
                    sumPos = pos.get(pos.size() - 1) - sumPos;

                    System.out.println(sumPos);
                    for (Pair p : pair) {
                        System.out.println(p.key + " " + p.value);
                    }
                    return;
                }
            }
            if(neg.size()>0){
                for(int i=1; i<neg.size(); i++){
                    pair.add(new Pair(sumNeg, (long)neg.get(i)));
                    sumNeg-=neg.get(i);
                }
                if(pos.size()==0){
                    System.out.println(sumNeg);
                    for (Pair p : pair) {
                        System.out.println(p.key + " " + p.value);
                    }
                    return;
            }
            else {
                if(pos.size()>1)
                    pair.add(new Pair(sumPos, (long) pos.get(pos.size()-1)));
                    sumPos -= pos.get(pos.size()-1);
            }
                pair.add(new Pair(sumNeg,sumPos));
                System.out.println(sumNeg-sumPos);
                for(Pair p: pair){
                    System.out.println(p.key + " " + p.value);
                }
        }
    }
}