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.*;
class Main {
    public static void main(String[] args) {
        Scanner sc =new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        long total = 0;

        for(int i = 0; i<n; i++) {
            a[i] = sc.nextInt();
            total += Math.abs(a[i]);
        }

        Arrays.sort(a);
        int cnt = 0;
        for(int i = 0; i<n; i++) {
            if(a[i]>=0) break;
            cnt++;
        }
        if(cnt == 0 ) {
            System.out.println(total-a[0]*2);
            System.out.println(a[0] +" "+ a[1]);
            a[1] = a[0]-a[1];
            for(int i = 1; i<n-2; i++) {
                System.out.println(a[i] +" "+ a[i+1]);
                a[i+1] = a[i] - a[i+1];
            }
            if(n!=2) System.out.println(a[n-1]+" "+a[n-2]);
            return;
        }
        if(cnt == n) {
            System.out.println(total+a[n-1]*2);
            System.out.println(a[0] +" "+ a[1]);
            a[n-2] = a[n-1]-a[n-2];
            for(int i = n-2; i>0; i--) {
                System.out.println(a[i] +" "+ a[i-1]);
                a[i-1] = a[i] - a[i-1];
            }
            return;
        }
        int minus = cnt;
        int plus = n-cnt;
        int left = 0;
        int right = n-1;
        System.out.println(total);
        for(int i = 0; i<n-1; i++) {
            if(minus<plus) {
                System.out.println(a[left] + " " + a[right]);

                plus--;
                a[left] = a[left]-a[right];
                right--;
            }
            else {
                System.out.println(a[right] + " " + a[left]);
                minus--;
                a[right] = a[right]-a[left];
                left++;
            }
        }


    }

}