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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.IO;
namespace I_am_the_brown_coder{
    class Inonoa{
        static void Main(){
            var sw = new StreamWriter(Console.OpenStandardOutput()){AutoFlush = false};
            Console.SetOut(sw);
            int n = int.Parse(Console.ReadLine());
            string[] sa = Console.ReadLine().Split();
            int[] a = new int[n];
            int mn = -1000000;
            int minindex = -1;
            for(int i=0;i<n;i++){
                a[i] = int.Parse(sa[i]);
            }

            int[,] ans = new int[n-1,2];
            int index = 0;

            Array.Sort(a);

            for(int i=0;i<n;i++){
                if(a[i]<=0 && a[i]>mn){
                    mn = a[i];
                    minindex = i;
                }
            }
            if(minindex==-1){
                mn = a[0];
                minindex = 0;
            }

            for(int i=minindex+1;i<n-1;i++){
                ans[index,0] = a[minindex];
                ans[index,1] = a[i];
                a[minindex] -= a[i];
                index ++;
            }
            if(minindex<n-1){
                ans[index,0] = a[n-1];
                ans[index,1] = a[minindex];
                index ++;
                a[minindex] -= a[n-1];
                a[minindex] *= -1;
            }
            for(int i=minindex-1;i>-1;i--){
                ans[index,0] = a[minindex];
                ans[index,1] = a[i];
                a[minindex] -= a[i];
                index ++;
            }
            

            Console.WriteLine(a[minindex]);
            for(int i=0;i<n-1;i++){
                Console.Write(ans[i,0]);
                Console.Write(" ");
                Console.WriteLine(ans[i,1]);
            }
            Console.Out.Flush();
        }
    }
}