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: Accepted)

using System;
using System.Collections.Generic;
class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            string[] s1 = Console.ReadLine().Split(' ');
            int[] a = new int[n];
            for (int i=0; i<n; i++) a[i] = int.Parse(s1[i]);

            int posSample = 0;
            int negSample = 0;
            int sum = 0;

            for (int i=0; i<n; i++)
            {
                if (a[posSample] < a[i]) posSample = i;
                if (a[negSample] > a[i]) negSample = i;
                sum += Math.Abs(a[i]);
            }

            if (a[posSample] < 0) //all sample is minus
            {
                Console.WriteLine(sum + a[posSample] * 2);
                int[] b = new int[n];
                int j = 0;
                for (int i=0; i<n; i++)
                {
                    if (i == posSample) continue;
                    b[j] = a[i];
                    j++;
                }
                b[n-1] = -1;
                int ans = a[posSample];
                for (int i=0; i<n-1; i++)
                {
                    if (b[i + 1] > 0)
                    {
                        Console.WriteLine(Math.Min(b[i], ans) + " " + Math.Max(b[i], ans));
                        ans = Math.Min(b[i], ans) - Math.Max(b[i], ans);
                    }
                    else{
                        Console.WriteLine(Math.Max(b[i], ans) + " " + Math.Min(b[i], ans));
                        ans = Math.Max(b[i], ans) - Math.Min(b[i], ans);
                    }
                }
            }
            else if (a[negSample] > 0) //all sample is plus
            {
                Console.WriteLine(sum - a[negSample] * 2);
                int[] b = new int[n];
                int j = 0;
                for (int i=0; i<n; i++)
                {
                    if (i == negSample) continue;
                    b[j] = a[i];
                    j++;
                }
                b[n-1] = -1;
                int ans = a[negSample];
                for (int i=0; i<n-1; i++)
                {
                    if (b[i + 1] > 0)
                    {
                        Console.WriteLine(Math.Min(b[i], ans) + " " + Math.Max(b[i], ans));
                        ans = Math.Min(b[i], ans) - Math.Max(b[i], ans);
                    }
                    else{
                        Console.WriteLine(Math.Max(b[i], ans) + " " + Math.Min(b[i], ans));
                        ans = Math.Max(b[i], ans) - Math.Min(b[i], ans);
                    }
                }
            }
            else{
                Console.WriteLine(sum);
                int[] b = new int[n];
                int j = 1;
                b[0] = a[posSample];
                for (int i=0; i<n; i++)
                {
                    if (i == negSample || i == posSample) continue;
                    b[j] = a[i];
                    j++;
                }
                b[n-1] = -1;
                int ans = a[negSample];
                for (int i=0; i<n-1; i++)
                {
                    if (b[i + 1] > 0)
                    {
                        Console.WriteLine(Math.Min(b[i], ans) + " " + Math.Max(b[i], ans));
                        ans = Math.Min(b[i], ans) - Math.Max(b[i], ans);
                    }
                    else{
                        Console.WriteLine(Math.Max(b[i], ans) + " " + Math.Min(b[i], ans));
                        ans = Math.Max(b[i], ans) - Math.Min(b[i], ans);
                    }
                }
            }
            
            
        }
    }
    //mcs Main.cs
    //mono Main.exe