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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
using System.Collections;
using static System.Math;
using System.Linq;
using static System.Array;

namespace ConsoleApp2
{
    class Program
    {
        //static int N;
        //static long mod = 1000000007;
        //static char[] az = Enumerable.Range('a', 'z' - 'a' + 1).Select(i => (Char)i).ToArray();
        static void Main(string[] args)
        {
            //var A = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            var N = long.Parse(Console.ReadLine());
            var A = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();

            Sort(A);
            var B = new long[N];
            for (int i = 0; i < N; i++)
            {
                B[i] = Abs(A[i]);
            }

            if (A[0] < 0 && A[N -1] < 0)
            {
                Console.WriteLine(B.Sum() - 2*B[0]);
                var sum = A[0];
                for (int i = 1; i < N; i++)
                {
                    Console.WriteLine(sum + " " + A[i]);
                    sum -= A[i];
                }
            }
            else if (A[0] >= 0 && A[N - 1] >= 0)
            {
                Console.WriteLine(B.Sum() - 2 * B[0]);
                var sum = A[0];
                for (int i = 1; i < N; i++)
                {
                    if (i == N - 1)
                    {
                        Console.WriteLine(A[i] + " " + sum);
                    }
                    else
                    {
                        Console.WriteLine(sum + " " + A[i]);
                        sum -= A[i];
                    }
                }

            }
            else
            {
                Console.WriteLine(B.Sum());
                var summ = A[0];
                var sumu = A[N-1];
                for (int i = 1; i < N; i++)
                {
                    if (i == N-1)
                    {
                        Console.WriteLine(sumu + " " + summ);
                        
                    }
                    else if (A[i] >= 0)
                    {
                        Console.WriteLine(summ + " " + A[i]);
                        summ -= A[i];
                    }else if (A[i] < 0)
                    {
                        Console.WriteLine(sumu + " " + A[i]);
                        sumu -= A[i];
                    }
                }
            }

        }
    }
}