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.Linq;

namespace ConsoleApp
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var ss = Console.ReadLine().Split();
            var A = new int[N];
            for (int i = 0; i < N; i++)
                A[i] = int.Parse(ss[i]);

            Array.Sort(A);
            Array.Reverse(A);

            var x = new int[N - 1];
            var y = new int[N - 1];
            var xI = 0;
            var yI = 0;

            var lastPlus = 0;
            for (int i = 1; i < N; i++)
            {
                if (A[i] > 0)
                {
                    if (i == N - 1)
                    {
                        lastPlus = i;
                    }
                    continue;
                }
                else
                {
                    lastPlus = i - 1;
                    break;
                }
            }

            var sum1 = A[A.Length - 1];
            if (lastPlus == N - 1)
            {
                x[xI++] = sum1;
                y[yI++] = A[A.Length - 2];
                sum1 -= A[A.Length - 2];
            }
            else
            {
                for (int i = 1; i <= lastPlus; i++)
                {
                    x[xI++] = sum1;
                    y[yI++] = A[i];
                    sum1 -= A[i];
                }
            }
            var sum2 = A[0];
            for (int i = lastPlus + 1; i < A.Length - 1; i++)
            {
                x[xI++] = sum2;
                y[yI++] = A[i];
                sum2 -= A[i];
            }
            x[xI] = sum2;
            y[yI] = sum1;

            Console.WriteLine(sum2 - sum1);
            for (int i = 0; i <= xI; i++)
            {
                Console.WriteLine(x[i] + " " + y[i]);
            }
        }
    }
}