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)

//#define TEST

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Numerics;
using System.Text;
using static System.Math;

class Program
{
    static int n;
    static long[] a;
    static void Main()
    {
        n = int.Parse(Console.ReadLine());
        a = Console.ReadLine().Split().Select(long.Parse).ToArray();

        Array.Sort(a);

        long[] sum = new long[n + 1];
        for (int i = 1; i <= n; i++)
            sum[i] = sum[i - 1] + a[i - 1];

        long min = long.MaxValue;
        int index = 0;
        for (int i = 1; i <= n - 1; i++)
        {
            if (min > sum[i])
            {
                min = sum[i];
                index = i;
            }
        }
        Console.WriteLine(a.Sum() - 2 * min);
        long temp = a[index - 1];
        for (int i = index; i < n - 1; i++)
        {
            Console.WriteLine("{0} {1}", temp, a[i]);
            temp -= a[i];
        }
        Console.WriteLine("{0} {1}", a[n - 1], temp);
        temp = a[n - 1] - temp;
        for (int i = 0; i < index - 1; i++)
        {
            Console.WriteLine("{0} {1}", temp, a[i]);
            temp -= a[i];
        }

    }
}