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;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using System.Collections;
static class Extensions
{
    public static int ToInt(this string s) => int.Parse(s);
    public static long ToLong(this string s) => long.Parse(s);
    public static char ToChar(this string s) => char.Parse(s);
    public static double ToDouble(this string s) => double.Parse(s);
    public static int[] ToIntArray(this string s) => s.Replace(',', ' ').Split(' ').Select(x => x.ToInt()).ToArray();
    public static long[] ToLongArray(this string s) => s.Replace(',', ' ').Split(' ').Select(x => x.ToLong()).ToArray();
    public static double[] ToDoubleArray(this string s) => s.Replace(',', ' ').Split(' ').Select(x => x.ToDouble()).ToArray();
}

class Program
{
    static string[] ReadLines(int n) => Enumerable.Range(0, n).Select(s => Console.ReadLine()).ToArray();

    static void Main()
    {
        int N = Console.ReadLine().ToInt();

        var aList = Console.ReadLine().ToLongArray().OrderByDescending(n => n).ToArray();

        
        var ddd1 = N / 2;
        var ddd2 = (int)Math.Ceiling(N / 2d);



        var ans1 = aList.Take(ddd1).Sum() - aList.Skip(ddd1).Sum();
        var ans2 = aList.Take(ddd2).Sum() - aList.Skip(ddd2).Sum();

        Console.WriteLine(Math.Max(ans1, ans2));

        var ddd = ans1 > ans2 ? ddd1 : ddd2;

        var q1 = new Queue<long>(aList.Take(ddd));
        var q2 = new Queue<long>(aList.Skip(ddd));

        while(q1.Any() && q2.Any())
        {
            if (q1.Count == 1 && q2.Count == 1)
            {
                Console.WriteLine($"{q1.Dequeue()} {q2.Dequeue()}");
                return;
            }
            else if (q1.Count >= q2.Count)
            {
                var v1 = q2.Dequeue();
                var v2 = q1.Dequeue();
                Console.WriteLine($"{v1} {v2}");
                var n = v1 - v2;
                q2.Enqueue(n);
            }
            else
            {
                var v1 = q1.Dequeue();
                var v2 = q2.Dequeue();
                Console.WriteLine($"{v1} {v2}");
                var n = v1 - v2;
                q1.Enqueue(n);
            }
        }
    }
}