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.IO;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Numerics;
using System.Threading.Tasks;
using System.Text.RegularExpressions;
using static System.Math;
using Debug = System.Diagnostics.Debug;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;

static class P
{
    static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var a = Console.ReadLine().Split().Select(long.Parse).OrderByDescending(x => x).ToArray();
        //+は1つからceil(n/2)個作れる
        var plus = a.Take(n / 2 + (n % 2 == 0 ? 0 : 1)).TakeWhile(x => 0 < x).ToList();
        if (plus.Count == 0) plus.Add(a[0]);

        int count = 0;

        var minus = a.Skip(plus.Count).ToList();
        List<long> mins = new List<long>();
        StringBuilder builder = new StringBuilder();
        for (int i = 0; i < plus.Count - 1; i++)
        {
            builder.AppendLine($"{minus[i]} {plus[i]}");
            mins.Add(minus[i] - plus[i]);
            count++;
        }
        var last = plus.Last();
        foreach (var item in mins.Concat(minus.Skip(plus.Count - 1)))
        {
            builder.AppendLine($"{last} {item}");
            last -= item;
            count++;
        }
        while (count != n - 1) ;
        Console.WriteLine(last);
        Console.Write(builder.ToString());
    }
}