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.Linq;
using System.Collections.Generic;

using E = System.Linq.Enumerable;

public class Program
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var seq = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();

        var set = new SortedSet<Tuple<int, int>>(seq.Select((x, i) => Tuple.Create(x, i)));
        var operations = new Tuple<int, int>[n - 1];
        var max = set.Max;
        set.Remove(max);
        for (int i = 1; i < operations.Length; i++)
        {
            var t = set.Max;
            var s = set.Min;
            set.Remove(t);
            set.Remove(s);
            operations[i - 1] = Tuple.Create(s.Item1, t.Item1);
            set.Add(Tuple.Create(s.Item1 - t.Item1, n + i - 1));
        }
        set.Add(max);
        var single = set.Max.Item1 - set.Min.Item1;
        operations[operations.Length - 1] = Tuple.Create(set.Max.Item1, set.Min.Item1);

        Console.WriteLine(single);
        Console.WriteLine(string.Join(Environment.NewLine, operations.Select(x => $"{x.Item1} {x.Item2}")));
    }
}