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.Threading.Tasks;
using System.Diagnostics;

static class CodeJam
{
    static int Solve(int N, int[] A, List<int[]> seq)
    {
        Array.Sort(A);
        int sum = A[0];
        for (int i = 1; i < N - 1; ++i)
        {
            if (A[i] >= 0)
            {
                sum -= A[i];
                seq.Add(new[] { sum, A[i] });
            }
        }
        sum = A[N - 1] - sum;
        seq.Add(new[] { A[N - 1], sum });
        for (int i = 1; i < N - 1; ++i)
        {
            if (A[i] < 0)
            {
                sum -= A[i];
                seq.Add(new[] { sum, A[i] });
            }
        }
        return sum;
    }

    static void Main(string[] args)
    {
        int N = int.Parse(Console.ReadLine());
        int[] A = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        var seq = new List<int[]>();
        Console.WriteLine(Solve(N, A, seq));
        foreach (int[] ans in seq) { Console.WriteLine(string.Join(" ", ans)); }
    }
}