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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static void Main()
    {
        //Console.WriteLine(Solve());
        Solve();
        return;
    }

    public static string Solve()
    {
        int N = ReadInt();
        int[] A = ReadInts();
        Array.Sort(A);
        long[,] output = new long[N - 1, 2];
        int m = 0;
        long sum = 0;
        //Console.WriteLine("[{0}]", string.Join(", ", A));
        if (A[0] <= 0 && A[N - 1] >= 0)
        {
            for (int i = 0; i < N; i++)
            {
                if (A[i] >= 0)
                {
                    int k = i;
                    sum = A[i];
                    for (int j = i - 1; j > 0; j--)
                    {
                        output[m, 0] = sum;
                        output[m, 1] = A[j];
                        m++;
                        sum = sum - A[j];
                    }
                    output[m, 0] = A[0];
                    output[m, 1] = sum;
                    m++;
                    sum = A[0] - sum;
                    for (int j = k + 1; j < N - 1; j++)
                    {
                        output[m, 0] = sum;
                        output[m, 1] = A[j];
                        m++;
                        sum = sum - A[j];
                    }
                    output[m, 0] = A[N - 1];
                    output[m, 1] = sum;
                    m++;
                    sum = A[N - 1] - sum;
                    break;
                }
            }
        }
        else
        {
            if (A[0] <= 0)
            {
                sum = A[0];
                for (int i = 1; i < N; i++)
                {
                    output[m, 0] = sum;
                    output[m, 1] = A[i];
                    m++;
                    sum = sum - A[i];
                }
            }
            else
            {
                sum = A[0];
                for (int i = 1; i < N - 1; i++)
                {
                    output[m, 0] = sum;
                    output[m, 1] = A[i];
                    m++;
                    sum = sum - A[i];
                }
                output[m, 0] = A[N - 1];
                output[m, 1] = sum;
                m++;
                sum = A[N - 1] - sum;
            }
        }
        Console.WriteLine(sum);
        for (int i = 0; i < N - 1; i++)
        {
            Console.WriteLine(output[i, 0].ToString() + " " + output[i, 1].ToString());
        }

        return sum.ToString();
    }

    private static string Read() { return Console.ReadLine(); }
    private static int ReadInt() { return int.Parse(Read()); }
    private static long ReadLong() { return long.Parse(Read()); }
    private static double ReadDouble() { return double.Parse(Read()); }
    private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
    private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
    private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
}