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;
using System.Collections.Generic;

class Program
{
    public static void Main()
    {
        var N = int.Parse(Console.ReadLine());
        List<int> A = new List<int>() { Capacity = N };

        var T = Console.ReadLine().Split(' ');
        for (int i = 0; i < N; i++)
            A.Add(int.Parse(T[i]));

        A.Sort((a, b) => a - b);

        int[] D = new int[N - 1];
        for (int i = 0; i < N - 1; i++)
            D[i] = i + 1;
        if (N % 2 == 0)
        {
            for (int i = 1; i < N - 1; i += 2)
                D[i] = -D[i];
        }
        else
        {
            for (int i = 0; i < N - 1; i += 2)
                D[i] = -D[i];
        }

        int x = A[(N - 1) / 2];
        int r = (N - 1) / 2;
        Queue<string> q = new Queue<string>();
        for (int i=0;i<N-1;i++)
        {
            r += D[i];
            q.Enqueue(A[r] + " " + x);
            x = A[r] - x;
        }
        Console.WriteLine(x);
        while (q.Count > 0)
            Console.WriteLine(q.Dequeue());
    }
}