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: Accepted)

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

namespace test
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = ReadLong();
            var A = ReadArrayLong();
            var plus = new List<long>();
            var minus = new List<long>();
            for (int i = 0; i < N; i++)
            {
                if (A[i] >= 0) plus.Add(A[i]);
                else minus.Add(A[i]);
            }
            plus.Sort();
            minus.Sort();
            if (N == 2)
            {
                if (plus.Count() == 0)
                {
                    Console.WriteLine(minus[1] - minus[0]);
                    Console.WriteLine(minus[1] + " " + minus[0]);
                }
                else if (minus.Count() == 0)
                {
                    Console.WriteLine(plus[1] - plus[0]);
                    Console.WriteLine(plus[1] + " " + plus[0]);
                }
                else
                {
                    Console.WriteLine(plus[0] - minus[0]);
                    Console.WriteLine(plus[0] + " " + minus[0]);
                }
                return;
            }
            var pQue = new Queue<long>();
            var mQue = new Queue<long>();
            var ans = new List<long[]>();
            if (minus.Count() == 0)
            {
                ans.Add(new long[] { plus[0], plus[plus.Count() - 1] });
                mQue.Enqueue(plus[0] - plus[plus.Count() - 1]);
                for (int i = 1; i < plus.Count() - 1; i++) pQue.Enqueue(plus[i]);
            }
            else if (plus.Count() == 0)
            {
                ans.Add(new long[] { minus[minus.Count() - 1], minus[0] });
                pQue.Enqueue(minus[minus.Count() - 1] - minus[0]);
                for (int i = 1; i < minus.Count() - 1; i++) mQue.Enqueue(minus[i]);
            }
            else
            {
                for (int i = 0; i < plus.Count(); i++) pQue.Enqueue(plus[i]);
                for (int i = 0; i < minus.Count(); i++) mQue.Enqueue(minus[i]);
            }
            while (pQue.Any() || mQue.Any())
            {
                if (pQue.Count() == 1 && mQue.Count() == 1)
                {
                    var p = pQue.Dequeue();
                    var m = mQue.Dequeue();
                    ans.Add(new long[] { p, m });
                    Console.WriteLine(p - m);
                }
                else if (pQue.Count() >= mQue.Count())
                {
                    var p = pQue.Dequeue();
                    var m = mQue.Dequeue();
                    ans.Add(new long[] { m, p });
                    mQue.Enqueue(m - p);
                }
                else
                {
                    var p = pQue.Dequeue();
                    var m = mQue.Dequeue();
                    ans.Add(new long[] { p, m });
                    pQue.Enqueue(p - m);
                }
            }

            foreach (var a in ans) Console.WriteLine(a[0] + " " + a[1]);

            Console.WriteLine();
            Console.ReadLine();
        }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}