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)

namespace Diverta2.C
{
    using System;
    using System.Collections.Generic;
    using System.Linq;
    using static System.Console;
    using static System.Math;
    public struct Operation
    {
        public int X { get; set; }
        public int Y { get; set; }
    }

    public class Program
    {
        public static void Main(string[] args)
        {
            var l = ReadInputAsInt();
            var p = ReadInputsAsInt().ToList();

            Solve(l, p);//.ToList().ForEach(i => WriteLine($"{i.X} {i.Y}"));
        }

        public static void Solve(int n, List<int> p)
        {                   
            var zero = 0;
            var firstIdx = 0;
            var firstTake = 0;
            if (!p.All(i => i > 0) && !p.All(k => k < 0))
            {
                var max_ans = p.Select(i => Abs(i)).Sum();
                WriteLine(max_ans);

                //Stack<bool> needPlusStack = new Stack<bool>();
                if (p.All(i => i >= 0) || p.All(i => i <= 0))
                {
                    if (p[0] != 0)
                    {
                        firstIdx = p.Select((x, i) => new { X = x, I = i }).Where(k => k.X == 0).First().I;
                    }
                    else
                    {
                        firstIdx = p.Select((x, i) => new { X = x, I = i }).Where(k => k.X != 0).First().I;
                    }
                }
                else
                {
                    firstIdx = p.Select((x, i) => new { X = x, I = i }).Where(k => p[0] * k.X < 0).First().I;
                }
                zero = p[0];
                firstTake = p[firstIdx];
                p.RemoveAt(0);
                p.RemoveAt(firstIdx);
            }
            else
            {
                var min = p.Select(k => Abs(k)).Min();// p.Select((x, i) => new { X = x, I = i }).Min(k => k.X).I;
                var zeroIdx = p.Select((x, i) => new { X = x, I = i }).Where(k => Abs(k.X) == min).First().I;

                zero = p[zeroIdx];
                p.RemoveAt(zeroIdx);

                var min2 = p.Select(k => Abs(k)).Min();// p.Select((x, i) => new { X = x, I = i }).Min(k => k.X).I;
                firstIdx = p.Select((x, i) => new { X = x, I = i }).Where(k => Abs(k.X) == min2).First().I;


                firstTake = p[firstIdx];
                p.RemoveAt(firstIdx);

                WriteLine(p.Select(i=>Abs(i)).Sum() - Abs(zero - firstTake));
            }


            var prev = zero;
            var now = firstTake;
            for (int i = 0; i < p.Count; i++)
            {

                if (p[i] <= 0)
                {
                    WriteLine("{0} {1}", Max(prev, now), Min(prev, now));
                    prev = Max(prev, now) - Min(prev, now);
                    now = p[0];
                }
                else
                {
                    WriteLine("{0} {1}", Min(prev, now), Max(prev, now));
                    prev = Min(prev, now) - Max(prev, now);
                    now = p[0];
                }
            }
            WriteLine("{0} {1}", Max(prev, now), Min(prev, now));
            return;
        }

        static int ReadInputAsInt() => int.Parse(ReadLine());

        static IEnumerable<int> ReadInputsAsInt() => ReadLine().Split(' ').Select(x => int.Parse(x));

    }
}