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;
using System.Text;

namespace diverta20192_C
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var A = Console.ReadLine().Split().Select(long.Parse).ToList();

            var numNeg = A.Where(x => x < 0).Count();

            long ans1 = 0;
            var ans2 = new List<Tuple<long, long>>();

            if (N == 2)
            {
                ans1 = A.Max() - A.Min();
                ans2.Add(new Tuple<long, long>(A.Max(), A.Min()));
            }
            else if (numNeg == 0)
            {
                var smallTwo = A.OrderBy(x => Math.Abs(x)).Take(2).ToList();
                ans1 = smallTwo[0] - smallTwo[1];
                ans2.Add(new Tuple<long, long>(smallTwo[0], smallTwo[1]));

                A.Remove(smallTwo[0]);
                A.Remove(smallTwo[1]);

                for (int i = 0; i < N - 3; i++)
                {
                    ans2.Add(new Tuple<long, long>(ans1, A[i]));
                    ans1 -= A[i];
                }

                ans2.Add(new Tuple<long, long>(A[N - 3], ans1));
                ans1 = A[N - 3] - ans1;
            }
            else if (numNeg == N)
            {
                var smallTwo = A.OrderBy(x => Math.Abs(x)).Take(2).ToList();
                ans1 = smallTwo[0] - smallTwo[1];
                ans2.Add(new Tuple<long, long>(smallTwo[0], smallTwo[1]));

                A.Remove(smallTwo[0]);
                A.Remove(smallTwo[1]);

                for (int i = 0; i < N - 3; i++)
                {
                    ans2.Add(new Tuple<long, long>(ans1, A[i]));
                    ans1 -= A[i];
                }

                ans2.Add(new Tuple<long, long>(ans1, A[N - 3]));
                ans1 -= A[N - 3];
            }
            else
            {
                var pos = A.Where(x => x >= 0).ToArray();
                var neg = A.Where(x => x < 0).ToArray();

                ans1 = pos[0];
                long temp = neg[0];
                for (var pIndex = 1; pIndex < pos.Length; pIndex++)
                {
                    ans2.Add(new Tuple<long, long>(temp, pos[pIndex]));
                    temp -= pos[pIndex];
                }

                for (var nIndex = 1; nIndex < neg.Length; nIndex++)
                {
                    ans2.Add(new Tuple<long, long>(ans1, neg[nIndex]));
                    ans1 -= neg[nIndex];
                }

                ans2.Add(new Tuple<long, long>(ans1, temp));
                ans1 -= temp;
            }

            Console.WriteLine(ans1);
            var sb = new StringBuilder();
            for (int i = 0; i < ans2.Count(); i++)
            {
                sb.AppendLine($"{ans2[i].Item1} {ans2[i].Item2}");
            }
            Console.WriteLine(sb.ToString());
        }
    }
}