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;
public class diverta2019PC2C {
    public static void Main() {
        int N, ApMin = 100000, AmMax = -100000, ApMinIndex = -1, AmMaxIndex = -1, ans = 100000, ansIndex = -1;
        List<int> Left = new List<int>(), Right = new List<int>();
        List<int> Ap = new List<int>(), Am = new List<int>();
        N = int.Parse(Console.ReadLine());
        string[] str = Console.ReadLine().Split(' ');
        int a;
        for (int i = 0; i < N; i++) {
            a = int.Parse(str[i]);
            if (a >= 0) {
                Ap.Add(a);
                if (ApMin > a) {
                    ApMin = a;
                    ApMinIndex = Ap.Count - 1;
                }
            } else {
                Am.Add(a);
                if (AmMax < a) {
                    AmMax = a;
                    AmMaxIndex = Am.Count - 1;
                }
            }
        }

        if (Ap.Count != 0) {
            if (Ap.Count == 1) {
                ans = Ap[0];
                ansIndex = 0;
            } else {
                if (ApMinIndex == 0) {
                    ans = Ap[1];
                    ansIndex = 1;
                } else {
                    ans = Ap[0];
                    ansIndex = 0;
                }
            }
        }

        for (int i = 0; i < Ap.Count; i++) {
            if (Am.Count != 0) {
                if (i == ansIndex) continue;
                Left.Add(Am[0]);
                Right.Add(Ap[i]);
                Am[0] -= Ap[i];
            } else {
                if (i == ansIndex || i == ApMinIndex) continue;
                Left.Add(ApMin);
                Right.Add(Ap[i]);
                ApMin -= Ap[i];
            }
        }
        if (Am.Count == 0) {
            Left.Add(ans);
            Right.Add(ApMin);
            ans -= ApMin;
        }

        if (Ap.Count != 0) {
            for (int i = 0; i < Am.Count; i++) {
                Left.Add(ans);
                Right.Add(Am[i]);
                ans -= Am[i];
            }
        } else {
            for (int i = 0; i < Am.Count; i++) {
                if (i == AmMaxIndex) continue;
                Left.Add(AmMax);
                Right.Add(Am[i]);
                AmMax -= Am[i];
            }
            ans = AmMax;
        }
        System.Console.WriteLine(ans);
        for (int i = 0; i < Left.Count; i++) {
            Console.WriteLine("{0} {1}", Left[i], Right[i]);
        }
    }
}