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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.InputStream;
import java.io.PrintStream;
import java.util.*;

public class Main {

  public static void main(String[] args) {
    solve(System.in, System.out);
  }

  static void solve(InputStream is, PrintStream os) {
    Scanner sc = new Scanner(is);

    /* read */
    int n = sc.nextInt();

    int[] a = new int[n];
    for (int i = 0; i < n; i++) {
      a[i] = sc.nextInt();
    }

    List<Long> negatives = new LinkedList<>();
    List<Long> positives = new LinkedList<>();
    int zeros = 0;

    for (long num : a) {
      if (num < 0) negatives.add(num);
      if (num > 0) positives.add(num);
      if (num == 0) zeros++;
    }

    while (zeros > 0) {
      if (positives.size() > negatives.size()) {
        negatives.add(0L);
      } else {
        positives.add(0L);
      }
      zeros--;
    }

    negatives.sort(Long::compareTo);
    positives.sort(Long::compareTo);

    List<long[]> operations = new ArrayList<>(n - 1);

    while (negatives.size() + positives.size() > 1) {
      if (negatives.size() == 0) {
        // create positives
        long min = positives.remove(0);
        long max = positives.remove(positives.size() - 1);
        long val = min - max;
        long[] operation = new long[2];
        operation[0] = min;
        operation[1] = max;
        operations.add(operation);

        negatives.add(val);
        // TODO
        negatives.sort(Long::compareTo);
      } else if (positives.size() == 0) {
        // create negatives
        long min = negatives.remove(0);
        long max = negatives.remove(negatives.size() - 1);
        long val = max - min;
        long[] operation = new long[2];
        operation[0] = max;
        operation[1] = min;
        operations.add(operation);

        positives.add(val);
        // TODO
        positives.sort(Long::compareTo);
      } else if (positives.size() > negatives.size() ) {
        long min = negatives.remove(0);
        long max = positives.remove(positives.size() - 1);

        long[] operation = new long[2];
        operation[0] = min;
        operation[1] = max;
        operations.add(operation);

        negatives.add(0, min - max);
      } else {
        long min = negatives.remove(0);
        long max = positives.remove(positives.size() - 1);

        long[] operation = new long[2];
        operation[0] = max;
        operation[1] = min;
        operations.add(operation);

        positives.add(max - min);
      }
    }
    if (positives.size() > 0) {
      os.println(positives.get(0));
    } else {
      os.println(negatives.get(0));
    }
    for (long[] operation : operations) {
      os.println(operation[0] + " " + operation[1]);
    }
  }
}