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 Python (3.4.3) (judge verdict: Wrong Answer)

from sys import stdin

if __name__ == '__main__':
    N = int(stdin.readline())
    A = [int(x) for x in stdin.readline().rstrip().split()]

    A.sort(reverse=True)
    A_max = A.pop(0)

    A_minus = [i for i in A if i < 0]
    A_plus = [j for j in A if j >= 0]

    if len(A_minus) > 0:
        print(A_max - sum(A_minus) + sum(A_plus))

        A_minus.sort()
        tmp = A_minus.pop(0)

        for j in range(len(A_plus)):
            print(str(tmp) + " " + str(A_plus[j]))
            tmp = tmp - A_plus[j]

        print(str(A_max) + " " + str(tmp))
        tmp = A_max - tmp

        for i in range(len(A_minus)):
            print(str(tmp) + " " + str(A_minus[i]))
            tmp = tmp - A_minus[i]

    else:
        A_plus.sort
        tmp = A_plus.pop(0)
        print(A_max - tmp + sum(A_plus))
        for i in range(N-2):
            print(str(tmp) + " " + str(A_plus[i]))
            tmp = tmp - A_plus[i]

        print(str(A_max) + ' ' + str(tmp))