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)



def input_from_console():
    n = int(input())
    a_list = list(map(int, input().split()))
    return n, a_list


import bisect


def solve(n, a_list):
    a_list.sort()

    steps = []
    m = 0

    while len(a_list) > 2:
        minimum = a_list.pop(0)
        maximum = a_list.pop(len(a_list) - 1)
        steps.append("{} {}".format(minimum, maximum))
        m = minimum - maximum
        bisect.insort(a_list, m)

    steps.append("{} {}".format(a_list[1], a_list[0]))
    result = str(a_list[1] - a_list[0]) + "\n" + "\n".join(steps)
    return result


def main():
    n, a_list = input_from_console()
    print(solve(n, a_list))


if __name__ == "__main__":
    import sys

    if sys.gettrace():  # Check if the python interpreter is in debug mode or not.
        check_cases()
    else:
        main()