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: Accepted)

import numpy as np

n = int(input())
A = list(map(int, input().split()))

A = np.array(A)

A = np.sort(A)

B = np.copy(A)
if n == 2:
    print(A[1] - A[0])
    print(A[1], A[0])

elif A[0] <= 0 and A[n-1] >= 0:
    for i in range(n-1):
        A[i] = min(A[i], -A[i])

    print(np.sum(A[:-1]) * -1 + A[n-1])

    k = n - 2
    a = B[0]
    while B[k] >= 0:
        print(a, B[k])
        a = a - B[k]
        k -= 1
        if k == 0:
            break

    b = B[n-1]

    while k != 0:
        print(b, B[k])
        b = b - B[k]
        k -= 1

    print(b, a)

elif A[n-1] < 0:
    A[n-1] = A[n-1] - A[n-2]
    A[n-2] = 0
    for i in range(n-1):
        A[i] = min(A[i], -A[i])

    print(np.sum(A[:-1]) * -1 + A[n-1])

    a = B[n-1]
    for i in range(n-1):
        print(a, B[i])
        a = a - B[i]

else:
    A[0] = A[0] - A[1]
    A[1] = 0
    for i in range(n-1):
        A[i] = min(A[i], -A[i])

    print(np.sum(A[:-1]) * -1 + A[n-1])

    k = n - 2
    a = B[0]
    while B[k] >= 0:
        print(a, B[k])
        a = a - B[k]
        k -= 1
        if k == 0:
            break

    b = B[n-1]

    while k != 0:
        print(b, B[k])
        b = b - B[k]
        k -= 1

    print(b, a)