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 PyPy3 (2.4.0) (judge verdict: Accepted)

from collections import deque


N = int(input())
A = list(map(int, input().split()))
A.sort()
queue_plus = deque()
queue_minus = deque()
for A_i in A:
    if A_i < 0:
        queue_minus.append(A_i)
    else:
        queue_plus.append(A_i)

xy = [[] for _ in range(N-1)]
cnt = 0
if len(queue_plus) == 0:
    x = queue_minus.pop()
    y = queue_minus.pop()
    xy[cnt] = [x, y]
    cnt += 1
    queue_plus.append(x - y)
elif len(queue_minus) == 0:
    x = queue_plus.popleft()
    y = queue_plus.popleft()
    xy[cnt] = [x, y]
    cnt += 1
    queue_minus.append(x - y)
while len(queue_plus) > 0 and len(queue_minus) > 1:
    x = queue_plus.pop()
    y = queue_minus.pop()
    xy[cnt] = [x, y]
    cnt += 1
    queue_plus.append(x - y)
while len(queue_plus) > 1 and len(queue_minus) > 0:
    x = queue_minus.pop()
    y = queue_plus.pop()
    xy[cnt] = [x, y]
    cnt += 1
    queue_minus.append(x - y)
if len(queue_plus) + len(queue_minus) == 1:
    if len(queue_plus) > 0:
        print(queue_plus.pop())
    else:
        print(queue_minus.pop())
else:
    x = queue_plus.pop()
    y = queue_minus.pop()
    xy[cnt] = [x, y]
    ans = x - y
    print(ans)
for x_y in xy:
    print(" ".join(map(str, x_y)))