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: Runtime Error)

from bisect import bisect_left
N, *A = map(int, open(0).read().split())

B = A[:]
A_MAX = max(B)
B.remove(A_MAX)

ans = []
while len(B) > 1:
    B.sort()
    x = B.pop()
    y = B.pop()
    if y >= 0:
        idx = bisect(B, x - y)
        B = B[:idx] + [x - y] + B[idx:]
        ans.append([x, y])
    else:
        idx = bisect(B, y - x)
        B = B[:idx] + [y - x] + B[idx:]
        ans.append([y, x])
    
if B[0] <= 0:
    print(A_MAX - B[0])
    ans.append([A_MAX, B[0]])
else:
    print(B[0] - A_MAX)
    ans.append([B[0], A_MAX])
for i in range(N - 1):
    print(*ans[i])