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: Runtime Error)

N = int(input())
A = list(map(int, input().split()))
A.sort()
A_plus = [a for a in A if a >= 0]
A_minus = [a for a in A if a < 0]

if len(A_minus) == 0:
    M = A[-1] - (A_plus[0] - sum(A_plus[1:-1]))
elif len(A_plus) == 0:
    M = A[-1] - sum(A_plus[:-1])
else:
    M = (A_plus[-1] - sum(A_minus[1:])) - (A_minus[0] - sum(A_plus[:-1]))
print(M)

opes = []
n_max = A[-1]
n_min = A[0]
for a in A[1:-1]:
    if a >= 0:
        print(n_min, a)
        n_min -= a
    else:
        print(n_max, a)
        m_max -= a

print(n_max, n_min)