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)

import numpy as np
N = int(input())
A = list(map(int,input().split()))

A.sort()
A = np.array(A)

if A[0] < 0 and A[N - 1] > 0:
	print(sum(np.abs(A)))
	total = A[0]
	i = N - 1
	first_ = 0
	second_ = 0
	while i > 1:
		if A[i-1] >= 0:
			first_ = total
			second_ = A[i]
		else:
			first_ = A[i]
			second_ = total
		print(first_,second_)
		total = first_ - second_
		i -= 1
	if A[1] >= 0:
		print(A[1],-1*abs(total))
	else:
		print((abs(total)),A[1])
		
elif A[0] >= 0:
	sum_A = sum(A)
	print(sum_A - A[0] * 2)
	total = A[0]
	for i in range(N-2):
		print(total,A[i+1])
		total = total - A[i+1]
	print(A[N-1],total)
	
else:
	sum_A = -1 * (sum(A))
	print(sum_A + A[N-1] * 2)
	total = A[N-1]
	for i in range(N-2):
		print(total,A[N-2-i])
		total = total - A[N-2-i]
	print(total,A[0])