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 Ruby (2.3.3) (judge verdict: Accepted)

N=gets
A=gets.split.map(&:to_i)
A.sort!
pos,neg=A.partition{|i| i>=0}
if neg.size==0
  puts pos.inject(:+)-pos[0]*2
	temp=pos.shift
	while pos.size>1
		a=pos.pop
		puts "#{temp} #{a}"
    temp-=a
  end
	a=pos.pop
	puts "#{a} #{temp}"
	temp=a-temp
elsif pos.size==0
  puts -(neg.inject(:+)-neg[-1]*2)
	temp=neg.pop
	while neg.size>0
		a=neg.shift
		puts "#{temp} #{a}"
    temp-=a
  end
else
  puts pos.inject(:+)-neg.inject(:+)
	temp=neg.pop
	while pos.size>1
		a=pos.pop
		puts "#{temp} #{a}"
    temp-=a
  end
	a=pos.pop
	puts "#{a} #{temp}"
	temp=a-temp
	while neg.size>0
		a=neg.shift
		puts "#{temp} #{a}"
		temp-=a
  end
end