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: Runtime Error)


N = gets.to_i
if N == 2
	s,t = gets.split.map(&:to_i)
	u =  [(s-t),(t-s)].max
	p u
	if s - t == u
		puts "#{s} #{t}"
	else
		puts "#{t} #{s}"
	end
	exit(0)
end
aa = gets.split.map(&:to_i).sort_by(&:abs)
t= aa.shift
res = t
resa = [[t,t]]

i

aa.each do |a|
	if (resa[-1][0]-a).abs > (resa[-1][1]-a).abs
		resa << [resa[-1][0]-a,a-resa[-1][0]]
	else
		resa << [resa[-1][1]-a,a-resa[-1][1]]
	end
end

#p resa
s = resa.pop[0].abs
p s
res = []
resa.reverse_each{|x|
	t = aa.pop
	if t - x[0] == s
		res.unshift [ t,s=x[0]]
	elsif t - x[1] == s
		res.unshift [t, s=x[1]]
	elsif x[0] - t == s
		res.unshift [s=x[0], t]
	elsif x[1] - t == s
		res.unshift [s=x[1], t]
	else
		#err
		exit(1)
	end

	#	end

}
res.each{|x|puts x*" "}