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: Wrong Answer)

N = gets.chomp.to_i
str = gets.split
p = Array.new(0)
m = Array.new(0)
z = Array.new(0)
a = 0
b = 0
c = 0
sum = 0
for x in 0...N
  a = str[x].to_i
  if a > 0
    p.push(a)
    sum += a
  elsif a < 0
    m.push(a)
    sum -= a
  else
    z.push(a)
  end
end

if p.size == 0
  if m.size == 0
    puts 0
    for x in 1...N
      puts "0 0"
    end
    exit
  elsif m.size == 1
    c = m[0]*(-1)
    puts c
    for x in 1...N-1
      print m[0]," 0"
      puts
    end
    print "0 ",m[0]
    puts
    exit
  elsif z.size != 0
    puts sum
    b = z.pop
    c = m.pop
    print "0 ",c
    puts
    p.push(-c)
  else
    m.sort!
    c = m.pop
    m.reverse!
    b = m.pop
    sum += b*2
    puts sum
    print b," ",c
    puts
    p.push(b-c)
  end
elsif m.size == 0
  if p.size == 1
    puts p[0]
    for x in 1...N
      print m[0]," 0"
      puts
    end
    exit
  elsif z.size != 0
    puts sum
    b = z.pop
    c = p.pop
    print "0 ",c
    puts
    m.push(-c)
  else
    p.sort!
    b = p.pop
    p.reverse!
    c = p.pop
    sum -= b*2
    puts sum
    print b," ",c
    puts
    m.push(b-c)
  end
else
  puts sum
end

b = p.pop
c = m.pop
while p.size > 0
  print c," ",b
  puts
  c -= b
  b = p.pop
end

while m.size > 0
  print b," ",c
  puts
  b -= c
  c = m.pop
end

print b," ",c
puts
b -= c

for x in 1..z.size
  print b," 0"
  puts
end