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 (2.7.1) (judge verdict: Wrong Answer)

#input of int(split by space)
def get_i()
  return gets.chomp.split(" ").map(&:to_i)
end
#input of float(split by space)
def get_f()
  return gets.chomp.split(" ").map(&:to_f)
end
#input of string(split by space)
def get()
  return gets.chomp.split(" ")
end
#input of string(split per one character)
def get_nsp()
  return gets.chomp.split("")
end
#yes or no decision
def yn_judge(bool,y="Yes",n="No")
  return bool ? y : n 
end
#create of array
def array(size1,init=nil,size2=-1)
  if size2==-1
      return Array.new(size1){init}
  else
      return Array.new(size2){Array.new(size1){init}}
  end
end

def max(a,b)
    return a>b ? a : b
end

def min(a,b)
    return a>b ? b : a
end

INF=Float::INFINITY

N=gets.to_i
a=get_i.sort!
cnt_ps=a.count{|x| x>=0}
cnt_ng=a.count{|x| x<=0}
if cnt_ps!=N and cnt_ng!=N
    ps=a.select{|x| x>0}
    ng=a.select{|x| x<=0}
    num1=ps.pop
    num2=ng.pop
    ans=[]
    ps.each do|n|
        ans.push([num2,n])
        num2-=n
    end
    ng.each do|n|
        ans.push([num1,n])
        num1-=n
    end
    ans.push([num1,num2])
    num1-=num2
    puts num1
    ans.each do|arr|
        puts arr.join(" ")
    end
    exit
end
ans=[]
if N.odd?
  (N/2).times do
    ans.push(a.pop)
    ans.push(a.shift)
  end
  ans.push(a.pop)
else
  (N/2).times do
      ans.push(a.shift)
      ans.push(a.pop)
  end
end
operate=[]
(N-1).times do|i|
  operate.push([ans[i+1],ans[i]])
  ans[i+1]-=ans[i]  
end
puts ans[N-1]
(N-1).times do|i|
    puts operate[i].join(" ")
end