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)

n=int(input())
a=list(map(int,input().split()))
a.sort()
if n==2:
  print(a[1]-a[0])
  print(str(a[1])+' '+str(a[0]))
  exit()
ans=0
for i in range(n):
  ans+=abs(a[i])
if a[0]>0:
  print(sum(a)-2*a[0])
elif a[-1]<0:
  print(2*a[-1]-sum(a))
else:
  print(ans)
plus=list()
minus=list()
for i in range(n):
  if a[i]>=0:
    plus.append(a[i])
  else:
    minus.append(a[i])
if len(minus)>0:
  while len(plus)>=2:
    p=plus.pop(0)
    m=minus.pop(0)
    minus.append(m-p)
    print(str(m)+' '+str(p))
if len(plus)>=2 and len(minus)==0:
  plus.sort()
  p1=plus.pop(0)
  p2=plus.pop(-1)
  minus.append(p1-p2)
  print(str(p1)+' '+str(p2))
if len(plus)==0:
  minus.sort()
  m1=minus.pop(-1)
  m2=minus.pop(-2)
  plus.append(m1-m2)
  print(str(m1)+' '+str(m2))
while len(minus)>0:
  p=plus.pop(0)
  m=minus.pop(0)
  plus.append(p-m)
  print(str(p)+' '+str(m))