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)

import bisect
n=int(input())
a=[int(i) for i in input().split()]
a.sort()
ans=[]
x=bisect.bisect_left(a, 0)
m=a[:x]
p=a[x:]
print(m,p)
if n==2 and len(p)==2:
    print(p[1]-p[0])
    print(p[1],p[0])
    exit()

if m==[]:
    m+=[p[0]-p[-1]]
    ans+=[[p[0],p[-1]]]
    del p[0]
    del p[-1]

if p==[]:
    p+=[m[-1]-m[0]]
    ans+=[[m[-1],m[0]]]
    del m[-1]
    del m[0]

while len(p)!=1:

    m+=[m[0]-p[0]]
    ans+=[[m[0],p[0]]]
    del p[0]
    del m[0]
cnt=p[0]
for i in m:
    ans+=[[cnt,i]]
    cnt-=i
print(cnt)
for i,j in ans:print(i,j)