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 = [0]*N
A = list(map(int, input().split()))
ans = int(0)
x = int(0)
y = int(0)

As = sorted(A)

if As[0]>0:
    for i in range(N):
        ans += As[i]

    ans -=As[0]*2
    print(ans)

    x = As[0]
    for i in range(N-2):
        y = As[i+1]
        print(x,y)
        x = x - y

    y = x
    x = As[N-1]
    print(x,y)

elif As[N-1]<0:
    for i in range(N):
        As[i] *= -1
    for i in range(N):
        ans += As[i]

    ans -=As[N-1]*2
    print(ans)

    As = sorted(As)

    x = As[0]
    for i in range(N-2):
        y = As[i+1]
        print(-x,-y)
        x = x - y

    y = x
    x = As[N-1]
    print(-y,-x)

##################################
else:
    for i in range(N):
        ans += abs(As[i])

    print(ans)

    x = As[N-1]
    for i in range(N-2):
        y = As[i]
        print(x,y)
        x = x - y

    y = As[N-2]
    print(x,y)