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 = [int(i) for i in input().split()]
a.sort()
if n % 2 == 0:
    k = n // 2
else:
    k = (n // 2) + 1
a_1 = a[0:k]
a_2 = a[k:]
ans = sum(a_2) - sum(a_1)
print(ans)
if n % 2 == 1:
    for i in range(n - 1):
        if i == 0:
            x = a_2.pop(0)
            y = a_1.pop(0)
            print(str(x) + " " + str(y))
        else:
            if i == n - 2:
                x = x - y
                y = a_1.pop(0)
                print(str(x) + " " + str(y))
            elif i % 2 == 0:
                y = x - y
                x = a_2.pop(0)
                print(str(x) + " " + str(y))
            elif i % 2 == 1:
                y = x - y
                x = a_1.pop(0)
                print(str(x) + " " + str(y))
                
elif n % 2 == 0:
    for i in range(n - 1):
        if i == 0:
            x = a_2.pop(0)
            y = a_1.pop(0)
            print(str(x) + " " + str(y))
        else:
            if i % 2 == 0:
                y = x - y
                x = a_2.pop(0)
                print(str(x) + " " + str(y))
            elif i % 2 == 1:
                y = x - y
                x = a_1.pop(0)
                print(str(x) + " " + str(y))