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: Runtime Error)

from collections import deque
N = int(input())
A = list(map(int, input().split()))
bb = deque(sorted(A))
x = [0]*(N-1)
y = [0]*(N-1)
start_bool = 1 if N % 2 == 0 else -1
for i in range(N-1):
    print(bb)
    l = bb.popleft()
    r = bb.pop()
    if start_bool < 0:
        if l > r:
            ret = r - l
            x[i] = r
            y[i] = l
        else:
            ret = l - r
            x[i] = l
            y[i] = r
    else:
        if l > r:
            ret = l - r
            x[i] = l
            y[i] = r
        else:
            ret = r - l
            x[i] = r
            y[i] = l
    if ret > 0:
        bb.append(ret)
    else:
        bb.appendleft(ret)
    start_bool *= -1
print(bb.pop())
for i in range(N-1):
    print(x[i], y[i])