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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

N=int(input())
a = list(reversed(sorted(map(int,input().split()))))

same = []
diff = []

while len(a) > 1:
    mx = a.pop(0)
    mn = a.pop(-1)
    if mx > 0 and mn < 0:
        same.append((mx,mn))
    else:
        if mx > 0 or mn > 0:
            # 両方+
            diff.append((mx,mn))
        else:
            # 両方-
            diff.append((mn,mx))

result = []
cs = []
c = True
if len(a) == 1 and a[0] > 0:
    cs.append(a[0])
    c = False

for x,y in same:
    if c:
        x,y = y,x
        c = False
    result.append((y,x))
    cs.append(y-x)

for x,y in diff:
    if c:
        x,y = y,x
        c = False
    if x < 0 or y < 0:
        x,y = y,x
        c = False
    result.append((y,x))
    cs.append(y-x)

if len(a) == 1 and a[0] < 0:
    cs.append(a[0])

sm = cs.pop(0)
while len(cs) > 0:
    y = cs.pop(0)
    result.append((sm, y))
    sm += -1*y

print(sm)

for r in result:
    print(r[0],r[1])