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: Accepted)

n = int(input())
arr = sorted(list(map(int,input().split())))
ans = 0
ok1 = False
ok2 = False
for i in arr:
    if i > 0:
        ok1 = True
    else:
        ok2 = True
if ok1 and ok2:
    for i in arr:
        ans += i if i > 0 else -i
    print(ans)
    ope1 = arr.pop()
    ope2 = arr.pop(0)
    for a in arr:
        if a > 0:
            print(ope2,a)
            ope2 -= a
        else:
            print(ope1,a)
            ope1 -= a
    print(ope1,ope2)
else:
    if ok1:
        ans = sum(arr) - 2*arr[0]
        print(ans)
        ope1 = arr.pop(0)
        for i in range(n-2):
            print(ope1,arr[i])
            ope1 -= arr[i]
        print(arr[-1],ope1)
    else:
        ans = -sum(arr) + 2*arr[-1]
        print(ans)
        ope2 = arr.pop(-1)
        for i in range(n-1):
            print(ope2,arr[i])
            ope2 -= arr[i]