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}

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}

Examples

Input

3
1 -1 2


Output

4
-1 1
2 -2


Input

3
1 1 1


Output

1
1 1
1 0
import bisect


def solve(n, nums):
    nums.sort()
    i = bisect.bisect(nums, 0)
    if i == n:
        i -= 1
    elif i == 0:
        i += 1
    tmp1 = nums[0]
    tmp2 = nums[-1]
    buf = []
    for m in nums[1:i]:
        buf.append('{} {}'.format(tmp2, m))
        tmp2 -= m
    for m in nums[i:-1]:
        buf.append('{} {}'.format(tmp1, m))
        tmp1 -= m
    buf.append('{} {}'.format(tmp2, tmp1))
    print(tmp2 - tmp1)
    print('\n'.join(buf))


n = int(input())
nums = list(map(int, input().split()))
solve(n, nums)
