p03007 diverta 2019 Programming Contest 2 - Successive Subtraction
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
```python
n,*a=map(int,open(0).read().split())
a.sort()
print(sum(abs(i)for i in a)-2*min(abs(a[-1]),abs(a[0]))*(a[0]*a[-1]>0))
if a[0]>0:
    print(a[0],a[-1])
    a[0]-=a[-1]
    for i in a[1:-2]:
        print(a[0],i)
        a[0]-=i
    print(a[-2],a[0])
elif a[-1]<0:
    for i in a[:-1]:
        print(a[-1],i)
        a[-1]-=i
else:
    for i in a[1:-1]:
        if i<0:
            print(a[-1],i)
            a[-1]-=i
        else:
            print(a[0],i)
            a[0]-=i
    print(a[-1],a[0])
```