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)

def bs_left(l, target): # l=sortedのリスト, target以上の値をもつ要素のうち一番左のindexを返す
    low, high = 0, len(l)
    while low < high:
        mid = (low+high)//2
        if l[mid] < target:
            low = mid+1
        else:
            high = mid
    if low == len(l):
        return -1
    return low
N = int(input())
A = list(map(int,input().split()))
A.sort()
if A[N-1] <= 0:
    print(2*A[N-1]-sum(A))
    x = A[N-1]
    for i in range(N-1):
        y = A[N-2-i]
        print(x,y)
        x = x-y

else:
    id = bs_left(A,0)
    #print(id)
    s = -A[0]
    for i in range(1,N):
        if i < id:
            s -= A[i]
        else:
            s += A[i]
    print(s)
    if id == 0:
        x = A[0]
        for i in range(1,N-1):
            y = A[i]
            print(x,y)
            x = x-y
        print(A[N-1],x)
    else:
        x = A[0]
        for i in range(id,N-1):
            y = A[i]
            print(x,y)
            x = x-y

        print(A[N-1],x)
        x = A[N-1]-x
        for i in range(1,id):
            y = A[i]
            print(x,y)
            x = x-y