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 Python (3.4.3) (judge verdict: Wrong Answer)

from collections import deque
import sys
INPUT = sys.stdin.readline

def SINGLE_INT(): return int(INPUT())
def MULTIPLE_INT_LIST(): return list(map(int, INPUT().split()))
def MULTIPLE_INT_MAP(): return map(int, INPUT().split())
def SINGLE_STRING(): return INPUT()
def MULTIPLE_STRING(): return INPUT().split()

N = SINGLE_INT()
arr = MULTIPLE_INT_LIST()
arr.sort()

if N == 2:
    print(arr[1] - arr[0])
    print(arr[1], arr[0])

else:
    left = 0
    right = N - 1

    positives = (N + 1) // 2

    print(sum(arr[-positives:]) - sum(arr[:-positives]))

    if N % 2 == 1:
        # init
        print(arr[0], arr[N-1])
        last = arr[0] - arr[N-1]
        right -= 1
        left += 1

        for i in range(1,N-1):
            if i % 2 == 1:
                print(arr[right], last)
                last = arr[right] - last
                right -= 1
            else:
                print(arr[left], last)
                last = arr[left] - last
                left += 1

    else:
        # init
        print(arr[N-1], arr[0])
        last = arr[N-1] - arr[0]
        right -= 1
        left += 1

        for i in range(1, N-1):
            if i % 2 == 1:
                print(arr[left], last)
                last = arr[left] - last
                left += 1
            else:
                print(arr[right], last)
                last = arr[right] - last
                right -= 1