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 (3.8.2) (judge verdict: Runtime Error)

import bisect, collections, copy, heapq, itertools, math, string, sys
input = lambda: sys.stdin.readline().rstrip() 
sys.setrecursionlimit(10**7)
INF = float('inf')
def I(): return int(input())
def F(): return float(input())
def SS(): return input()
def LI(): return [int(x) for x in input().split()]
def LI_(): return [int(x)-1 for x in input().split()]
def LF(): return [float(x) for x in input().split()]
def LSS(): return input().split()

def resolve():
    H, W = LI()
    A = [SS() for _ in range(H)]

    d = ((1, 0), (0, 1), (-1, 0), (0, -1))

    dist = [[INF] * W for i in range(H)]
    que = collections.deque()

    for i, j in itertools.product(range(H), range(W)):
        if A[i][j] == '#':
            que.append((i, j))
            dist[i][j] = 0

    while que:
        cy, cx = que.popleft()
        for dy, dx in d:
            ny = cy + dy
            nx = cx + dx
            if 0 <= ny < H and 0 <= nx < W and dist[cy][cx] + 1 < dist[ny][nx]:
                dist[ny][nx] = dist[cy][cx] + 1
                que.append((ny, nx))

    # for i in dist:
    #     print(i)

    ans = max([max(i) for i in dist])
    print(ans)

if __name__ == '__main__':
    resolve()