Problem: For a vector \vec{v} = (x, y), define |v| = √{x^2 + y^2}.

Allen had a bit too much to drink at the bar, which is at the origin. There are n vectors \vec{v_1}, \vec{v_2}, ⋅⋅⋅, \vec{v_n}. Allen will make n moves. As Allen's sense of direction is impaired, during the i-th move he will either move in the direction \vec{v_i} or -\vec{v_i}. In other words, if his position is currently p = (x, y), he will either move to p + \vec{v_i} or p - \vec{v_i}.

Allen doesn't want to wander too far from home (which happens to also be the bar). You need to help him figure out a sequence of moves (a sequence of signs for the vectors) such that his final position p satisfies |p| ≤ 1.5 ⋅ 10^6 so that he can stay safe.

Input

The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of moves.

Each of the following lines contains two space-separated integers x_i and y_i, meaning that \vec{v_i} = (x_i, y_i). We have that |v_i| ≤ 10^6 for all i.

Output

Output a single line containing n integers c_1, c_2, ⋅⋅⋅, c_n, each of which is either 1 or -1. Your solution is correct if the value of p = ∑_{i = 1}^n c_i \vec{v_i}, satisfies |p| ≤ 1.5 ⋅ 10^6.

It can be shown that a solution always exists under the given constraints.

Examples

Input

3
999999 0
0 999999
999999 0


Output

1 1 -1 


Input

1
-824590 246031


Output

1 


Input

8
-67761 603277
640586 -396671
46147 -122580
569609 -2112
400 914208
131792 309779
-850150 -486293
5272 721899


Output

1 1 1 1 1 1 1 -1 

Solution (in PYTHON3):

Solution:

import random
n = int(input())

V = [tuple(map(int,input().split())) for i in range(n)]

dist = lambda x,y:x*x+y*y
indices = sorted((dist(*v),i) for i,v in enumerate(V))

result = [0]*n
vx,vy = 0,0

for d,i in reversed(indices):
  x,y = V[i]
  _,c = min(((dist(vx+x,vy+y),1),(dist(vx-x,vy-y),-1)))

  vx += c*x
  vy += c*y
  result[i] = c

LIMIT = 2.25 * 10**12

while dist(vx,vy) > LIMIT:
  i = random.randrange(n)
  c = result[i]
  x,y = V[i]
  if dist(vx,vy) > dist(vx-2*c*x,vy-2*c*y):
    vx -= 2*c*x
    vy -= 2*c*y
    result[i] = -c

print(' '.join(map(str,result)))