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 PYTHON):

Solution:
# randomized greedy solution

from sys import stdin, stdout
from random import seed, shuffle

seed(0x5ad5eed)

n = input()
inp = stdin.readlines()

pts = [0 for i in xrange(n)]
pos = [i for i in xrange(n)]
ans = [0 for i in xrange(n)]

i = 0
for line in inp:
    pts[i] = tuple(map(int, line.split()))
    i += 1

R = 1500000 ** 2

while True:
    X, Y = 0, 0
    
    for i in pos:
        x1, y1 = X + pts[i][0], Y + pts[i][1]
        x2, y2 = X - pts[i][0], Y - pts[i][1]

        if (x1 * x1 + y1 * y1 < x2 * x2 + y2 * y2):
            ans[i] = 1
            X, Y = x1, y1
        else:
            ans[i] = -1
            X, Y = x2, y2
        
    if X * X + Y * Y <= R: break

    shuffle(pos)
        
out = [str(ans[i]) for i in xrange(n)]
stdout.write(' '.join(out))