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:
"""
n=8
ttt=[[-67761, 603277],
[640586, -396671],
[46147, -122580],
[569609, -2112],
[400, 914208],
[131792, 309779],
[-850150, -486293],
[5272, 721899]]
"""

n=int(raw_input())
a=[]
xt,yt=0,0
for i in range(n):
    x,y=map(int,raw_input().split())
    #x,y=ttt[i]
    a.append([x*x+y*y,x,y,i])
    xt+=x
    yt+=y

L=1500000*1500000

an=[1 for i in range(n)]
if xt*xt+yt*yt<=L:
    sa=map(str,an)
    print ' '.join(sa)
    exit()

a.sort(reverse=True)

Dis=a[0][0]
x,y=a[0][1],a[0][2]

for i in range(1,n):
    if (x+a[i][1])*(x+a[i][1])+(y+a[i][2])*(y+a[i][2])> (x-a[i][1])*(x-a[i][1])+(y-a[i][2])*(y-a[i][2]):
        an[a[i][3]]=-1
    x+=an[a[i][3]]*a[i][1]
    y+=an[a[i][3]]*a[i][2]

if x*x+y*y<=L:
    sa=map(str,an)
    print ' '.join(sa)
    exit()

for i in range(n):
    xd=2*an[a[i][3]]*a[i][1]
    yd=2*an[a[i][3]]*a[i][2]
    if (x-xd)*(x-xd)+(y-yd)*(y-yd)<=L:
        an[a[i][3]]*=-1
        sa=map(str,an)
        print ' '.join(sa)
        exit()