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:
n=int(input())
l=[]
def d(x,y):
	return x**2 + y**2
lv=[0 for i in range(n)]
for i in range(n):
	l1=list(map(int,input().strip().split()))
	l.append(l1)
vx=l[0][0]
vy=l[0][1]
lv[0]=1
for i in range(1,n-1,2):
	vx1,vy1,vx2,vy2=l[i][0],l[i][1],l[i+1][0],l[i+1][1]
	_,c1,c2=min((d(vx+vx1+vx2,vy+vy1+vy2),1,1),(d(vx+vx1-vx2,vy+vy1-vy2),1,-1),(d(vx-vx1+vx2,vy-vy1+vy2),-1,1),(d(vx-vx1-vx2,vy-vy1-vy2),-1,-1))
	vx=vx+c1*vx1+c2*vx2
	vy=vy+vy1*c1+vy2*c2
	lv[i]=c1
	lv[i+1]=c2
if (lv[n-1]==0):
	_,c1=min((d(vx+l[n-1][0],vy+l[n-1][1]),1),(d(vx-l[n-1][0],vy-l[n-1][1]),-1))
	lv[n-1]=c1
print (" ".join(map(str,lv)))