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 = int(input())
pairs = []
x,y = 0,0
ans = []

for i in range(n):
    a,b = map(int,raw_input().split(" "))
    pairs.append((a,b))

dires =[ [1,1],[1,-1],[-1,1],[-1,-1]]
def do(a,b):
    minv = 1e18
    mini = 0
    tmp = (x,y)
    for i in range(4):
        v1,v2 = dires[i]
        s,t = x+v1*pairs[a][0]+v2*pairs[b][0],y+v1*pairs[a][1]+v2*pairs[b][1]
        if s*s+t*t<minv:
            minv = s*s+t*t
            mini = i
            tmp = (s,t)

    ans.extend(dires[mini])
    return tmp

x,y = pairs[0]
ans.append(1)
i = 1
while i+1<n:
    x,y = do(i,i+1)
    i += 2
if i<n:
    a,b = pairs[-1]
    if (x+a)*(x+a)+(y+b)*(y+b) <=(x-a)*(x-a)+(y-b)*(y-b):
        ans.append(1)
    else:
        ans.append(-1)

print " ".join(map(str,ans))