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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
struct vec {
  long long l;
  long long x;
  long long y;
  int in;
};
bool cmp(vec a, vec b) { return a.x * a.x < b.x * b.x; }
int main() {
  vector<vec> v(100000);
  int ans[100000];
  long long n, xt = 0, yt = 0;
  cin >> n;
  for (int i(0); i < n; i++) {
    cin >> v[i].x >> v[i].y;
    v[i].in = i;
    v[i].l = v[i].x * v[i].x + v[i].y * v[i].y;
  }
  sort(v.begin(), v.begin() + n, cmp);
  for (int i(n - 1); i >= 0; i--) {
    if ((xt + v[i].x) * (xt + v[i].x) + (yt + v[i].y) * (yt + v[i].y) <
        (xt - v[i].x) * (xt - v[i].x) + (yt - v[i].y) * (yt - v[i].y)) {
      ans[v[i].in] = 1;
      xt += v[i].x;
      yt += v[i].y;
    } else {
      ans[v[i].in] = -1;
      xt -= v[i].x;
      yt -= v[i].y;
    }
  }
  for (int i(0); i < n; i++) cout << ans[i] << ' ';
}