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;
bool cmp(pair<pair<long long, long long>, long long> x,
         pair<pair<long long, long long>, long long> y) {
  long long x1 = x.first.first, y1 = x.first.second;
  long long x2 = y.first.first, y2 = y.first.second;
  long long p = x1 * x1 + y1 * y1;
  long long n = x2 * x2 + y2 * y2;
  return (p < n);
}
int main(int argc, char const *argv[]) {
  int n;
  cin >> n;
  vector<pair<pair<long long, long long>, long long> > v(n);
  for (int i = 0; i < n; i++)
    cin >> v[i].first.first >> v[i].first.second, v[i].second = i;
  vector<int> ar(n);
  long long x = 0, y = 0;
  for (int i = n - 1; i >= 0; i--) {
    long long x1 = x + v[i].first.first, y1 = y + v[i].first.second;
    long long x2 = x - v[i].first.first, y2 = y - v[i].first.second;
    long long p = x1 * x1 + y1 * y1;
    long long n = x2 * x2 + y2 * y2;
    if (p > n) {
      x = x2;
      y = y2;
      ar[v[i].second] = -1;
    } else {
      x = x1;
      y = y1;
      ar[v[i].second] = 1;
    }
  }
  for (int i = 0; i < n; i++) cout << ar[i] << " ";
  cout << endl;
  return 0;
}