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;
const long long INF = 1e9 + 5;
const double eps = 1e-7;
pair<double, double> operator+(pair<double, double> a, pair<double, double> b) {
  return make_pair(a.first + b.first, a.second + b.second);
}
pair<double, double> operator-(pair<double, double> a, pair<double, double> b) {
  return make_pair(a.first - b.first, a.second - b.second);
}
double dist(pair<double, double> a) {
  return sqrt(a.first * a.first + a.second * a.second);
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  srand(time(NULL));
  int n;
  cin >> n;
  vector<int> ans(n);
  vector<pair<pair<double, double>, int>> aa(n);
  pair<double, double> p;
  for (long long i = 0; i < (long long)n; i++) {
    cin >> aa[i].first.first >> aa[i].first.second;
    aa[i].second = i;
  }
  random_shuffle(aa.begin(), aa.end());
  for (long long i = 0; i < (long long)n; i++) {
    if (dist(p + aa[i].first) < dist(p - aa[i].first)) {
      p = p + aa[i].first;
      ans[aa[i].second] = 1;
    } else {
      p = p - aa[i].first;
      ans[aa[i].second] = -1;
    }
  }
  assert(dist(p) <= 1.5e6 + eps);
  for (long long i = 0; i < (long long)n; i++) {
    cout << ans[i] << " ";
  }
}