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 x, y;
};
long double mag(vec a) { return sqrt(a.x * a.x + a.y * a.y); }
vec operator+(vec a, vec b) { return {a.x + b.x, a.y + b.y}; }
vec operator-(vec a, vec b) { return {a.x - b.x, a.y - b.y}; }
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  cin >> n;
  vector<pair<vec, int>> v(n);
  for (int i = 0; i < n; ++i) {
    long long x, y;
    cin >> x >> y;
    v[i] = {{x, y}, i};
  }
  reverse(begin(v), end(v));
  vec cur = v[0].first;
  vector<int> vals(n);
  vals[v[0].second] = 1;
  for (int i = 1; i < n; ++i) {
    if (mag(cur + v[i].first) < mag(cur - v[i].first)) {
      cur = cur + v[i].first;
      vals[v[i].second] = 1;
    } else {
      cur = cur - v[i].first;
      vals[v[i].second] = -1;
    }
  }
  for (int i : vals) cout << i << " ";
  cout << "\n";
}