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 double PI = acos(-1.0);
const int INF = 0x3f3f3f3f;
const long long INFF = 0x3f3f3f3f3f3f3f3f;
const long long mod = 1e9 + 7;
const double eps = 1e-8;
const int maxn = 100005;
const int maxm = 200005;
struct node {
  int x, y;
  long double len;
  int id;
  bool operator<(const node b) { return len > b.len; }
};
vector<node> v;
int ans[maxn];
int n;
void solve() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    long double len = (long long)x * x + (long long)y * y;
    v.push_back((node){x, y, len, i});
  }
  long long ansx = 0, ansy = 0;
  for (int i = n - 1; i >= 0; i--) {
    double p, n;
    p = (ansx + v[i].x) * (ansx + v[i].x) + (ansy + v[i].y) * (ansy + v[i].y);
    n = (ansx - v[i].x) * (ansx - v[i].x) + (ansy - v[i].y) * (ansy - v[i].y);
    if (p <= n) {
      ans[v[i].id] = 1;
      ansx += v[i].x;
      ansy += v[i].y;
    } else {
      ans[v[i].id] = -1;
      ansx -= v[i].x;
      ansy -= v[i].y;
    }
  }
  for (int i = 0; i < n; i++) {
    printf("%d%c", ans[i], i == n - 1 ? '\n' : ' ');
  }
  return;
}
int main() {
  solve();
  return 0;
}