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 point {
  long long x, y;
  point() { x = y = (long long)0; }
  point(long long _x, long long _y) : x(_x), y(_y) {}
  bool operator<(point other) const {
    return x * x + y * y < other.x * other.x + other.y * other.y;
  }
};
struct vec {
  long long x, y, idx;
  vec() { x = y = idx = (long long)0; }
  vec(long long _x, long long _y, long long _i) : x(_x), y(_y), idx(_i) {}
};
int main() {
  long long n, x, y;
  cin >> n;
  vector<vec> vc(n);
  for (long long i = 0; i < n; i++) {
    cin >> x >> y;
    vc[i] = vec(x, y, i);
  }
  bool res[n];
  while (true) {
    point p = point(0, 0);
    random_shuffle(vc.begin(), vc.end());
    for (long long i = 0; i < n; i++) {
      point p1, p2;
      p1 = point(p.x + vc[i].x, p.y + vc[i].y);
      p2 = point(p.x - vc[i].x, p.y - vc[i].y);
      if (p2 < p1) {
        p = p2;
        res[vc[i].idx] = false;
      } else {
        p = p1;
        res[vc[i].idx] = true;
      }
    }
    if (p.x * p.x + p.y * p.y <= 2.25 * (1e12)) break;
  }
  for (long long i = 0; i < n; i++) cout << (res[i] ? 1 : -1) << " ";
}