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;
int n;
int pos[100003];
struct vetr {
  long long int x, y, p;
};
vetr a[100003];
long long int cal(long long int x, long long int y) {
  if (x == 0) {
    return abs(y);
  } else if (y == 0)
    return abs(x);
  else {
    long long ans = sqrt(x * x + y * y);
    return ans;
  }
}
int main() {
  cin >> n;
  int count = 0;
  for (int i = 0; i < n; ++i) {
    pos[i] = 1;
  }
  vetr ans;
  ans.x = ans.y = ans.p = 0;
  for (int i = 0; i < n; ++i) {
    cin >> a[i].x >> a[i].y;
    ans.x += a[i].x;
    ans.y += a[i].y;
  }
  ans.p = cal(ans.x, ans.y);
  if (ans.p <= 1500000) {
    for (int i = 0; i < n; ++i) {
      if (i == n - 1) {
        cout << pos[i] << endl;
      } else
        cout << pos[i] << ' ';
    }
    return 0;
  }
  for (int i = 0; i < n; ++i) {
    long long int p = ans.p;
    ans.x = ans.x - 2 * a[i].x;
    ans.y = ans.y - 2 * a[i].y;
    ans.p = cal(ans.x, ans.y);
    if (ans.p >= p) {
      ans.x = ans.x + 2 * a[i].x;
      ans.y = ans.y + 2 * a[i].y;
    } else {
      pos[i] = -1;
      if (ans.p <= 1500000) break;
    }
  }
  for (int i = 0; i < n; ++i) {
    if (i == n - 1) {
      cout << pos[i] << endl;
    } else
      cout << pos[i] << ' ';
  }
  return 0;
}