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 int maxn = 500005;
const long long Mod = 1000000007;
struct node {
  long long x, y, f;
} a[maxn];
int p[maxn];
int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  ;
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i].x >> a[i].y;
  }
  for (int i = 1; i <= n; i++) {
    p[i] = i;
  }
  long long x = 0, y = 0;
  long long sum1, sum2;
  int id;
  while (1) {
    x = 0ll;
    y = 0ll;
    random_shuffle(p + 1, p + n + 1);
    for (int i = 1; i <= n; i++) {
      id = p[i];
      sum1 = 1ll * (x + a[id].x) * (x + a[id].x) +
             1ll * (y + a[id].y) * (y + a[id].y);
      sum2 = 1ll * (x - a[id].x) * (x - a[id].x) +
             1ll * (y - a[id].y) * (y - a[id].y);
      if (sum1 <= sum2) {
        a[id].f = 1;
      } else
        a[id].f = -1;
      x += a[id].f * a[id].x;
      y += a[id].f * a[id].y;
    }
    if (x * x + y * y <= 1500000ll * 1500000ll) {
      break;
    }
  }
  for (int i = 1; i <= n; i++) {
    cout << a[i].f << ' ';
  }
  cout << endl;
  return 0;
}