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 node {
  int index;
  long long x;
  long long y;
};
node make_node(long long x, long long y) {
  node newnode;
  newnode.x = x;
  newnode.y = y;
  return newnode;
}
long long dist(node pos) { return (pos.x * pos.x + pos.y * pos.y); }
bool sort_by_index(node& p1, node& p2) { return p1.index < p2.index; }
int main() {
  int n;
  cin >> n;
  node a[n];
  node curr;
  int c[n];
  for (int i = 0; i < n; ++i) {
    cin >> a[i].x >> a[i].y;
    a[i].index = i;
  }
  for (int iter = 0; iter < 5; ++iter) {
    curr = a[0];
    c[a[0].index] = 1;
    for (int i = 1; i < n; ++i) {
      if (dist(make_node((curr.x + a[i].x), (curr.y + a[i].y))) <
          dist(make_node((curr.x - a[i].x), (curr.y - a[i].y)))) {
        c[a[i].index] = 1;
        curr.x += a[i].x;
        curr.y += a[i].y;
      } else {
        c[a[i].index] = -1;
        curr.x -= a[i].x;
        curr.y -= a[i].y;
      }
    }
    if (dist(curr) < 2.25e12) {
      break;
    } else {
      random_shuffle(a, a + n);
    }
  }
  for (int i = 0; i < n; ++i) {
    cout << c[i] << " ";
  }
  cout << "\n";
}