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>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
ifstream in("test.in");
ofstream out("test.out");
const int DIM = 1e5 + 5;
int vx[DIM], vy[DIM], ans[DIM];
long long value(int x, int y) { return 1LL * x * x + 1LL * y * y; }
int main(void) {
  int n;
  cin >> n;
  int x = 0, y = 0;
  for (int i = 1; i <= n; ++i) {
    cin >> vx[i] >> vy[i];
  }
  for (int i = n; i >= 1; --i) {
    if (value(x + vx[i], y + vy[i]) <= value(x - vx[i], y - vy[i])) {
      ans[i] = 1;
      x += vx[i];
      y += vy[i];
    } else {
      ans[i] = -1;
      x -= vx[i];
      y -= vy[i];
    }
  }
  for (int i = 1; i <= n; ++i) {
    cout << ans[i] << " ";
  }
  return 0;
}