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 long long N = 1e5 + 5;
long long read() {
  long long s = 0;
  char c = getchar(), lc = '+';
  while (c < '0' || '9' < c) lc = c, c = getchar();
  while ('0' <= c && c <= '9') s = s * 10 + c - '0', c = getchar();
  return lc == '-' ? -s : s;
}
void write(long long first) {
  if (first < 0) {
    putchar('-');
    first = -first;
  }
  if (first < 10)
    putchar(first + '0');
  else {
    write(first / 10);
    putchar(first % 10 + '0');
  }
}
void print(long long first, char c = '\n') {
  write(first);
  putchar(c);
}
struct point {
  long long first, second;
  bool operator<(const point &a) const {
    return first * first + second * second <
           a.first * a.first + a.second * a.second;
  }
  point operator+(pair<long long, long long> a) const {
    point ret = *this;
    ret.first += a.first;
    ret.second += a.second;
    return ret;
  }
} now;
pair<pair<long long, long long>, long long> a[N];
long long ans[N];
signed main() {
  long long n = read();
  for (long long i = 1; i <= n; i++) {
    a[i].first.first = read();
    a[i].first.second = read();
    a[i].second = i;
  }
  while (1) {
    now.first = now.second = 0;
    for (long long i = 1; i <= n; i++)
      if ((now + make_pair(a[i].first.first, a[i].first.second)) <
          (now + make_pair(-a[i].first.first, -a[i].first.second))) {
        now = now + make_pair(a[i].first.first, a[i].first.second);
        ans[a[i].second] = 1;
      } else {
        now = now + make_pair(-a[i].first.first, -a[i].first.second);
        ans[a[i].second] = -1;
      }
    if (sqrt(now.first * now.first + now.second * now.second) <= 1.5e6) {
      for (long long i = 1; i <= n; i++) print(ans[i], ' ');
      return 0;
    }
    random_shuffle(a + 1, a + 1 + n);
  }
  return 0;
}