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>
const long long maxn = 1e5 + 10;
inline long long Max(long long a, long long b) { return a > b ? a : b; }
inline long long Min(long long a, long long b) { return a > b ? b : a; }
inline long long read() {
  long long f = 1, r = 0;
  char c = getchar();
  while (!isdigit(c)) {
    if (c == '-') {
      f = -1;
    }
    c = getchar();
  }
  while (isdigit(c)) {
    r = 10 * r + c - '0';
    c = getchar();
  }
  return f * r;
}
inline void write(long long x) {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) write(x / 10);
  putchar(x % 10 + '0');
}
inline void writesp(long long x) { write(x), putchar(' '); }
inline void writeln(long long x) { write(x), puts(""); }
long long N, ans[maxn];
struct {
  long long x, y, id;
} nodes[maxn];
signed main() {
  N = read();
  std::srand(time(NULL));
  for (register long long i = 1; i <= N; ++i) {
    nodes[i].x = read(), nodes[i].y = read(), nodes[i].id = i;
  }
  while (true) {
    long long px = nodes[1].x, py = nodes[1].y;
    ans[nodes[1].id] = 1;
    for (register long long i = 2; i <= N; ++i) {
      long long x1 = px + nodes[i].x, y1 = py + nodes[i].y;
      long long x2 = px - nodes[i].x, y2 = py - nodes[i].y;
      long long t1 = x1 * x1 + y1 * y1, t2 = x2 * x2 + y2 * y2;
      if (t1 > t2) {
        ans[nodes[i].id] = -1, px = x2, py = y2;
      } else {
        ans[nodes[i].id] = 1, px = x1, py = y1;
      }
    }
    if (px * px + py * py <= 2250000000000LL) {
      break;
    } else {
      std::random_shuffle(nodes + 1, nodes + 1 + N);
    }
  }
  for (long long i = 1; i <= N; i++) writesp(ans[i] == 1 ? 1 : -1);
  return 0;
}