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 N = 1e5 + 10;
double eps = 1.5 * 1000000;
struct node {
  long long x, y;
  double mo() { return sqrt(1.0 * x * x + y * y); }
  node operator+(node b) {
    b.x += x;
    b.y += y;
    return b;
  }
  node operator-(node b) {
    b.x = x - b.x;
    b.y = y - b.y;
    return b;
  }
} now, nxt[2], a[N];
int dir[N];
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%I64d%I64d", &a[i].x, &a[i].y);
  now.x = now.y = 0;
  a[n + 1].x = a[n + 1].y = 0;
  for (int i = 1; i <= n; i++) {
    nxt[0] = now + a[i];
    nxt[1] = now - a[i];
    if ((nxt[0] + a[i + 1]).mo() > (nxt[0] - a[i + 1]).mo())
      nxt[0] = nxt[0] - a[i + 1];
    else
      nxt[0] = nxt[0] + a[i + 1];
    if ((nxt[1] + a[i + 1]).mo() > (nxt[1] - a[i + 1]).mo())
      nxt[1] = nxt[1] - a[i + 1];
    else
      nxt[1] = nxt[1] + a[i + 1];
    if (nxt[0].mo() < nxt[1].mo()) {
      now = now + a[i];
      dir[i] = 1;
    } else {
      now = now - a[i];
      dir[i] = -1;
    }
  }
  for (int i = 1; i <= n; i++) printf("%d ", dir[i]);
  printf("\n");
  return 0;
}