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;
using ll = long long;
using l = long;
const ll FINAL_SAFE = 2250000000000LL;
const ll L = 1000000000000LL;
bool safe(ll x1, ll y1, ll x2, ll y2) {
  return (x1 + x2) * (x1 + x2) + (y1 + y2) * (y1 + y2) <= L;
}
bool fsafe(ll x1, ll y1, ll x2, ll y2) {
  return (x1 + x2) * (x1 + x2) + (y1 + y2) * (y1 + y2) <= FINAL_SAFE;
}
int trace(l i, vector<l>& pred, vector<int>& sgn) {
  if (i != pred[i]) {
    sgn[i] = sgn[i] * trace(pred[i], pred, sgn);
    pred[i] = i;
  }
  return sgn[i];
}
int main() {
  l n;
  while (cin >> n) {
    if (n == 1) {
      ll x;
      cin >> x >> x;
      cout << 1 << endl;
    } else if (n == 2) {
      ll x1, y1, x2, y2;
      cin >> x1 >> y1 >> x2 >> y2;
      if (safe(x1, y1, x2, y2))
        cout << 1 << " " << 1 << endl;
      else
        cout << 1 << " " << -1 << endl;
    } else {
      vector<l> pred(2 * n);
      vector<int> sgn(2 * n);
      l next = n - 1;
      l it = 3;
      ll x1, y1, x2, y2, x3, y3;
      l i1, i2, i3;
      cin >> x1 >> y1;
      cin >> x2 >> y2;
      i1 = 0;
      i2 = 1;
      i3 = 2;
      while (cin >> x3 >> y3) {
        if (safe(x1, y1, x2, y2)) {
          sgn[i1] = 1;
          sgn[i2] = 1;
          pred[i1] = pred[i2] = ++next;
          i1 = next;
          x1 = x1 + x2;
          y1 = y1 + y2;
          i2 = i3;
          x2 = x3;
          y2 = y3;
          i3 = it++;
        } else if (safe(x1, y1, -x2, -y2)) {
          sgn[i1] = 1;
          sgn[i2] = -1;
          pred[i1] = pred[i2] = ++next;
          i1 = next;
          x1 = x1 - x2;
          y1 = y1 - y2;
          i2 = i3;
          x2 = x3;
          y2 = y3;
          i3 = it++;
        } else if (safe(x1, y1, x3, y3)) {
          sgn[i1] = 1;
          sgn[i3] = 1;
          pred[i1] = pred[i3] = ++next;
          i1 = next;
          x1 = x1 + x3;
          y1 = y1 + y3;
          i2 = i2;
          x2 = x2;
          y2 = y2;
          i3 = it++;
        } else if (safe(x1, y1, -x3, -y3)) {
          sgn[i1] = 1;
          sgn[i3] = -1;
          pred[i1] = pred[i3] = ++next;
          i1 = next;
          x1 = x1 - x3;
          y1 = y1 - y3;
          i2 = i2;
          x2 = x2;
          y2 = y2;
          i3 = it++;
        } else if (safe(x2, y2, x3, y3)) {
          sgn[i2] = 1;
          sgn[i3] = 1;
          pred[i2] = pred[i3] = ++next;
          ll temp_x = x2 + x3;
          ll temp_y = y2 + y3;
          i2 = i1;
          x2 = x1;
          y2 = y1;
          i1 = next;
          x1 = temp_x;
          y1 = temp_y;
          i3 = it++;
        } else if (safe(x2, y2, -x3, -y3)) {
          sgn[i2] = 1;
          sgn[i3] = -1;
          pred[i2] = pred[i3] = ++next;
          ll temp_x = x2 - x3;
          ll temp_y = y2 - y3;
          i2 = i1;
          x2 = x1;
          y2 = y1;
          i1 = next;
          x1 = temp_x;
          y1 = temp_y;
          i3 = it++;
        } else
          cout << "never safe pre" << endl;
      }
      if (fsafe(x1, y1, x2, y2)) {
        sgn[i1] = 1;
        sgn[i2] = 1;
      } else if (fsafe(x1, y1, -x2, -y2)) {
        sgn[i1] = 1;
        sgn[i2] = -1;
      } else
        cout << "never safe" << endl;
      pred[i1] = i1;
      pred[i2] = i2;
      for (l i = 0; i < n; ++i) {
        trace(i, pred, sgn);
        cout << sgn[i] << (i != n - 1 ? " " : "");
      }
      cout << endl;
    }
  }
}