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;
long long x, y;
int n, i, ans[100010];
vector<pair<bool, pair<int, int> > > v;
vector<pair<bool, int> > fren[100010];
deque<pair<int, pair<long long, long long> > > q;
void dfs(int poz) {
  for (auto it : fren[poz])
    if (!ans[it.second]) {
      if (!it.first)
        ans[it.second] = ans[poz];
      else
        ans[it.second] = -ans[poz];
      dfs(it.second);
    }
  return;
}
int main() {
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> x >> y;
    q.push_back({i, {x, y}});
  }
  while (q.size() > 2) {
    pair<long long, long long> a = q.front().second;
    int A = q.front().first;
    q.pop_front();
    pair<long long, long long> b = q.front().second;
    int B = q.front().first;
    q.pop_front();
    pair<long long, long long> c = q.front().second;
    int C = q.front().first;
    q.pop_front();
    if (((a.first + b.first) * (a.first + b.first) +
         (a.second + b.second) * (a.second + b.second)) <= 1e12) {
      a.first += b.first;
      a.second += b.second;
      v.push_back({0, {A, B}});
      q.push_back({A, a});
      q.push_back({C, c});
      continue;
    }
    if (((a.first - b.first) * (a.first - b.first) +
         (a.second - b.second) * (a.second - b.second)) <= 1e12) {
      a.first -= b.first;
      a.second -= b.second;
      v.push_back({1, {A, B}});
      q.push_back({A, a});
      q.push_back({C, c});
      continue;
    }
    if (((a.first + c.first) * (a.first + c.first) +
         (a.second + c.second) * (a.second + c.second)) <= 1e12) {
      a.first += c.first;
      a.second += c.second;
      v.push_back({0, {A, C}});
      q.push_back({A, a});
      q.push_back({B, b});
      continue;
    }
    if (((a.first - c.first) * (a.first - c.first) +
         (a.second - c.second) * (a.second - c.second)) <= 1e12) {
      a.first -= c.first;
      a.second -= c.second;
      v.push_back({1, {A, C}});
      q.push_back({A, a});
      q.push_back({B, b});
      continue;
    }
    if (((b.first + c.first) * (b.first + c.first) +
         (b.second + c.second) * (b.second + c.second)) <= 1e12) {
      b.first += c.first;
      b.second += c.second;
      v.push_back({0, {B, C}});
      q.push_back({A, a});
      q.push_back({B, b});
      continue;
    }
    if (((b.first - c.first) * (b.first - c.first) +
         (b.second - c.second) * (b.second - c.second)) <= 1e12) {
      b.first -= c.first;
      b.second -= c.second;
      v.push_back({1, {B, C}});
      q.push_back({A, a});
      q.push_back({B, b});
      continue;
    }
    cout << "jew";
  }
  pair<long long, long long> a = q.front().second;
  int A = q.front().first;
  q.pop_front();
  pair<long long, long long> b = q.front().second;
  int B = q.front().first;
  if (((a.first + b.first) * (a.first + b.first) +
       (a.second + b.second) * (a.second + b.second)) <= 1e12 * 1.5 * 1.5) {
    a.first += b.first;
    a.second += b.second;
    v.push_back({0, {A, B}});
  } else if (((a.first - b.first) * (a.first - b.first) +
              (a.second - b.second) * (a.second - b.second)) <=
             1e12 * 1.5 * 1.5) {
    a.first -= b.first;
    a.second -= b.second;
    v.push_back({1, {A, B}});
  }
  for (auto it : v) {
    fren[it.second.first].push_back({it.first, it.second.second});
    fren[it.second.second].push_back({it.first, it.second.first});
  }
  ans[1] = 1;
  dfs(1);
  for (i = 1; i <= n; i++) cout << ans[i] << ' ';
  return 0;
}