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 C = 1000000000000;
pair<long long, long long> v[100005];
long long ans[100005];
long long sumnorm(pair<long long, long long> u, pair<long long, long long> w) {
  return ((u.first + w.first) * (u.first + w.first) +
          (u.second + w.second) * (u.second + w.second));
}
long long diffnorm(pair<long long, long long> u, pair<long long, long long> w) {
  return ((u.first - w.first) * (u.first - w.first) +
          (u.second - w.second) * (u.second - w.second));
}
int32_t main() {
  long long N;
  cin >> N;
  if (N == 1) {
    cout << 1 << endl;
    return 0;
  }
  for (long long i = 0; i < N; i++) cin >> v[i].first >> v[i].second;
  vector<pair<pair<long long, long long>, vector<pair<bool, long long>>>> vect;
  vector<pair<pair<long long, long long>,
              vector<pair<bool, long long>>>>::iterator it,
      iu, iv;
  vector<pair<bool, long long>> temp, temq, temr, tems;
  for (long long i = 0; i < N; i++) {
    temp.clear();
    temp.push_back(make_pair(1, i));
    vect.push_back(make_pair(v[i], temp));
  }
  while (vect.size() > 2) {
    it = vect.end();
    it--;
    iu = vect.end();
    iu--;
    iu--;
    iv = vect.end();
    iv--;
    iv--;
    iv--;
    if (sumnorm((*it).first, (*iu).first) <= C) {
      if (((*it).second).size() >= ((*iu).second).size()) {
        for (vector<pair<bool, long long>>::iterator itr =
                 ((*iu).second).begin();
             itr != ((*iu).second).end(); itr++)
          ((*it).second).push_back(*itr);
        (*it).first =
            make_pair((((*it).first).first) + (((*iu).first).first),
                      (((*it).first).second) + (((*iu).first).second));
        vect.erase(iu);
      } else {
        for (vector<pair<bool, long long>>::iterator itr =
                 ((*it).second).begin();
             itr != ((*it).second).end(); itr++)
          ((*iu).second).push_back(*itr);
        (*iu).first =
            make_pair((((*it).first).first) + (((*iu).first).first),
                      (((*it).first).second) + (((*iu).first).second));
        vect.erase(it);
      }
    } else if (sumnorm((*it).first, (*iv).first) <= C) {
      if (((*it).second).size() >= ((*iv).second).size()) {
        for (vector<pair<bool, long long>>::iterator itr =
                 ((*iv).second).begin();
             itr != ((*iv).second).end(); itr++)
          ((*it).second).push_back(*itr);
        (*it).first =
            make_pair((((*it).first).first) + (((*iv).first).first),
                      (((*it).first).second) + (((*iv).first).second));
        vect.erase(iv);
      } else {
        for (vector<pair<bool, long long>>::iterator itr =
                 ((*it).second).begin();
             itr != ((*it).second).end(); itr++)
          ((*iv).second).push_back(*itr);
        (*iv).first =
            make_pair((((*it).first).first) + (((*iv).first).first),
                      (((*it).first).second) + (((*iv).first).second));
        vect.erase(it);
      }
    } else if (sumnorm((*iu).first, (*iv).first) <= C) {
      if (((*iu).second).size() >= ((*iv).second).size()) {
        for (vector<pair<bool, long long>>::iterator itr =
                 ((*iv).second).begin();
             itr != ((*iv).second).end(); itr++)
          ((*iu).second).push_back(*itr);
        (*iu).first =
            make_pair((((*iu).first).first) + (((*iv).first).first),
                      (((*iu).first).second) + (((*iv).first).second));
        vect.erase(iv);
      } else {
        for (vector<pair<bool, long long>>::iterator itr =
                 ((*iu).second).begin();
             itr != ((*iu).second).end(); itr++)
          ((*iv).second).push_back(*itr);
        (*iv).first =
            make_pair((((*iu).first).first) + (((*iv).first).first),
                      (((*iu).first).second) + (((*iv).first).second));
        vect.erase(iu);
      }
    } else if (diffnorm((*it).first, (*iu).first) <= C) {
      if (((*it).second).size() >= ((*iu).second).size()) {
        for (vector<pair<bool, long long>>::iterator itr =
                 ((*iu).second).begin();
             itr != ((*iu).second).end(); itr++) {
          ((*it).second).push_back(make_pair(!(*itr).first, (*itr).second));
        }
        (*it).first =
            make_pair((((*it).first).first) - (((*iu).first).first),
                      (((*it).first).second) - (((*iu).first).second));
        vect.erase(iu);
      } else {
        for (vector<pair<bool, long long>>::iterator itr =
                 ((*it).second).begin();
             itr != ((*it).second).end(); itr++)
          ((*iu).second).push_back(make_pair(!(*itr).first, (*itr).second));
        (*iu).first =
            make_pair((((*iu).first).first) - (((*it).first).first),
                      (((*iu).first).second) - (((*it).first).second));
        vect.erase(it);
      }
    } else if (diffnorm((*it).first, (*iv).first) <= C) {
      if (((*it).second).size() >= ((*iv).second).size()) {
        for (vector<pair<bool, long long>>::iterator itr =
                 ((*iv).second).begin();
             itr != ((*iv).second).end(); itr++) {
          ((*it).second).push_back(make_pair(!(*itr).first, (*itr).second));
        }
        (*it).first =
            make_pair((((*it).first).first) - (((*iv).first).first),
                      (((*it).first).second) - (((*iv).first).second));
        vect.erase(iv);
      } else {
        for (vector<pair<bool, long long>>::iterator itr =
                 ((*it).second).begin();
             itr != ((*it).second).end(); itr++)
          ((*iv).second).push_back(make_pair(!(*itr).first, (*itr).second));
        (*iv).first =
            make_pair((((*iv).first).first) - (((*it).first).first),
                      (((*iv).first).second) - (((*it).first).second));
        vect.erase(it);
      }
    } else if (diffnorm((*iu).first, (*iv).first) <= C) {
      if (((*iu).second).size() >= ((*iv).second).size()) {
        for (vector<pair<bool, long long>>::iterator itr =
                 ((*iv).second).begin();
             itr != ((*iv).second).end(); itr++)
          ((*iu).second).push_back(make_pair(!(*itr).first, (*itr).second));
        (*iu).first =
            make_pair((((*iu).first).first) - (((*iv).first).first),
                      (((*iu).first).second) - (((*iv).first).second));
        vect.erase(iv);
      } else {
        for (vector<pair<bool, long long>>::iterator itr =
                 ((*iu).second).begin();
             itr != ((*iu).second).end(); itr++)
          ((*iv).second).push_back(make_pair(!(*itr).first, (*itr).second));
        (*iv).first =
            make_pair((((*iv).first).first) - (((*iu).first).first),
                      (((*iv).first).second) - (((*iu).first).second));
        vect.erase(iu);
      }
    }
  }
  it = vect.begin();
  iu = vect.begin();
  iu++;
  if (sumnorm((*it).first, (*iu).first) <= 2 * C) {
    if (((*it).second).size() >= ((*iu).second).size()) {
      for (vector<pair<bool, long long>>::iterator itr = ((*iu).second).begin();
           itr != ((*iu).second).end(); itr++)
        ((*it).second).push_back(*itr);
      vect.erase(iu);
    } else {
      for (vector<pair<bool, long long>>::iterator itr = ((*it).second).begin();
           itr != ((*it).second).end(); itr++)
        ((*iu).second).push_back(*itr);
      vect.erase(it);
    }
  } else {
    if (((*it).second).size() >= ((*iu).second).size()) {
      for (vector<pair<bool, long long>>::iterator itr = ((*iu).second).begin();
           itr != ((*iu).second).end(); itr++)
        ((*it).second).push_back(make_pair(!(*itr).first, (*itr).second));
      vect.erase(iu);
    } else {
      for (vector<pair<bool, long long>>::iterator itr = ((*it).second).begin();
           itr != ((*it).second).end(); itr++)
        ((*iu).second).push_back(make_pair(!(*itr).first, (*itr).second));
      vect.erase(it);
    }
  }
  it = vect.begin();
  for (vector<pair<bool, long long>>::iterator itr = ((*it).second).begin();
       itr != ((*it).second).end(); itr++) {
    if ((*itr).first)
      ans[(*itr).second] = 1;
    else
      ans[(*itr).second] = -1;
  }
  for (long long i = 0; i < N; i++) cout << ans[i] << " ";
}