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;
template <typename T1, typename T2>
inline void chkmin(T1 &x, T2 y) {
  if (x > y) x = y;
}
template <typename T1, typename T2>
inline void chkmax(T1 &x, T2 y) {
  if (x < y) x = y;
}
template <typename T, typename U>
inline ostream &operator<<(ostream &_out, const pair<T, U> &_p) {
  _out << _p.first << ' ' << _p.second;
  return _out;
}
template <typename T, typename U>
inline istream &operator>>(istream &_in, pair<T, U> &_p) {
  _in >> _p.first >> _p.second;
  return _in;
}
template <typename T>
inline ostream &operator<<(ostream &_out, const vector<T> &_v) {
  if (_v.empty()) {
    return _out;
  }
  _out << _v.front();
  for (auto _it = ++_v.begin(); _it != _v.end(); ++_it) {
    _out << ' ' << *_it;
  }
  return _out;
}
template <typename T>
inline istream &operator>>(istream &_in, vector<T> &_v) {
  for (auto &_i : _v) {
    _in >> _i;
  }
  return _in;
}
template <typename T>
inline ostream &operator<<(ostream &_out, const set<T> &_s) {
  if (_s.empty()) {
    return _out;
  }
  _out << *_s.begin();
  for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) {
    _out << ' ' << *_it;
  }
  return _out;
}
template <typename T>
inline ostream &operator<<(ostream &_out, const multiset<T> &_s) {
  if (_s.empty()) {
    return _out;
  }
  _out << *_s.begin();
  for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) {
    _out << ' ' << *_it;
  }
  return _out;
}
template <typename T>
inline ostream &operator<<(ostream &_out, const unordered_set<T> &_s) {
  if (_s.empty()) {
    return _out;
  }
  _out << *_s.begin();
  for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) {
    _out << ' ' << *_it;
  }
  return _out;
}
template <typename T>
inline ostream &operator<<(ostream &_out, const unordered_multiset<T> &_s) {
  if (_s.empty()) {
    return _out;
  }
  _out << *_s.begin();
  for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) {
    _out << ' ' << *_it;
  }
  return _out;
}
template <typename T, typename U>
inline ostream &operator<<(ostream &_out, const map<T, U> &_m) {
  if (_m.empty()) {
    return _out;
  }
  _out << '(' << _m.begin()->first << ": " << _m.begin()->second << ')';
  for (auto _it = ++_m.begin(); _it != _m.end(); ++_it) {
    _out << ", (" << _it->first << ": " << _it->second << ')';
  }
  return _out;
}
template <typename T, typename U>
inline ostream &operator<<(ostream &_out, const unordered_map<T, U> &_m) {
  if (_m.empty()) {
    return _out;
  }
  _out << '(' << _m.begin()->first << ": " << _m.begin()->second << ')';
  for (auto _it = ++_m.begin(); _it != _m.end(); ++_it) {
    _out << ", (" << _it->first << ": " << _it->second << ')';
  }
  return _out;
}
const string FILENAME = "input";
const int MAXN = 100001;
int n;
int x[MAXN], y[MAXN];
int c[MAXN];
int a[MAXN];
int id[MAXN];
int reals[MAXN];
int xs[MAXN], ys[MAXN];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  int curx = 0, cury = 0;
  int last = 0;
  int st = 0;
  for (int i = 0; i < n; i++) {
    cin >> x[i] >> y[i];
    id[i] = i;
    xs[i] = x[i];
    ys[i] = y[i];
  }
  while (true) {
    random_shuffle(id, id + n);
    for (int i = 0; i < n; i++) {
      x[i] = xs[i];
      y[i] = ys[i];
    }
    long long lst = 0;
    curx = 0;
    cury = 0;
    last = 0;
    st = 0;
    for (int i1 = 0; i1 < n; i1++) {
      int i = id[i1];
      long long res = 1e18;
      for (int t = 0; t < 2; t++) {
        for (int t1 = 0; t1 < 2; t1++) {
          int nx = curx + x[i];
          int ny = cury + y[i];
          chkmin(res, 1LL * nx * nx + 1LL * ny * ny);
          x[i] *= -1;
          y[i] *= -1;
        }
        curx *= -1;
        cury *= -1;
      }
      bool was = false;
      for (int t = 0; t < 2; t++) {
        int nx = curx + x[i];
        int ny = cury + y[i];
        if ((1LL * nx * nx + 1LL * ny * ny) == res) {
          c[i1] = last ^ t;
          if (i == 0) {
            st = t;
          }
          was = true;
          curx = nx;
          cury = ny;
          last = t;
          break;
        }
        x[i] *= -1;
        y[i] *= -1;
      }
      if (!was) {
        st ^= 1;
        last ^= 1;
        curx *= -1;
        cury *= -1;
        for (int t = 0; t < 2; t++) {
          int nx = curx + x[i];
          int ny = cury + y[i];
          if ((1LL * nx * nx + 1LL * ny * ny) == res) {
            c[i1] = t ^ last;
            if (i == 0) {
              st = t;
            }
            was = true;
            curx = nx;
            cury = ny;
            last = t;
            break;
          }
          x[i] *= -1;
          y[i] *= -1;
        }
      }
      lst = res;
    }
    if (lst <= 1500000LL * 1500000LL) {
      break;
    }
  }
  for (int i = 0; i < n; i++) {
    if (i == 0) {
      a[i] = st;
    } else {
      if (c[i]) {
        a[i] = a[i - 1] ^ 1;
      } else {
        a[i] = a[i - 1];
      }
    }
    reals[id[i]] = a[i];
  }
  for (int i = 0; i < n; i++) {
    if (reals[i] == 0) {
      cout << 1 << ' ';
    } else {
      cout << -1 << ' ';
    }
  }
  cout << '\n';
  return 0;
}