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;
vector<pair<pair<long long, long long>, pair<long long, long long> > > vec(
    100000);
vector<int> adj[100001];
void dfs(int i, int curr = 1) {
  vec[i].second.second *= curr;
  for (int j = 0; j < adj[i].size(); j++) {
    dfs(adj[i][j], vec[i].second.second);
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n;
  cin >> n;
  stack<long long> st;
  long long x, y;
  for (int i = 0; i < n; i++) {
    cin >> x >> y;
    vec[i] = (make_pair(make_pair(x, y), make_pair(i, 1)));
    st.push(i);
  }
  long long x1, x2, x3, y1, y2, y3, i1, i2, i3;
  while (st.size() > 2) {
    i1 = st.top();
    st.pop();
    x1 = vec[i1].first.first;
    y1 = vec[i1].first.second;
    i2 = st.top();
    st.pop();
    x2 = vec[i2].first.first;
    y2 = vec[i2].first.second;
    i3 = st.top();
    st.pop();
    x3 = vec[i3].first.first;
    y3 = vec[i3].first.second;
    if ((((x1) + (x2)) * ((x1) + (x2)) + ((y1) + (y2)) * ((y1) + (y2))) <=
        1000000000000) {
      vec[i2].second.first = i1;
      vec[i1].first.first += vec[i2].first.first;
      vec[i1].first.second += vec[i2].first.second;
      st.push(i1);
      st.push(i3);
    } else if ((((x1) + (-x2)) * ((x1) + (-x2)) +
                ((y1) + (-y2)) * ((y1) + (-y2))) <= 1000000000000) {
      vec[i2].second.first = i1;
      vec[i2].second.second *= -1;
      vec[i1].first.first -= vec[i2].first.first;
      vec[i1].first.second -= vec[i2].first.second;
      st.push(i1);
      st.push(i3);
    } else if ((((x3) + (x2)) * ((x3) + (x2)) +
                ((y3) + (y2)) * ((y3) + (y2))) <= 1000000000000) {
      vec[i2].second.first = i3;
      vec[i3].first.first += vec[i2].first.first;
      vec[i3].first.second += vec[i2].first.second;
      st.push(i3);
      st.push(i1);
    } else if ((((x3) + (-x2)) * ((x3) + (-x2)) +
                ((y3) + (-y2)) * ((y3) + (-y2))) <= 1000000000000) {
      vec[i2].second.first = i3;
      vec[i2].second.second *= -1;
      vec[i3].first.first -= vec[i2].first.first;
      vec[i3].first.second -= vec[i2].first.second;
      st.push(i3);
      st.push(i1);
    } else if ((((x3) + (x1)) * ((x3) + (x1)) +
                ((y3) + (y1)) * ((y3) + (y1))) <= 1000000000000) {
      vec[i1].second.first = i3;
      vec[i3].first.first += vec[i1].first.first;
      vec[i3].first.second += vec[i1].first.second;
      st.push(i3);
      st.push(i2);
    } else if ((((x3) + (-x1)) * ((x3) + (-x1)) +
                ((y3) + (-y1)) * ((y3) + (-y1))) <= 1000000000000) {
      vec[i1].second.first = i3;
      vec[i1].second.second *= -1;
      vec[i3].first.first -= vec[i1].first.first;
      vec[i3].first.second -= vec[i1].first.second;
      st.push(i2);
      st.push(i3);
    }
  }
  for (int i = 0; i < n; i++) {
    if (i != vec[i].second.first) {
      adj[vec[i].second.first].push_back(i);
    }
  }
  dfs(st.top());
  int temp = st.top();
  st.pop();
  if (!st.empty()) {
    if ((((vec[temp].first.first) + (vec[st.top()].first.first)) *
             ((vec[temp].first.first) + (vec[st.top()].first.first)) +
         ((vec[temp].first.second) + (vec[st.top()].first.second)) *
             ((vec[temp].first.second) + (vec[st.top()].first.second))) >
        1000000000000) {
      vec[st.top()].second.second *= -1;
    }
    dfs(st.top());
    st.pop();
  }
  for (int i = 0; i < n; i++) {
    cout << vec[i].second.second << " ";
  }
  return 0;
}