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 lim = 1000000000000;
struct p {
  long long x, y;
};
p operator+(p a, p b) { return {a.x + b.x, a.y + b.y}; }
p operator-(p a, p b) { return {a.x - b.x, a.y - b.y}; }
long long norm(p a) { return a.x * a.x + a.y * a.y; }
int main() {
  int n;
  cin >> n;
  if (n == 1) {
    cout << 1 << endl;
    return 0;
  }
  vector<p> points(2 * n - 1);
  vector<pair<int, int>> parents(2 * n - 1);
  vector<int> sign(2 * n - 1, 1);
  for (int i = 0; i < n; i++) {
    cin >> points[i].x >> points[i].y;
  }
  vector<pair<p, int>> workset;
  workset.push_back({points[0], 0});
  workset.push_back({points[1], 1});
  int j = 2;
  int k = n;
  while (j < k) {
    workset.push_back({points[j], j});
    j++;
    vector<pair<p, int>> nextset;
    if (norm(workset[0].first + workset[1].first) <= lim) {
      sign[k] = 1;
      parents[k] = {workset[0].second, workset[1].second};
      points[k] = workset[0].first + workset[1].first;
      nextset.push_back(workset[2]);
      nextset.push_back({points[j], j});
      j++;
      k++;
    } else if (norm(workset[0].first - workset[1].first) <= lim) {
      sign[k] = -1;
      parents[k] = {workset[0].second, workset[1].second};
      points[k] = workset[0].first - workset[1].first;
      nextset.push_back(workset[2]);
      nextset.push_back({points[j], j});
      j++;
      k++;
    } else if (norm(workset[0].first + workset[2].first) <= lim) {
      sign[k] = 1;
      parents[k] = {workset[0].second, workset[2].second};
      points[k] = workset[0].first + workset[2].first;
      nextset.push_back(workset[1]);
      nextset.push_back({points[j], j});
      j++;
      k++;
    } else if (norm(workset[0].first - workset[2].first) <= lim) {
      sign[k] = -1;
      parents[k] = {workset[0].second, workset[2].second};
      points[k] = workset[0].first - workset[2].first;
      nextset.push_back(workset[1]);
      nextset.push_back({points[j], j});
      j++;
      k++;
    } else if (norm(workset[1].first + workset[2].first) <= lim) {
      sign[k] = 1;
      parents[k] = {workset[1].second, workset[2].second};
      points[k] = workset[1].first + workset[2].first;
      nextset.push_back(workset[0]);
      nextset.push_back({points[j], j});
      j++;
      k++;
    } else {
      sign[k] = -1;
      parents[k] = {workset[1].second, workset[2].second};
      points[k] = workset[1].first - workset[2].first;
      nextset.push_back(workset[0]);
      nextset.push_back({points[j], j});
      j++;
      k++;
    }
    nextset.swap(workset);
  }
  if (norm(workset[0].first + workset[1].first) <
      norm(workset[0].first - workset[1].first)) {
    sign[2 * n - 2] = 1;
    parents[2 * n - 2] = {workset[0].second, workset[1].second};
    points[2 * n - 2] = workset[0].first + workset[1].first;
  } else {
    sign[2 * n - 2] = -1;
    parents[2 * n - 2] = {workset[0].second, workset[1].second};
    points[2 * n - 2] = workset[0].first - workset[1].first;
  }
  queue<pair<int, int>> work;
  work.push({2 * n - 2, 1});
  while (!work.empty()) {
    auto cur = work.front();
    work.pop();
    if (cur.first < n) {
      sign[cur.first] = cur.second;
    } else {
      work.push({parents[cur.first].first, cur.second});
      work.push({parents[cur.first].second, cur.second * sign[cur.first]});
    }
  }
  for (int i = 0; i < n; i++) {
    if (i != 0) cout << " ";
    cout << sign[i];
  }
  cout << endl;
  return 0;
}