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 JAVA):

Solution:
import java.io.BufferedReader;
// import java.io.FileInputStream;
// import java.io.FileOutputStream;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.*;

import static java.lang.Math.abs;
import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.util.Arrays.copyOf;
import static java.util.Arrays.fill;
import static java.util.Arrays.sort;
import static java.util.Collections.sort;
import static java.util.Comparator.comparingInt;

public class Main {
    FastScanner in;
    PrintWriter out;

    private void solve() throws IOException {
        solveE();
    }

    class PairE implements Comparable<PairE> {
        long x, y;
        int id;
        boolean b;

        PairE(long x, long y, int id) {
            this.x = x;
            this.y = y;
            this.id = id;
            b = false;
        }

        @Override
        public int compareTo(PairE o) {
            return x != o.x ? Long.compare(x, o.x) : Long.compare(y, o.y);
        }
    }

    private void solveE() throws IOException {
        int n = in.nextInt();
        PairE[] p = new PairE[n];
        for (int i = 0; i < n; i++)
            p[i] = new PairE (in.nextLong(), in.nextLong(), i);

        
        long X = 0, Y = 0;
        for (int i = n - 1; i >= 0; i--) {
            if ((X + p[i].x) * (X + p[i].x) + (Y + p[i].y) * (Y + p[i].y) <= (X - p[i].x) * (X - p[i].x) + (Y - p[i].y) * (Y - p[i].y)) {
                p[i].b = true;
                X += p[i].x;
                Y += p[i].y;
            } else {
                p[i].b = false;
                X -= p[i].x;
                Y -= p[i].y;
            }
        }

        for (int i = 0; i < n; i++) {
            out.print(p[i].b ? 1 : -1);
            if (i + 1 < n)
                out.print(" ");
        }
        out.println();
    }

    class FastScanner {
        StringTokenizer st;
        BufferedReader br;

        FastScanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        boolean hasNext() throws IOException {
            return br.ready() || (st != null && st.hasMoreTokens());
        }

        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        double nextDouble() throws IOException {
            return Double.parseDouble(next().replace(',', '.'));
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

        boolean hasNextLine() throws IOException {
            return br.ready();
        }
    }

    private void run() throws IOException {
        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);

        solve();

        out.flush();
        out.close();
    }

    public static void main(String[] args) throws IOException {
        new Main().run();
    }
}