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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.util.Collections;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author ijxjdjd
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        int[] moves = new int[100000];

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int N = in.nextInt();
            ArrayList<Vector> arr = new ArrayList<>();
            for (int i = 0; i < N; i++) {
                arr.add(new Vector(in.nextLong(), in.nextLong()));
                arr.get(arr.size() - 1).id = i;
            }
            while (true) {
                Vector cur = new Vector(0, 0);
                Collections.shuffle(arr);
                for (Vector v : arr) {
                    cur = cur.minNorm(v);
                }
                if (cur.norm() < 2250000000000L) {
                    for (int i = 0; i < N; i++) {
                        out.print(moves[i] + " ");
                    }
                    return;
                }
            }
        }

        long pow2(long a) {
            return a * a;
        }

        class Vector {
            long x;
            long y;
            int id;

            Vector(long x, long y) {
                this.x = x;
                this.y = y;
            }

            Vector minNorm(Vector next) {
                if (norm(this, next) < norm(this, flip(next))) {
                    moves[next.id] = 1;
                    return add(this, next);
                }
                moves[next.id] = -1;
                return add(this, flip(next));
            }

            Vector add(Vector a, Vector b) {
                return new Vector(a.x + b.x, a.y + b.y);
            }

            long norm(Vector a, Vector b) {
                return pow2(a.x + b.x) + pow2(a.y + b.y);
            }

            Vector flip(Vector c) {
                return new Vector(-c.x, -c.y);
            }

            long norm() {
                return pow2(x) + pow2(y);
            }

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

    }
}