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.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Random;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.FileNotFoundException;
import java.util.Objects;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.InputStream;

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

    static class TaskE {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            GeometryUtils.Point[] points = in.readPolygon(n);
            int[] coef = new int[n];
            Arrays.fill(coef, 1);

            Pair<GeometryUtils.Point, Integer>[] pairs = new Pair[n];
            for (int i = 0; i < n; ++i) {
                pairs[i] = new Pair<>(points[i], i);
            }

            long p = (long) 1.5e6;
            p *= p;

            GeometryUtils.Point temp = new GeometryUtils.Point(0, 0);
            GeometryUtils.Point temp1, temp2;
            do {
                temp.x = 0;
                temp.y = 0;
                for (int i = 0; i < n; ++i) {
                    temp1 = new GeometryUtils.Point(temp.x + pairs[i].first.getX(), temp.y + pairs[i].first.getY());

                    temp2 = new GeometryUtils.Point(temp.x - pairs[i].first.getX(), temp.y - pairs[i].first.getY());

                    if (temp1.sqrValue() < temp2.sqrValue()) {
                        coef[pairs[i].second] = 1;
                        temp = temp1;
                    } else {
                        coef[pairs[i].second] = -1;
                        temp = temp2;
                    }
                }
                ArrayUtils.shuffle(pairs);
            } while (temp.sqrValue() >= p);

            out.println(coef);
        }

    }

    static class ArrayUtils {
        static final Random random = new Random(9876543210L);

        public static <T> void shuffle(T[] array) {
            for (int i = 0; i < array.length; ++i) {
                int j = i + random.nextInt(array.length - i);
                T temp = array[i];
                array[i] = array[j];
                array[j] = temp;
            }
        }

    }

    static class Pair<K extends Comparable<K>, V> implements Comparable<Pair<K, V>> {
        public K first;
        public V second;

        public Pair(K first, V second) {
            this.first = first;
            this.second = second;
        }


        public int compareTo(Pair<K, V> o) {
            return first.compareTo(o.first);
        }


        public boolean equals(Object o) {
            if (this == o) return true;
            if (!(o instanceof Pair)) return false;
            Pair<K, V> pair = (Pair<K, V>) o;
            return this.compareTo(pair) == 0;
        }


        public int hashCode() {
            return Objects.hash(first, second);
        }


        public String toString() {
            return String.format("{" + first + ", " + second + '}');
        }

    }

    static class InputReader extends BufferedReader {
        StringTokenizer tokenizer;

        public InputReader(InputStream inputStream) {
            super(new InputStreamReader(inputStream), 32768);
        }

        public InputReader(String filename) {
            super(new InputStreamReader(Thread.currentThread().getContextClassLoader().getResourceAsStream(filename)));
        }

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

        public Integer nextInt() {
            return Integer.valueOf(next());
        }

        public GeometryUtils.Point[] readPolygon(int n) {
            GeometryUtils.Point[] vertex = new GeometryUtils.Point[n];
            for (int i = 0; i < n; ++i)
                vertex[i] = new GeometryUtils.Point(nextInt(), nextInt());

            return vertex;
        }

    }

    static class GeometryUtils {
        public static class Point implements Comparable<GeometryUtils.Point> {
            public int x;
            public int y;

            public Point(int x, int y) {
                this.x = x;
                this.y = y;
            }


            public boolean equals(Object that) {
                GeometryUtils.Point other = (GeometryUtils.Point) that;
                return this.x == other.x && this.y == other.y;
            }


            public int compareTo(GeometryUtils.Point o) {
                if (x != o.x) return Integer.compare(x, o.x);
                return Integer.compare(y, o.y);
            }

            public long sqrValue() {
                return x * (long) x + y * (long) y;
            }

            public int getX() {
                return x;
            }

            public int getY() {
                return y;
            }


            public String toString() {
                return "Point{" +
                        "x=" + x +
                        ", y=" + y +
                        '}';
            }

        }

    }

    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream outputStream) {
            super(outputStream);
        }

        public OutputWriter(Writer writer) {
            super(writer);
        }

        public OutputWriter(String filename) throws FileNotFoundException {
            super(filename);
        }

        public void println(int[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i > 0) print(' ');
                print(array[i]);
            }
            println();
        }

        public void close() {
            super.close();
        }

    }
}