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.FileNotFoundException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Scanner;

public class Solution {

    private static final boolean DEBUG = false;
    private static final Vector ZERO = new Vector(0, 0);
    
    private static class Vector {
        final int x;
        final int y;

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

        public long getSquareLength() {
            return (long) x * x + (long) y * y;
        }
        
        @Override
        public String toString() {
            return "Vector{" + "x=" + x + ", y=" + y + "}";
        }
    }
    
    public static void main(String[] args) throws FileNotFoundException {
        long beginTime = System.nanoTime();
        InputStream is = DEBUG ? new FileInputStream("resources/codeforces/ProblemE-1.in") : System.in;
        try (Scanner scanner = new Scanner(new BufferedReader(new InputStreamReader(is)))) {
            int n = scanner.nextInt();
            Vector[] vectors = new Vector[n];
            for (int i = 0; i < n; i++) {
                Vector v = new Vector(scanner.nextInt(), scanner.nextInt());
                vectors[i] = v;
            }
            int[] signs = new int[n + 2];
            signs[0] = 1;
            Vector last = vectors[0];
            for (int i = 1; i < vectors.length; i += 2) {
                Vector v1 = vectors[i];
                Vector v2 = i < vectors.length - 1 ? vectors[i + 1] : ZERO;
                Vector v = new Vector(last.x + v1.x + v2.x, last.y + v1.y + v2.y);
                Vector min = v;
                long minLength = min.getSquareLength();
                signs[i] = 1;
                signs[i + 1] = 1;
                v = new Vector(last.x + v1.x - v2.x, last.y + v1.y - v2.y);
                long l = v.getSquareLength();
                if (l < minLength) {
                    minLength = l;
                    min = v;
                    signs[i] = 1;
                    signs[i + 1] = -1;
                }
                v = new Vector(last.x - v1.x + v2.x, last.y - v1.y + v2.y);
                l = v.getSquareLength();
                if (l < minLength) {
                    minLength = l;
                    min = v;
                    signs[i] = -1;
                    signs[i + 1] = 1;
                }
                v = new Vector(last.x - v1.x - v2.x, last.y - v1.y - v2.y);
                l = v.getSquareLength();
                if (l < minLength) {
                    minLength = l;
                    min = v;
                    signs[i] = -1;
                    signs[i + 1] = -1;
                }
                last = min;
            }
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < vectors.length; i++) {
                if (sb.length() > 0) sb.append(' ');
                sb.append(signs[i]);
            }
            System.out.println(sb);
        }
        System.err.println( "Done in " + ((System.nanoTime() - beginTime) / 1e9) + " seconds.");
    }
}