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.util.*;
import java.io.*;
public class Main {
    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

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

        public Scanner(FileReader fileReader) {
            br = new BufferedReader(fileReader);
        }

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

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

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

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

        public boolean ready() throws IOException {
            return br.ready();
        }
    }
    static p[] arr;
    static p cur;
    static int[] ans;
    public static class p{
        int x;int y;
        p(int x,int y){
            this.x=x;this.y=y;
        }
    }
    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);PrintWriter pw = new PrintWriter(System.out);
        int n=sc.nextInt();arr = new p[n];for (int i=0;i<n;i++)arr[i] = new p(sc.nextInt(),sc.nextInt());
        cur=arr[0];ans=new int[n];ans[0]=1;
        for (int i=n-1;i>=1;i--){
            ans[i]=move(i);
        }
        for (int i=0;i<ans.length;i++) System.out.print(ans[i]+" ");
    }
    private static int move(int i) {
        p a = new p(cur.x+arr[i].x,cur.y+arr[i].y);
        p b = new p(cur.x-arr[i].x,cur.y-arr[i].y);
        if (dist(a)<dist(b)) {cur=a;return 1;}
        else cur=b;return -1;
    }
    private static double dist(p a) {
        double x = (double) a.x;double y = (double)a.y;
        return Math.abs(Math.sqrt(x*x+y*y));
    }
}