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:
//package contests.CF492;

import java.io.*;
import java.util.Arrays;
import java.util.StringTokenizer;

public class C {

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);

        int n = sc.nextInt();
        Vector[] arr = new Vector[n];
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < n; i++) {
            arr[i] = new Vector(sc.nextInt(), sc.nextInt(), i);
        }

        int[] sign = new int[n];
        while(true){
            shuffle(arr);
            Vector cur = new Vector(0, 0, -1);
            for (int i = 0; i < n; i++) {
                Vector plus = cur.add(arr[i]);
                Vector minus = cur.sub(arr[i]);
                if(plus.abs() < minus.abs()){
                    cur = plus;
                    sign[arr[i].idx] = 1;
                }else{
                    cur = minus;
                    sign[arr[i].idx] = -1;
                }
            }

            if(cur.abs()<1.5e6 + 1e-9) {
                for (int i = 0; i < n; i++) {
                    pw.print(sign[i] + " ");
                }
                break;
            }
        }

        pw.flush();
        pw.close();
    }


    static class Vector implements Comparable<Vector>{
        long x, y;
        int idx;
        public Vector(long x, long y, int idx){
            this.x = x;
            this.y = y;
            this.idx = idx;
        }

        double abs(){
            return Math.sqrt(x*x + y*y);
        }


        @Override
        public int compareTo(Vector vector) {
            return Double.compare(vector.abs(), abs());
        }

        public Vector add(Vector v){
            return new Vector(x + v.x, y + v.y, -1);
        }

        public Vector sub(Vector v){
            return new Vector(x - v.x, y - v.y, -1);
        }
    }

    static int[][] packD(int n, int[] from, int[] to) {
        int[][] g = new int[n][];
        int[] p = new int[n];
        for (int f : from) if(f != -1) p[f]++;
        for (int i = 0; i < n; i++) g[i] = new int[p[i]];
        for (int i = 0; i < from.length; i++) if(from[i] != -1) {g[from[i]][--p[from[i]]] = to[i];}
        return g;
    }

    static void shuffle(Object[] a)
    {
        int n = a.length;
        for(int i = 0; i < n; i++)
        {
            int r = i + (int)(Math.random() * (n - i));
            Object tmp = a[i];
            a[i] = a[r];
            a[r] = tmp;
        }
    }

    static class Scanner
    {
        StringTokenizer st; BufferedReader br;
        public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}
        public Scanner(String s) throws FileNotFoundException {	br = new BufferedReader(new FileReader(new File(s)));}
        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();}
    }
}