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.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class C_ {

    static ArrayList<Integer>[] adj;
    static int idx;
    static int[] sign;

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

        int n = sc.nextInt();
        if(n == 1){
            System.out.println(1);
            return;
        }
        ArrayList<Vector> v = new ArrayList<>();

        idx = n;
        adj = new ArrayList[200005];
        for (int i = 0; i < adj.length; i++)
            adj[i] = new ArrayList<>();
        sign = new int[200005];

        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < n; i++) {
            v.add(new Vector(sc.nextInt(), sc.nextInt(), i+1));
        }

        while(v.size() > 2){
            Vector a = v.remove(v.size()-1);
            Vector b = v.remove(v.size()-1);
            Vector c = v.remove(v.size()-1);

            Vector[] res = add2(a,b,c);
            v.add(res[0]);
            v.add(res[1]);
        }

        if(v.get(0).add(v.get(1), -1).abs() <= 1.5e6){
            adj[++idx].add(Math.abs(v.get(0).idx));
            adj[idx].add(Math.abs(v.get(1).idx));
            sign[v.get(0).idx] = 1;
            sign[v.get(1).idx] = 1;
            System.err.println(v.get(0).add(v.get(1), -1).abs());
        }else{
            adj[++idx].add(Math.abs(v.get(0).idx));
            adj[idx].add(Math.abs(v.get(1).idx));
            sign[v.get(0).idx] = 1;
            sign[v.get(1).idx] = -1;
            System.err.println(v.get(0).sub(v.get(1), -1).abs());
        }

        sign[idx] = 1;
        dfs(idx);

        for (int i = 0; i < n; i++)
            pw.print(sign[i+1] + " ");

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

    static void dfs(int u){
        for (int v: adj[u]) {
            sign[v]*=sign[u];
            dfs(v);
        }
    }

    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, int idx){
            return new Vector(x + v.x, y + v.y, idx);
        }

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

    static Vector[] add2(Vector a, Vector b, Vector c){
        Vector[] arr = {a, new Vector(-a.x, -a.y, -a.idx), b, new Vector(-b.x, -b.y, -b.idx), c, new Vector(-c.x, -c.y, -c.idx)};
        int taken1 = -1;
        int taken2 = -1;
        out:for (int i = 0; i < arr.length; i++) {
            for (int j = i+1; j < arr.length; j++) {
                if(i/2 != j/2){
                    if(arr[i].add(arr[j], -1).abs()<=1000000)
                    {
                        taken1 = i;
                        taken2 = j;
                        break out;
                    }
                }
            }
        }

        for (int i = 0; i < arr.length; i++) {
            if(i/2 != taken1/2 && i/2 != taken2/2){
                if(arr[taken1].idx > 0)
                    sign[arr[taken1].idx] = 1;
                else
                    sign[-arr[taken1].idx] = -1;
                if(arr[taken2].idx > 0)
                    sign[arr[taken2].idx] = 1;
                else
                    sign[-arr[taken2].idx] = -1;
                adj[++idx].add(Math.abs(arr[taken1].idx));
                adj[idx].add(Math.abs(arr[taken2].idx));
                return new Vector[]{arr[i], arr[taken1].add(arr[taken2], idx)};
            }
        }

        return null;
    }

    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();}
    }
}