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.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;



public class ELR {


	static class Vector {
		long x,y;
		int ind;
		public Vector(long x,long y,int ind) {
			this.x = x;
			this.y = y;
			this.ind = ind;
		}
	}
	static long sq(long x) {
		return 1L*x * x;
	}
	static long d(Vector v,Vector b) {
		return sq (v.x + b.x) + sq (v.y + b.y); 
	}
	public static void main(String[]args) throws Throwable {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		ArrayList<Vector> arr = new ArrayList();
		int n = sc.nextInt();
		for (int i = 0 ; i < n ; ++i) {
			arr.add(new Vector(sc.nextLong(),sc.nextLong(),i));
		}
		long max = (1L*1500000*1500000);
		int ans[] = new int[n];
		while (true) {
			Collections.shuffle(arr);
			Vector cur = new Vector(0,0,0);
			for (int i = 0 ; i < n ; ++i) {
				
				Vector pos = arr.get(i);
				Vector neg = new Vector(-arr.get(i).x,-arr.get(i).y,arr.get(i).ind);
				if (d(cur,pos) < d(cur,neg) ) {
					ans[pos.ind] = 1;
					cur.x += pos.x; cur.y += pos.y;
				} else {
					ans[neg.ind] = -1;
					cur.x += neg.x; cur.y += neg.y;

				}
			}
		//System.out.println(sq(cur.x) + " "+sq(cur.y));
			if (sq(cur.x) + sq(cur.y) <= max) {
				break;
			}
		}
		for (int i = 0 ; i < n ; ++i) {
			out.print(ans[i]+" ");
		}
		out.flush();
		out.close();
	}


	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 double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}
	}
}