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.*;
import java.util.*;

public class E996{
	
	long max = 9L*1000000L*1000000L;
	
	private void solve() throws Exception {
		n = nextInt();
		V[] v = new V[n];
		for(int i = 0; i < n; i++) v[i] = new V(i, nextLong(), nextLong());
		ArrayDeque<V>[][] quad = new ArrayDeque[2][3];
		for(int q = 0; q < 3; q++) quad[0][q] = new ArrayDeque<V>();
		for(int i = 0; i < n; i++) quad[0][v[i].quad()].add(v[i]);
		int idx = 0;
		while(quad[idx%2][0].size() > 1 || quad[idx%2][1].size() > 1 || quad[idx%2][2].size() > 1 ) {
			for(int q = 0; q < 3; q++) quad[(idx+1)%2][q] = new ArrayDeque<V>();
			for(int q = 0; q < 3; q++) {
				while(quad[idx%2][q].size() >= 1) {
					if((quad[idx%2][q].size() > 1)) {
						V v1 = quad[idx%2][q].removeLast();
						V v2 = quad[idx%2][q].removeLast();
						V v3 = diff(v1, v2);
						quad[(idx+1)%2][v3.quad()].addFirst(v3);
					} else if (quad[idx%2][q].size() == 1)  quad[(idx+1)%2][q].addFirst(quad[idx%2][q].removeFirst());
				}
			}
			idx++;
		}
		ArrayDeque<V> res = new ArrayDeque<V>();
		for(int i = 0; i < 3; i++) if(quad[idx%2][i].size() > 0) res.add(quad[idx%2][i].removeFirst());
		V[] resArray = res.toArray(new V[0]);
		c = new int[n];
		doit(resArray, 0, new V(-1,0,0));
		for(int i = 0; i < n; i++) out.print(c[i] + " ");
	}
	
	int n;
	int[] c;
	
	long best = 1L<<60;
	
	void doit(V[] v, int idx, V u) {
		if(idx == v.length) {
			long cost = u.x*u.x + u.y*u.y; 
			if(cost < best) {
				getCoeff(u,1);
				best = cost;
			}
		} else {
			doit(v, idx+1, diff(v[idx], u));
			doit(v, idx+1, diff(v[idx], u));
		}
	}
	
	void getCoeff(V v, int sgn) {
		if(v.idx >= 0) c[v.idx] = sgn*v.c;
		for(V next : v.added ) getCoeff(next, sgn*v.c);
	}
	

	V diff(V u, V v) {
		v.changeSignal();
		V res = new V(-1, u.x+v.x, u.y+v.y);
		res.added.add(u);
		res.added.add(v);
		return res;
	}
	
	class V{
		long x;
		long y;
		int idx;
		int c;
		ArrayList<V> added;
		
		public V(int idx, long x, long y) {
			this.x = x;
			this.y = y;
			this.idx = idx;
			this.c = 1;
			added = new ArrayList<V>();
			fix();
		}
		
		void changeSignal() {
			x = -x;
			y = -y;
			c = -c;
		}
		
		public void fix() {
			if(y < 0) changeSignal();
		}
		
		int quad() {
			fix();
			if(x >= 0 && 3L*x*x >= y*y) return 0;
			else if(x <= 0 && 3L*(-x)*(-x) >= y*y ) return 2;
			else return 1;
		}
		
	}
	
	
	public static void main(String[] args) {
		(new E996()).run();
	}

	private BufferedReader in;
	private PrintWriter out;
	private StringTokenizer tokenizer;

	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			tokenizer = null;
			out = new PrintWriter(System.out);
			solve();
			in.close();
			out.close();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	private int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	private long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	private float nextFloat() throws IOException {
		return Float.parseFloat(nextToken());
	}

	private String nextLine() throws IOException {
		return new String(in.readLine());
	}

	private String nextToken() throws IOException {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			tokenizer = new StringTokenizer(in.readLine());
		}
		return tokenizer.nextToken();
	}


}