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.ArrayList;
import java.util.Scanner;
import java.lang.StringBuilder;
import java.util.Arrays;
import java.util.Stack;
import java.util.TreeMap;
public class Test10   {  
    public static void main(String[] Args)   {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] c = new int[n];
        for (int i = 0;i < n; i++) c[i] = 1;
        long[] x = new long[n];
        long[] y = new long[n];
        for (int i = 0; i < n;i++)  {
            x[i] = sc.nextInt();
            y[i] = sc.nextInt();
        }    
        int n1 = 1;
        int n2 = 2;
        long limit = new Long("1000000000000");
        int[] father = new int[n];
        int[] self = new int[n];
        father[0] = 0;
        self[0] = 1;
        while (n2 < n)  {
            if ((x[0] + x[n1]) * (x[0] + x[n1])  + (y[0] +y[n1]) * (y[0] +y[n1]) <= limit)  {
                father[n1] = 0;
                x[0] = x[0] + x[n1];
                y[0] = y[0] + y[n1];
                self[n1] = 1;
                n1 = n2;
                n2++;
            }    
            else if ((x[0] + x[n2]) * (x[0] + x[n2])  + (y[0] +y[n2]) * (y[0] +y[n2]) <= limit)  {
                father[n2] = 0;
                x[0] = x[0] + x[n2];
                y[0] = y[0] + y[n2];
                self[n2] = 1;
                n2++;
            }    
            else if ((x[0] - x[n1]) * (x[0] - x[n1])  + (y[0] - y[n1]) * (y[0] - y[n1]) <= limit)  {
                father[n1] = 0;
                x[0] = x[0] - x[n1];
                y[0] = y[0] - y[n1];
                self[n1] = -1;
                n1 = n2;
                n2++;
            }    
            else if ((x[0] - x[n2]) * (x[0] - x[n2])  + (y[0] - y[n2]) * (y[0] - y[n2]) <= limit)  {
                father[n2] = 0;
                x[0] = x[0] - x[n2];
                y[0] = y[0] - y[n2];
                self[n2] = -1;
                n2++;
            }    
            else if ((x[n2] + x[n1]) * (x[n2] + x[n1])  + (y[n2] +y[n1]) * (y[n2] +y[n1]) <= limit)  {
                father[n2] = n1;
                x[n1] = x[n2] + x[n1];
                y[n1] = y[n2] + y[n1];
                self[n2] = 1;
                n2++;
            }    
            else if ((x[n2] - x[n1]) * (x[n2] - x[n1])  + (y[n2] - y[n1]) * (y[n2] - y[n1]) <= limit)  {
                father[n2] = n1;
                x[n1] = - x[n2] + x[n1];
                y[n1] = - y[n2] + y[n1];
                self[n2] = -1;
                n2++;
            }  
        }  
        if (n1 < n) { if (x[0] * x[n1] + y[0] * y[n1] < 0)  {
                father[n1] = 0;
                self[n1] = 1;
        }  
        else  {
            father[n1] = 0;
             self[n1] = -1;
        }    
        }
        StringBuilder ans = new StringBuilder();
        for (int i = 0; i < n; i++)  {
            c[i] = c[father[i]] * self[i];
            ans.append(c[i]);
            ans.append(" ");
        }    
        System.out.println(ans);
   }
}