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.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws Exception {
        new Solver().run(1);
    }
}

class Solver {

    private BufferedReader reader = null;
    private StringTokenizer st = null;

    private int[] ans;
    private Vector[] vectors;
    private int n;

    private int[] pos1 = {0, 0, 0, 0, 1, 1};
    private int[] pos2 = {1, 1, 2, 2, 2, 2};
    private int[] signInPos = {1, -1, 1, -1, 1, -1};

    public void run(int inputType) throws Exception {
        if (inputType == 0)
            reader = new BufferedReader(new FileReader("input.txt"));
        else
            reader = new BufferedReader(new InputStreamReader(System.in));

        n = Integer.parseInt(reader.readLine());
        vectors = new Vector[n];
        ans = new int[n];
        Arrays.fill(ans, 1);

        for (int i = 0; i < n; ++i) {
            st = new StringTokenizer(reader.readLine());
            vectors[i] = new Vector(Long.parseLong(st.nextToken()), Long.parseLong(st.nextToken()), i, 1);
        }

        reader.close();

        if (n == 1) {
            System.out.println(1);
            return;
        }

        for (int i = 0; i < n - 1; ++i) {

            if (i == n - 2) {

                if (getSignSqrDist(vectors[i], vectors[i + 1], 1) > getSignSqrDist(vectors[i], vectors[i + 1], -1)) {
                    vectors[i].sign *= -1;
                    vectors[i].x *= -1;
                    vectors[i].y *= -1;
                }

                mergeVectors(vectors[i], vectors[i + 1]);
                if (vectors[i + 1].lst == null) {
                    Vector tmp = vectors[i + 1];
                    vectors[i + 1] = vectors[i];
                    vectors[i] = tmp;
                }

                continue;
            }

            int minPos = 0;
            long mindist = (long)1e15;
            for (int j = 0; j < 6; ++j) {
                long d = getSignSqrDist(vectors[i + pos1[j]], vectors[i + pos2[j]], signInPos[j]);
                if (d < mindist) {
                    minPos = j;
                    mindist = d;
                }
            }

            int indx1 = i + pos1[minPos];
            int indx2 = i + pos2[minPos];
            vectors[indx1].sign *= signInPos[minPos];
            vectors[indx1].x *= signInPos[minPos];
            vectors[indx1].y *= signInPos[minPos];

            mergeVectors(vectors[indx1], vectors[indx2]);
            if (vectors[indx1].lst == null) {

                Vector tmp = vectors[indx1];
                vectors[indx1] = vectors[i];
                vectors[i] = tmp;

            } else {

                Vector tmp = vectors[indx2];
                vectors[indx2] = vectors[i];
                vectors[i] = tmp;
            }
        }

        for (int i = 0; i < n; ++i) {
            System.out.print(ans[i] + " ");
        }
    }

    long getSignSqrDist(Vector v1, Vector v2, int s) {
        return (s * v1.x + v2.x) * (s * v1.x + v2.x) +
                (s * v1.y + v2.y) * (s * v1.y + v2.y);
    }

    void mergeVectors(Vector v1, Vector v2) {

        Vector u, v;
        if (v1.lst.size() > v2.lst.size()) {
            u = v1;
            v = v2;
        } else {
            u = v2;
            v = v1;
        }

        u.x += v.x;
        u.y += v.y;
        int s = u.sign * v.sign;
        if (s == -1) {
            for(Integer i : v.lst) {
                ans[i] *= s;
            }
        }

        u.lst.addAll(v.lst);
        v.lst.clear();
        v.lst = null;
    }

    class Vector {
        long x;
        long y;
        int sign;
        List<Integer> lst;

        Vector(long x, long y, int indx, int sign) {
            this.x = x;
            this.y = y;
            this.sign = sign;
            lst = new LinkedList<>();
            lst.add(indx);
        }
    }
}