Problem: You are given the set of vectors on the plane, each of them starting at the origin. Your task is to find a pair of vectors with the minimal non-oriented angle between them.

Non-oriented angle is non-negative value, minimal between clockwise and counterclockwise direction angles. Non-oriented angle is always between 0 and π. For example, opposite directions vectors have angle equals to π.

Input

First line of the input contains a single integer n (2 ≤ n ≤ 100 000) — the number of vectors.

The i-th of the following n lines contains two integers xi and yi (|x|, |y| ≤ 10 000, x2 + y2 > 0) — the coordinates of the i-th vector. Vectors are numbered from 1 to n in order of appearing in the input. It is guaranteed that no two vectors in the input share the same direction (but they still can have opposite directions).

Output

Print two integer numbers a and b (a ≠ b) — a pair of indices of vectors with the minimal non-oriented angle. You can print the numbers in any order. If there are many possible answers, print any.

Examples

Input

4
-1 0
0 -1
1 0
1 1


Output

3 4


Input

6
-1 0
0 -1
1 0
1 1
-4 -5
-4 -6


Output

6 5

Solution (in JAVA):

Solution:

import com.sun.org.apache.xml.internal.utils.Trie;

import java.awt.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.lang.Math.*;

import static java.lang.Math.abs;

public class Main {

    public static void main(String[] args) throws IOException {

        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

        final PolarComparator polarComparator = new PolarComparator();

        ArrayList<Triplet> treeSet = new ArrayList<>();



        int count = Integer.parseInt(reader.readLine());

        for (int i = 0; i < count; i++) {

            final String str = reader.readLine();
            final String[] pointNum = str.split(" ");

            Triplet newP = new Triplet(Integer.parseInt(pointNum[0]), Integer.parseInt(pointNum[1]), i);

            treeSet.add(newP);

        }

        Collections.sort(treeSet, polarComparator);

        MinAnglePoints minAnglePoints = new MinAnglePoints(treeSet.get(treeSet.size() - 1), treeSet.get(0));

        for (int i = 0; i < treeSet.size() - 1; i++) {

            if(angleLess(minAnglePoints.indP1,
                    minAnglePoints.indP2,
                    treeSet.get(i),
                    treeSet.get(i + 1))) {
                minAnglePoints.indP1 =  treeSet.get(i);
                minAnglePoints.indP2 = treeSet.get(i + 1);
            }

        }

        System.out.printf("%d %d", minAnglePoints.indP1.ind + 1 ,minAnglePoints.indP2.ind + 1);

    }

    private static class Triplet {
        long x;
        long y;
        int ind;

        public Triplet(long x, long y, int ind) {
            this.x = x;
            this.y = y;
            this.ind = ind;
        }
    }

    public static class PolarComparator implements Comparator<Triplet> {

        @Override
        public int compare(final Triplet o1, final Triplet o2) {

            boolean topO1 = top(o1);
            boolean topO2 = top(o2);

            if(topO1 != topO2)
                if(topO1 == false) return -1; else return 1;

            long solve = cross(o1, o2);
            if(solve > 0) return -1;
            return 1;
        }

        private boolean top(Triplet point){
            return point.y < 0 || point.y == 0 && point.x < 0;
        }
    }

    static boolean angleLess(final Triplet a1, final Triplet b1, final Triplet a2, final Triplet b2){

        Triplet p1 = new Triplet(dot(a1, b1), abs(cross(a1, b1)), 0);
        Triplet p2 = new Triplet(dot(a2, b2), abs(cross(a2, b2)), 0);

        return cross(p1, p2) < 0;
    }

    private static class MinAnglePoints{

        public Triplet indP1;

        public Triplet indP2;

        public MinAnglePoints(final Triplet p1, final Triplet p2) {
            this.indP1 = p1;
            this.indP2 = p2;
        }

    }


    static long cross(final Triplet o1, final Triplet o2) {
        return o1.x * o2.y - o1.y * o2.x;
    }

    static long dot(final Triplet o1, final Triplet o2) {
        return o1.x * o2.x + o1.y * o2.y;
    }

}