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 java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;

/**
 * Created by slycer on 12/2/15.
 */
public class Nearestvectors {

    public static void main ( String [] args ) throws IOException {
        BufferedReader reader = new BufferedReader ( new InputStreamReader( System.in ) );
//        Point p = new Point( 10000000, -1 );
//        Point b = new Point( -1, 1 );
//        Fraction f = p.polarAngle();
//        System.out.println( f );
        int n = Integer.valueOf( reader.readLine() );
        List<Point> points = new ArrayList<>();

        for ( int i=0; i<n; i++ ){
            String [] aux = reader.readLine().split( " " );
            int a = Integer.valueOf( aux[0] );
            int b = Integer.valueOf( aux[1] );
            points.add( new Point( i + 1, a, b ) );
        }

        Collections.sort(points);

        points.add( points.get( 0 ) );

        Fraction bestAngle = null;
        int bestIndex = -1;

        for ( int i=0; i<points.size(); i++ ){
           // System.out.println( points.get( i ).polarAngle() );
        }

        for ( int i=1; i<points.size(); i++ ){
            Fraction angle = points.get(i).angle( points.get(i-1 ) );
            //System.out.println( i + " " + angle + " " + points.get(i) );
            if ( bestAngle == null || bestAngle.compareTo( angle ) < 0 ){
                bestAngle = angle;
                bestIndex = i;
            }
        }

        System.out.println( points.get( bestIndex - 1 ).id + " " +  points.get( bestIndex ).id );
    }

    public static class Point implements Comparable<Point>{

        public static Point identity = new Point( 1, 0 );
        public static Fraction minus2 = new Fraction( -2, 1 );
        public long a, b;
        public int id;

        public Point( long a, long b ){
            this( 0, a, b );
        }
        public Point( int id, long a, long b ){
            this.a = a;
            this.b = b;
            this.id = id;
        }

        public Fraction polarAngle(){
            Fraction angle = angle( Point.identity );
            if ( b < 0 ){
                angle = minus2.add( angle.negate() );
            }
            return angle;
        }

        public Fraction angle( Point p ){
            long k = a * p.a + b * p.b;
            long sgn = Long.signum( k );
            long k1 =  estimateLength()*p.estimateLength();
            return new Fraction( sgn*k*k, k1 );
        }

        public long estimateLength(){
            return a*a + b*b;
        }

        public String toString(){
            return "id=" + id + " " +  a + " " + b ;
        }
        @Override
        public int compareTo(Point o) {
            return polarAngle().compareTo( o.polarAngle() );
        }
    }

    public static class Fraction implements  Comparable<Fraction> {
        BigInteger a,b;

        public Fraction( BigInteger a, BigInteger b ){
            this.a = a;
            this.b = b;
        }

        public  Fraction( long a, long b ){
            this.a = BigInteger.valueOf( a );
            this.b = BigInteger.valueOf( b );
        }

        public String toString(){
            return "{" + a + " " + b + "}";
        }

        public Fraction negate(){
            return new Fraction( a.multiply( BigInteger.ONE.negate() ), b );
        }

        public Fraction add( Fraction f ){
            return new Fraction( a .multiply( f.b ).add( b .multiply( f.a ) ), b .multiply( f.b ) );
        }

        @Override
        public int compareTo( Fraction f ) {
            return   a .multiply( f.b ).compareTo( b.multiply( f.a ) );
        }
    }

}