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:
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
//package EducationalContest1.C;
import java.math.BigInteger;
import java.util.*;
/**
 *
 * @author VmCHURA
 */
public class Main {
    public static void main(String[] args){
       
        Scanner sc = new Scanner(System.in);
        ArrayList<MyVector> vectors= new ArrayList<>();
        int N = sc.nextInt();
        for(int i=0;i<N;i++){
            int x= sc.nextInt();
            int y= sc.nextInt();
            MyVector mv= new MyVector(x, y, i);
            vectors.add(mv);
        }
        Collections.sort(vectors);
       
        TupleNum2Den2 ans = null;
        for(int i=0;i<N;i++){
            int j = i+1;
            if(j>=N) j-=N;
            MyVector a=vectors.get(i);
            MyVector b=vectors.get(j);
            TupleNum2Den2 next =  new TupleNum2Den2(a, b);
            //System.out.println("next: "+(next.a.indx+1)+" - "+(next.b.indx+1));
            if(ans == null){
                ans = next;
            }else{
                if( ans.compareTo(next) == 1){
                    ans = next;
                }
                
            }
            //System.out.println("ans: "+(ans.a.indx+1)+" - "+(ans.b.indx+1));
        }
        System.out.println(ans.a.indx+1);
        System.out.println(ans.b.indx+1);
        
    }
    
    
    
}
class MyVector implements Comparable<MyVector>{
    long x;
    long y;
    int indx;
    MyVector(long x,long y,int indx){
        this.x=x;
        this.y=y;
        this.indx=indx;
        
    }
    MyVector rotate90ClockWise(){
        return new MyVector(y, -x, indx);
    }
    @Override
    public int compareTo(MyVector o) {
        if(cuadrante()!=o.cuadrante()){
            return ((Integer)cuadrante()).compareTo(o.cuadrante());
        }
        if(cuadrante()==1){
            if(y*o.x <= o.y*x){
                return -1;
            }else{
                return 1;
            }
        }
        return rotate90ClockWise().compareTo(o.rotate90ClockWise());
    }
    private int cuadrante(){
        if(x==0 || y==0){
            if(x==0){
                if(y>0)
                    return 2;
                return 4;
            }
            if(y == 0){
                if( x>0)
                    return 1;
                return 3;
            }
        }
        if(x>0 ){
            if(y>0){
                return 1;
            }else{
                return 4;
            }
            
        }else{
            if(y>0){
                return 2;
            }else{
                return 3;
            }
        }
    }
}

class TupleNum2Den2 implements Comparable<TupleNum2Den2>{
    public MyVector a;
    public MyVector b;
    long num;
    BigInteger num2;
    BigInteger den2;
    public TupleNum2Den2(MyVector a, MyVector b){
        this.a = a;
        this.b = b;
        this.num = a.x*b.x+a.y*b.y;
        this.num2 = new BigInteger((Long.toString(num*num)));
        BigInteger modA = new BigInteger((new Long(a.x*a.x+a.y*a.y)).toString()) ;
        BigInteger modB = new BigInteger((new Long(b.x*b.x+b.y*b.y)).toString()) ;
        this.den2 = modA.multiply(modB);
        
    }
    
    @Override
    public int compareTo(TupleNum2Den2 o) {
        
        if(this.num == 0 && o.num==0)
            return 0;
        if(this.num == 0){
            if(o.num>0){
                return 1;
            }else{
                return -1;
            }
        }
        if(o.num==0){
            if(num>0){
                return -1;
            }else{
                return 1;
            }
        }
        if(this.num > 0){
            if(o.num > 0){
                //debe retornar aquel que tenga mas num/den
                //                                    num2/den2
               // System.out.println("comparando: "+(num2)+"*"+(o.den2)+" con "+(o.num2)+"*"+(den2));
                //System.out.println("comparando: "+(num2*o.den2)+" con "+(o.num2*den2));
                int k = (num2.multiply(o.den2)).compareTo(o.num2.multiply(den2));
                //System.out.println("result : "+k);
                return  -k;
            }else{
                return -1;
            }
        }else{
            if(o.num > 0){
                return 1;
            }else{
                //debe retornar aquel que tenga mas num/den
                //                              o menos num2/den2
                //System.out.println("comparando - : "+(num2*o.den2)+" con "+(o.num2*den2));
                int k = (num2.multiply(o.den2)).compareTo(o.num2.multiply(den2));
                //System.out.println("result : "+k);
                return k;
            }
        }
    }
    
}