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.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.StringTokenizer;

public class NearestVectors {
	public static class Vector implements Comparable<Vector> {
		int idx;
		long xcor, ycor, upp, down;
		
		public Vector(int idx, int xcor, int ycor) {
			this.idx = idx;
			this.xcor = xcor;
			this.ycor = ycor;
			computeAngle();
		}
		public void computeAngle(){
			upp = (xcor *1) + (ycor * 0);
			upp *= upp;
			down = ((xcor*xcor) + (ycor *ycor)) * ((1*1) + (0 *0));
			
		}
		@Override
		public int compareTo(Vector o) {
			if(checkQuadrant(xcor, ycor) < checkQuadrant(o.xcor, o.ycor)){
				return -1;
			}else if(checkQuadrant(xcor, ycor) > checkQuadrant(o.xcor, o.ycor)){
				return 1;
			}else{				
				if(checkQuadrant(xcor, ycor) == 1){
					return Long.compare(o.upp*down, upp*o.down);
				} else if(checkQuadrant(xcor, ycor) == 2){
					return Long.compare(upp*o.down, o.upp*down);
				} else if(checkQuadrant(xcor, ycor) == 3){
					return Long.compare(o.upp*down, upp*o.down);
				} else {
					return Long.compare(upp*o.down, o.upp*down);
				}
			}
			
		}
		public int checkQuadrant(long x, long y){
			if( x >=0 && y >=0){
				return 1;
			} else if (x <0 && y>=0){
				return 2;
			} else if (x <0 && y <0){
				return 3;
			}else{
				return 4;
			}
		}
		@Override
		public String toString() {
			return xcor+" "+ycor + "_"+idx;
		}
	}

	public static void main(String[] args) throws Exception {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);
		int n = Integer.parseInt(in.readLine().trim());
		StringTokenizer st;
		Vector[] vectors = new Vector[n];
		for (int i = 0; i < n; ++i) {
			st = new StringTokenizer(in.readLine());
			int xcor = Integer.parseInt(st.nextToken());
			int ycor = Integer.parseInt(st.nextToken());
			vectors[i] = new Vector(i + 1, xcor, ycor);
		}
		Arrays.sort(vectors);
		int a = vectors[0].idx, b = vectors[n-1].idx;
		long minUpp = (vectors[0].xcor * vectors[n-1].xcor) + (vectors[0].ycor*vectors[n-1].ycor);
		long mult = 1;
		if(minUpp <0)
			mult = -1;
		minUpp *= minUpp;
		minUpp *=mult;
		long minDown = ((vectors[0].xcor * vectors[0].xcor)+ (vectors[0].ycor * vectors[0].ycor))
						* ((vectors[n-1].xcor * vectors[n-1].xcor)+ (vectors[n-1].ycor * vectors[n-1].ycor));
		
		for (int i = 1; i < n; ++i) {
			
			long upp = (vectors[i-1].xcor * vectors[i].xcor) + (vectors[i-1].ycor*vectors[i].ycor);
			mult = 1;
			if(upp <0)
				mult = -1;
			upp *= upp;
			upp *= mult;
			long down = ((vectors[i-1].xcor * vectors[i-1].xcor)+ (vectors[i-1].ycor * vectors[i-1].ycor))
							* ((vectors[i].xcor * vectors[i].xcor)+ (vectors[i].ycor * vectors[i].ycor));
			
			BigInteger minU = BigInteger.valueOf(minUpp);
			BigInteger minD = BigInteger.valueOf(minDown);
			BigInteger U = BigInteger.valueOf(upp);
			BigInteger D = BigInteger.valueOf(down);
			BigInteger left = minU.multiply(D);
			BigInteger right = U.multiply(minD);
			if ( left.compareTo(right) == -1) {
				minUpp = upp;
				minDown = down;
				a = vectors[i].idx;
				b = vectors[i - 1].idx;
			}
		}
		out.println(a + " " + b);
		in.close();
		out.close();
	}
}