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:
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	static class Vector implements Comparable<Vector> {
		int x, y, i;
		Vector(int x, int y, int i) {this.x = x; this.y = y; this.i = i;}
		// cross product of two 2d vectors is like that of 3d vectors with z component = 0
		// http://blackpawn.com/texts/pointinpoly/default.html
		int crossProduct(Vector b) {
			return this.x*b.y - this.y*b.x;
		}
		boolean upperQuadrant(Vector v) {
			return v.y > 0 || v.y == 0 && v.x > 0;
		}
		public int compareTo(Vector b) {
			boolean upA = upperQuadrant(this);
			boolean upB = upperQuadrant(b);
			if (!upA && upB) return 1;
			else if (upA && !upB) return -1;
			else return crossProduct(b) > 0 ? -1 : 1;
		}
	}
	
	static class Rational implements Comparable<Rational> {
		long p, q;
		Rational(Vector a, Vector b) {
			// p = dist(a.x, a.y) + dist(b.x, b.y) - dist(a.x - b.x, a.y - b.y);\
			p = a.x * b.x + a.y * b.y;
			p *= p*(p < 0 ? -1 : 1);
			q = dist(a.x, a.y) * dist(b.x, b.y);// * 4;
			// System.out.println(a.x + " " + a.y + ", " + b.x + " " + b.y + ", p: " + p + ", q: " + q);
			
		}
		
		long dist(long x, long y) {
			return x*x + y*y;
		}
		
		public int compareTo(Rational b) {
			// System.out.println("p: " + p + ", q: " + q + " , b.p: " + b.p + ", b.q: " + b.q);
			BigInteger product1 = BigInteger.valueOf(p).multiply(BigInteger.valueOf(b.q));
			BigInteger product2 = BigInteger.valueOf(q).multiply(BigInteger.valueOf(b.p));
			// System.out.println("product1: " + product1 + ", product2: " + product2);
			return product2.compareTo(product1);
		}
	}
	public static void main (String[] args) throws java.lang.Exception
	{
		BufferedReader b = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(b.readLine());
		Vector[] vectors = new Vector[n];
		for (int i = 0; i < n; i++) {
			String[] temp = b.readLine().split(" ");
			vectors[i] = new Vector(Integer.parseInt(temp[0]), Integer.parseInt(temp[1]), i+1);
		}
		Arrays.sort(vectors);
		// System.out.print("Vectors: ");
		// for (Vector v : vectors) System.out.print(v.x + " " + v.y + ", ");
		Rational cur = new Rational(vectors[0], vectors[n-1]);
		int imin = vectors[0].i, jmin = vectors[n-1].i;
		// System.out.println("Initial: " + vectors[0].x + " " + vectors[0].y + ", " + vectors[n-1].x + " " + vectors[n-1].y);
		// System.out.println("Comparing:");
		for (int i = 1; i < n; i++) {
			Rational r1 = new Rational(vectors[i], vectors[i-1]);
			// System.out.println(vectors[i].x + " " + vectors[i].y + ", " + vectors[i-1].x + " " + vectors[i-1].y + ", compare: " + r1.compareTo(cur));
			// System.out.println("p: " + r1.p + ", q: " + r1.q);
			if (r1.compareTo(cur) < 0) {
				cur = r1;
				imin = vectors[i].i;
				jmin = vectors[i-1].i;
				// System.out.println("New: " + imin + " " + jmin);
			}
		}
		
		System.out.println(imin + " " + jmin);
	}
}