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.math.BigDecimal;
import java.math.RoundingMode;
import java.util.Arrays;
import java.util.Scanner;


public class CF_598C {
	public static boolean PRECISION = false;
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		Vector[] vecs = new Vector[n];
		if(n < 300) {
			PRECISION = true;
		}
		for(int i=0;i<n;i++) {
			vecs[i] = new Vector(i+1,scan.nextInt(),scan.nextInt());
			//vecs[i].normalize();
		}
		Arrays.sort(vecs);
		Vector l = vecs[vecs.length-1];
		//double minAngle = 10;
		//double bestAns = Double.MAX_VALUE;
		BigDecimal bestAns = null;
		int bestA = 1;
		int bestB = 2;
		for(int i=0;i<n;i++) {
			Vector v = vecs[i];
			if(PRECISION) {
				BigDecimal y = v.y.subtract(l.y);
				BigDecimal x = v.x.subtract(l.x);
				BigDecimal ans = y.multiply(y).add(x.multiply(x));
				//System.out.println(y + " ^2" + "="+y.multiply(y));
				//System.out.println(x + " ^2" + "="+x.multiply(x));
				//double ans = y*y+x*x;
				//ans = Math.abs(ans);
				//ans = Math.min(4-ans,ans);
				
				//if(ans < bestAns) {
				if(bestAns == null || ans.compareTo(bestAns) < 0) {
					bestA = l.idx;
					bestB = v.idx;
					bestAns = ans;
				}
			} else {
				double y = v.y.subtract(l.y).doubleValue();
				double x = v.x.subtract(l.x).doubleValue();
				BigDecimal ans = new BigDecimal(y*y+x*x);
				//double ans = y*y+x*x;
				//ans = Math.abs(ans);
				//ans = Math.min(4-ans,ans);
				
				//if(ans < bestAns) {
				if(bestAns == null || ans.compareTo(bestAns) < 0) {
					bestA = l.idx;
					bestB = v.idx;
					bestAns = ans;
				}
			}
			l = v;
		}
		System.out.println(bestA + " " + bestB);
	}
	static class Vector implements Comparable<Vector>{
		double angle;
		BigDecimal x,y;
		int idx;
		public Vector(int idx, int x, int y) {
			this.idx = idx;
			this.x = BigDecimal.valueOf(x);
			this.y = BigDecimal.valueOf(y);
			this.angle = Math.atan2(y, x);
			
			if(PRECISION) {
				BigDecimal magsq = BigDecimal.valueOf(x*(long)x+y*(long)y);
				magsq = bigSqrt(magsq);
				if(x != 0 || y != 0) {
					// fuck these stupid precision hacks
					this.x = this.x.divide(magsq, 50, RoundingMode.HALF_UP);
					this.y = this.y.divide(magsq, 50, RoundingMode.HALF_UP);
				}
			} else {
				double mag = Math.sqrt(x*(long)x+y*(long)y);
				this.x = new BigDecimal(x/mag);
				this.y = new BigDecimal(y/mag);
			}
		}
		
		@Override
		public int compareTo(Vector o) {
			return Double.compare(angle, o.angle);
		}
		
	}
	
	// fuck these stupid precision hacks
	private static final BigDecimal SQRT_DIG = new BigDecimal(150);
	private static final BigDecimal SQRT_PRE = new BigDecimal(10).pow(SQRT_DIG.intValue());
	private static BigDecimal sqrtNewtonRaphson  (BigDecimal c, BigDecimal xn, BigDecimal precision){
	    BigDecimal fx = xn.pow(2).add(c.negate());
	    BigDecimal fpx = xn.multiply(new BigDecimal(2));
	    BigDecimal xn1 = fx.divide(fpx,2*SQRT_DIG.intValue(),RoundingMode.HALF_DOWN);
	    xn1 = xn.add(xn1.negate());
	    BigDecimal currentSquare = xn1.pow(2);
	    BigDecimal currentPrecision = currentSquare.subtract(c);
	    currentPrecision = currentPrecision.abs();
	    if (currentPrecision.compareTo(precision) <= -1){
	        return xn1;
	    }
	    return sqrtNewtonRaphson(c, xn1, precision);
	}
	public static BigDecimal bigSqrt(BigDecimal c){
	    return sqrtNewtonRaphson(c,new BigDecimal(1),new BigDecimal(1).divide(SQRT_PRE));
	}
}