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.BufferedInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.math.BigInteger;
import java.util.Arrays;

public class codeforces {
	public static void main(String[] args) {
		
		JS scan = new JS();
		int N = scan.nextInt();
		Vector[] list = new Vector[N];
		for(int i=0;i<N;i++){
			list[i] = new Vector(scan.nextLong(), scan.nextLong(), i+1);
		}
		
		Arrays.sort(list);
//		System.out.println(Arrays.toString(list));
		Vector A = list[0], B = list[1];
		for(int i=0;i<N;i++){
			Vector a = list[i], b = list[(i+1)%N];
			if(a.cross(b) <= 0) {
				if(i==0) {
					A=list[1];
					B=list[2%N];
				}
				continue;
			}
			BigInteger p1 = BigInteger.valueOf((long)Math.signum(A.dot(B))*A.dot(B)*A.dot(B)), q1 = BigInteger.valueOf(A.dot(A)*B.dot(B));
			BigInteger p2 = BigInteger.valueOf((long)Math.signum(a.dot(b))*a.dot(b)*a.dot(b)), q2 = BigInteger.valueOf(a.dot(a)*b.dot(b));
//			System.out.println(p1+" "+q1+" "+p2+" "+q2+" "+a+" "+b+" -- "+A+" "+B);
			if((p1.multiply(q2)).compareTo(p2.multiply(q1)) < 0) {
				A = a;
				B = b;
			}
		}
		System.out.println(A.idx+" "+B.idx);
	}
	
	private static class Vector implements Comparable<Vector> {
		long x, y;
		int idx;
		public Vector(long x, long y, int idx) {
			this.x=x;
			this.y=y;
			this.idx=idx;
		}
		public int compareTo(Vector v) {
			if(y >= 0 && v.y >= 0) {
				if(y==0 && v.y == 0 && Math.signum(x) != Math.signum(v.x))
					return -((int)Math.signum(x) - (int)Math.signum(v.x));
				return x*v.y-v.x*y > 0 ? -1 : 1; 
			}
			else if(y < 0 && v.y < 0)
				return x*v.y-v.x*y > 0 ? -1 : 1; 
			else 
				return y >= 0 ? -1 : 1;
		}
		public long cross(Vector v) {
			return x*v.y-v.x*y;
		}
		public long dot(Vector v) {
			return x*v.x+y*v.y;
		}
		public double mag() {
			return Math.sqrt(this.dot(this));
		}
		public String toString() {
			return "("+x+","+y+")";
		}
	}
	

	static class JS{
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;
		
		public JS() {
			in = new BufferedInputStream(System.in, BS);
		}
		
		public JS(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}
		
		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}				
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}
		
		public int nextInt() {
			return (int)nextLong();
		}
		
		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}
		
		public double nextDouble() {
		    while(c!='.'&&c!='-'&&(c <'0' || c>'9')) c = nextChar();
		    boolean neg = c=='-';
		    if(neg)c=nextChar();
		    boolean fl = c=='.';
		    double cur = nextLong();
		    if(fl) return neg ? -cur/num : cur/num;
		    if(c == '.') {
			double next = nextLong();
			return neg ? -cur-next/num : cur+next/num;
		    }
		    else return neg ? -cur : cur;
		}
		
		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}
		
		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
	}
}