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 static java.util.Arrays.*;
import java.util.*;

import java.io.*;
import java.math.BigInteger;

public class Main {

	void solve() {
		int n = sc.nextInt();
		int[] xs = new int[n];
		int[] ys = new int[n];
		for (int i = 0; i < n; i++) {
			xs[i] = sc.nextInt();
			ys[i] = sc.nextInt();
		}
		Integer[] order = sortByAngle(xs, ys);
		
		long bestValue = Long.MAX_VALUE;
		long bestDis = -1;
		
		int a = 0, b = 0;
		
		for (int p = 0; p < n; p++) {
			int i = order[p];
			int j = order[(p + 1) % n];
			int x1 = xs[i], y1 = ys[i];
			int x2 = xs[j], y2 = ys[j];
			long a2b2 = d2(x1, y1) * d2(x2, y2);
			long abc = (x1 * x2 + y1 * y2);
			long abs = (x1 * y2 - x2 * y1);
			long a2b2s2 = Math.abs(abc > 0 ? abs * abs : 2 * a2b2 - abs * abs);
			if (bestDis < 0 ||
				BigInteger.valueOf(bestValue).multiply(BigInteger.valueOf(a2b2))
				.compareTo(
				BigInteger.valueOf(a2b2s2).multiply(BigInteger.valueOf(bestDis))
				) > 0) {
				bestValue = a2b2s2;
				bestDis = a2b2;
				a = i;
				b = j;
			}
		}
		out.println((a+1) + " " + (b+1));
	}
	static long d2(int x, int y) {
		return x * x + y * y;
	}

	Integer[] sortByAngle(final int[] xs, final int[] ys) {
		int n = xs.length;
		Integer[] id = new Integer[n];
		for (int i = 0; i < n; i++) id[i] = i;
		Arrays.sort(id, new Comparator<Integer>() {
			public int compare(Integer a, Integer b) {
				int x1 = xs[a], y1 = ys[a];
				int x2 = xs[b], y2 = ys[b];
				if (y1 >= 0 != y2 >= 0)
					return y1 > y2 ? -1 : +1;
				else if (y1 == 0 && y2 == 0)
					return x1 > x2 ? -1 : +1;
				else
					return (long)x1 * y2 > (long)x2 * y1 ? -1 : +1;
			}
		});
		return id;
	}
	
	static void tr(Object... os) { System.err.println(deepToString(os)); }
	static void tr(int[][] as) { for (int[] a : as) tr(a); }

	void print(int[] a) {
		out.print(a[0]);
		for (int i = 1; i < a.length; i++) out.print(" " + a[i]);
		out.println();
	}

	public static void main(String[] args) throws Exception {
		new Main().run();
	}

	MyScanner sc = null;
	PrintWriter out = null;
	public void run() throws Exception {
		sc = new MyScanner(System.in);
		out = new PrintWriter(System.out);
		for (;sc.hasNext();) {
			solve();
			out.flush();
		}
		out.close();
	}

	class MyScanner {
		String line;
		BufferedReader reader;
		StringTokenizer tokenizer;

		public MyScanner(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream));
			tokenizer = null;
		}
		public void eat() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					line = reader.readLine();
					if (line == null) {
						tokenizer = null;
						return;
					}
					tokenizer = new StringTokenizer(line);
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
		}
		public String next() {
			eat();
			return tokenizer.nextToken();
		}
		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		public boolean hasNext() {
			eat();
			return (tokenizer != null && tokenizer.hasMoreElements());
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++) a[i] = nextInt();
			return a;
		}
	}
}