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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Iterator;


public class Main_Educational1_C {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		Printer pr = new Printer(System.out);

		int n = sc.nextInt();
		Pair[] vec = new Pair[n];

		for (int i = 0; i < n; i++) {
			vec[i] = new Pair(i + 1, sc.nextInt(), sc.nextInt());
		}
		Arrays.sort(vec);

		double min = vec[n - 1].arc - vec[0].arc;
		double mintan = Double.MAX_VALUE;
		if (min > Math.PI) {
			min = Math.PI * 2 - min;
			mintan = -(double)Geom.cross(vec[0].x, vec[0].y, vec[n - 1].x, vec[n - 1].y) / Geom.dot(vec[0].x, vec[0].y, vec[n - 1].x, vec[n - 1].y);
		} else if (min < Math.PI / 2) {
			mintan = (double)Geom.cross(vec[0].x, vec[0].y, vec[n - 1].x, vec[n - 1].y) / Geom.dot(vec[0].x, vec[0].y, vec[n - 1].x, vec[n - 1].y);
		}
		int min1 = vec[n - 1].index;
		int min2 = vec[0].index;

		for (int i = 1; i < n; i++) {
			double tmp = vec[i].arc - vec[i - 1].arc;
			double tmptan = Double.MAX_VALUE;
			if (tmp > Math.PI) {
				tmp = Math.PI * 2 - tmp;
				tmptan = -(double)Geom.cross(vec[i - 1].x, vec[i - 1].y, vec[i].x, vec[i].y) / Geom.dot(vec[i - 1].x, vec[i - 1].y, vec[i].x, vec[i].y);
			} else if (tmp < Math.PI / 2) {
				tmptan = (double)Geom.cross(vec[i - 1].x, vec[i - 1].y, vec[i].x, vec[i].y) / Geom.dot(vec[i - 1].x, vec[i - 1].y, vec[i].x, vec[i].y);
			}
			if (min < Math.PI / 2 && tmp < Math.PI / 2) {
				if (mintan > tmptan) {
					min = tmp;
					mintan = tmptan;
					min1 = vec[i - 1].index;
					min2 = vec[i].index;
				}
			} else {
				if (min > tmp) {
					min = tmp;
					mintan = tmptan;
					min1 = vec[i - 1].index;
					min2 = vec[i].index;
				}
			}
		}

		pr.printf("%d %d\n", min1, min2);

		pr.close();
		sc.close();
	}

	@SuppressWarnings("unused")
	private static class Geom {
		static int dot(int xa, int ya, int xb, int yb) {
			return xa * xb + ya * yb;
		}

		static int cross(int xa, int ya, int xb, int yb) {
			return xa * yb - xb * ya;
		}

		static int sumofsquare(int xa, int ya) {
			return xa * xa + ya * ya;
		}
	}

	private static class Pair implements Comparable<Pair>{
		int index;
		int x;
		int y;
		double arc;

		Pair(int i, int x, int y) {
			this.index = i;
			this.x = x;
			this.y = y;
			this.arc = Math.atan2(y, x);
		}

		@Override
		public int compareTo(Pair o) {
			return Double.compare(this.arc, o.arc);
		}
	}

	@SuppressWarnings("unused")
	private static class Scanner {
		BufferedReader br;
		Iterator<String> it;

		Scanner (InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}

		String next() throws RuntimeException  {
			try {
				if (it == null || !it.hasNext()) {
					it = Arrays.asList(br.readLine().split(" ")).iterator();
				}
				return it.next();
			} catch (IOException e) {
				throw new IllegalStateException();
			}
		}

		int nextInt() throws RuntimeException {
			return Integer.parseInt(next());
		}

		long nextLong() throws RuntimeException {
			return Long.parseLong(next());
		}

		float nextFloat() throws RuntimeException {
			return Float.parseFloat(next());
		}

		double nextDouble() throws RuntimeException {
			return Double.parseDouble(next());
		}

		void close() {
			try {
				br.close();
			} catch (IOException e) {
//				throw new IllegalStateException();
			}
		}
	}

	private static class Printer extends PrintWriter {
		Printer(PrintStream out) {
			super(out);
		}
	}
}