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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.math.BigInteger;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            Point[] p = new Point[n];
            for (int i = 0; i < n; ++i) {
                int x = in.nextInt(), y = in.nextInt();
                p[i] = new Point(x, y, i + 1);
            }
            Arrays.sort(p);
            Node best = new Node(p[0].dot(p[1]), p[0].len2, p[1].len2);
            int a = p[0].id, b = p[1].id;
            for (int i = 0; i < n; ++i) {
                Point q = p[i], r = p[(i + 1) % n];
                Node tmp = new Node(q.dot(r), q.len2, r.len2);
                if (tmp.compareTo(best) < 0) {
                    best = tmp;
                    a = q.id;
                    b = r.id;
                }
            }
            out.println(a + " " + b);
        }

        class Point implements Comparable<Point> {
            int x;
            int y;
            int id;
            int len2;
            double rad;

            public Point(int x, int y, int id) {
                this.x = x;
                this.y = y;
                this.id = id;
                len2 = x * x + y * y;
                rad = Math.atan2(y, x);
            }


            public int compareTo(Point o) {
                return rad < o.rad ? -1 : (rad > o.rad ? 1 : 0);
            }

            public int dot(Point o) {
                return x * o.x + y * o.y;
            }

        }

        class Node implements Comparable<Node> {
            long dot;
            long l1;
            long l2;

            public Node(long dot, long l1, long l2) {
                this.dot = dot;
                this.l1 = l1;
                this.l2 = l2;
            }


            public int compareTo(Node o) {
                int s1 = Long.signum(dot), s2 = Long.signum(o.dot);
                if (s1 != s2) {
                    return s1 > s2 ? -1 : 1;
                }
                if (s1 == 0) return 0;
                BigInteger a = BigInteger.valueOf(dot * dot).multiply(BigInteger.valueOf(o.l1 * o.l2));
                BigInteger b = BigInteger.valueOf(o.dot * o.dot).multiply(BigInteger.valueOf(l1 * l2));
                return s1 > 0 ? -a.compareTo(b) : a.compareTo(b);
            }

        }

    }

    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }
}