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.*;
import java.math.BigInteger;
import java.util.*;

public class cf598C {
    private FastScanner in;
    private PrintWriter out;

    private void solve() {
        int n = in.nextInt();
        Point p[] = new Point[n];
        for (int i = 0; i < n; ++i) {
            p[i] = new Point();
            p[i].x = in.nextInt();
            p[i].y = in.nextInt();
            p[i].idx = i;
        }

        Arrays.sort(p);

        int ii = 0, jj = 1;
        for (int i = 1; i < n; ++i) {
            final int j = (i + 1) % n;
            if (cmp_angle(p[i], p[j], p[ii], p[jj])) {
                ii = i;
                jj = j;
            }
        }

        out.printf("%d %d", p[ii].idx + 1, p[jj].idx + 1);
    }

    boolean cmp_angle(Point a, Point b, Point p, Point q) {
        final int dot_ab = a.dot(b);
        final int dot_pq = p.dot(q);

        if (dot_ab >= 0 && dot_pq < 0) {
            return true;
        }

        if (dot_ab < 0 && dot_pq >= 0) {
            return false;
        }

        BigInteger l = BigInteger.valueOf(dot_ab).multiply(BigInteger.valueOf(dot_ab));
        l = l.multiply(BigInteger.valueOf(p.sq_norm()));
        l = l.multiply(BigInteger.valueOf(q.sq_norm()));

        BigInteger r = BigInteger.valueOf(dot_pq).multiply(BigInteger.valueOf(dot_pq));
        r = r.multiply(BigInteger.valueOf(a.sq_norm()));
        r = r.multiply(BigInteger.valueOf(b.sq_norm()));

        final boolean cmp = l.compareTo(r) >= 0;

        if (dot_ab >= 0 && dot_pq >= 0) {
            return cmp;
        }

        // dot_ab < 0 && dot_pq < 0
        return !cmp;
    }

    private void run() {
        try {
            in = new FastScanner(new File("input.txt"));
            out = new PrintWriter(new File("output.txt"));
            solve();
            out.close();
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }

    private void runIO() {
        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }

    class Point implements Comparable<Point> {
        int x, y;
        int idx;

        boolean upper() {
            return y > 0 || (y == 0 && x > 0);
        }

        public int cross(Point p) {
            return x * p.y - y * p.x;
        }

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

        public int sq_norm() {
            return x * x + y * y;
        }

        public int compareTo(Point p) {
            if (upper() && !p.upper()) {
                return -1;
            }
            if (p.upper() && !upper()) {
                return 1;
            }
            return -cross(p);
        }
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return null;
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

        boolean hasMoreTokens() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return false;
                st = new StringTokenizer(s);
            }
            return true;
        }

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

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

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

    public static void main(String[] args) {
        new cf598C().runIO();
    }
}