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.math.BigInteger;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Comparator;
import java.util.Collections;
import java.util.ArrayList;
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);
        CNearestVectors solver = new CNearestVectors();
        solver.solve(1, in, out);
        out.close();
    }

    static class CNearestVectors {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            ArrayList<Point> up = new ArrayList<>();
            ArrayList<Point> lw = new ArrayList<>();
            Point ref = new Point(1, 0);
            for (int i = 0; i < n; i++) {
                Point P = new Point(in.nextInt(), in.nextInt());
                P.ind = i + 1;
                long cr = ref.cross(P);
                long dt = ref.dot(P);
                if (cr == 0 && dt >= 0) {
                    up.add(P);
                } else if (cr == 0 && dt < 0) {
                    lw.add(P);
                } else if (cr > 0) {
                    up.add(P);
                } else if (cr < 0) {
                    lw.add(P);
                }
            }
            Collections.sort(up, new Comparator<Point>() {

                public int compare(Point o1, Point o2) {
                    return o2.ccw(o1);
                }
            });
            Collections.sort(lw, new Comparator<Point>() {

                public int compare(Point o1, Point o2) {
                    return o2.ccw(o1);
                }
            });
            ArrayList<Point> All = new ArrayList<>();
            for (Point ele : up) {
                All.add(ele);
            }
            for (Point ele : lw) {
                All.add(ele);
            }

            int i1 = 0;
            int i2 = 1;
            BigInteger mina = BigInteger.valueOf(-100);
            BigInteger minb = BigInteger.valueOf(1);
            for (int i = 0; i < n; i++) {

                BigInteger x1 = (BigInteger.valueOf(All.get(i).x));
                BigInteger y1 = BigInteger.valueOf(All.get(i).y);
                BigInteger x2 = BigInteger.valueOf(All.get((i + 1) % n).x);
                BigInteger y2 = BigInteger.valueOf(All.get((i + 1) % n).y);
                BigInteger dot = x1.multiply(x2).add(y1.multiply(y2));
                int s = (dot.compareTo(BigInteger.valueOf(0)) < 0) ? -1 : 1;
                BigInteger numer = dot.multiply(dot).multiply(BigInteger.valueOf(s));
                BigInteger denom = BigInteger.valueOf(All.get((i + 1) % n).abs()).multiply(BigInteger.valueOf(All.get(i).abs()));

                if (comp(numer, denom, mina, minb)) {
                    mina = numer;
                    minb = denom;
                    i2 = All.get((i + 1) % n).ind;
                    i1 = All.get(i).ind;
                }
            }

            out.println(i1 + " " + i2);
        }

        boolean comp(BigInteger a1, BigInteger b1, BigInteger a2, BigInteger b2) {
            return (a1.multiply(b2).subtract(a2.multiply(b1)).compareTo((BigInteger.valueOf(0))) > 0);
        }

        class Point {
            long x;
            long y;
            int ind;

            Point(long x1, long y1) {
                x = x1;
                y = y1;
            }

            long dot(Point a) {
                return x * a.x + y * a.y;
            }

            long cross(Point a) {
                return x * a.y - y * a.x;
            }

            long abs() {
                return dot(this);
            }

            int ccw(Point a) {
                return (int) Math.signum(cross(a));
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}