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.FilterInputStream;
import java.io.BufferedInputStream;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Jenish
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(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, ScanReader in, PrintWriter out) {
            int n = in.scanInt();
            long arr[][] = new long[n][3];
            for (int i = 0; i < n; i++) arr[i] = new long[]{in.scanInt(), in.scanInt(), i + 1};
            Arrays.sort(arr, new Comparator<long[]>() {

                public int compare(long[] a, long[] b) {
                    long ax = a[0], ay = a[1];
                    long bx = b[0], by = b[1];
                    int za = ay > 0 || ay == 0 && ax > 0 ? 0 : 1;
                    int zb = by > 0 || by == 0 && bx > 0 ? 0 : 1;
                    if (za != zb) return za - zb;
                    if (ay * bx - ax * by != 0) return Long.signum(ay * bx - ax * by);
                    return Long.signum((ax * ax + ay * ay) - (bx * bx + by * by));
                }
            });


            double angle = Double.MAX_VALUE;
            long bnum = -1;
            long bden = 0;
            int index = -1;
            for (int i = 0; i < n; i++) {
                int j = (i + 1) % n;
                long sig = Long.signum(dot(arr[i], arr[j]));
                long num = dot(arr[i], arr[j]) * dot(arr[i], arr[j]) * sig;
                long den = dot(arr[i], arr[i]) * dot(arr[j], arr[j]);
                if (comp(bnum, bden, num, den) < 0) {
                    bnum = num;
                    bden = den;
                    index = i;
                }
            }
            out.println(arr[index][2] + " " + arr[(index + 1) % n][2]);


        }

        long comp(long an, long ad, long bn, long bd) {
            double bal = (double) an * bd - (double) bn * ad;
            if (Math.abs(bal) > 1e18) return (int) Math.signum(bal);

            return an * bd - bn * ad;
        }

        public static long dot(long[] a, long[] b) {
            return a[0] * b[0] + a[1] * b[1];
        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int INDEX;
        private BufferedInputStream in;
        private int TOTAL;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (INDEX >= TOTAL) {
                INDEX = 0;
                try {
                    TOTAL = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (TOTAL <= 0) return -1;
            }
            return buf[INDEX++];
        }

        public int scanInt() {
            int I = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    I *= 10;
                    I += n - '0';
                    n = scan();
                }
            }
            return neg * I;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }
}