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.*;
import java.util.*;

public class C {

  static BufferedReader in;
  static PrintWriter out;
  static StringTokenizer stk;

  public static class Pair {

    int id;
    public BigInteger x;
    public BigInteger y;

    public Pair(int id, BigInteger x, BigInteger y) {
      this.id = id;
      this.x = x;
      this.y = y;
    }

  }

  static BigInteger cross(Pair a, Pair b) {
    return a.x.multiply(b.y).subtract(a.y.multiply(b.x));
  }

  static BigInteger dot(Pair a, Pair b) {
    return a.x.multiply(b.x).add(a.y.multiply(b.y));
  }

  public static void main(String[] args) throws Exception {
    in = new BufferedReader(new InputStreamReader(System.in));
    out = new PrintWriter(new OutputStreamWriter(System.out));

    preproc();

    /** Choose single or multiple */

    single(0);
    // multiple();

    out.flush();
  }

  static void preproc() {
    // add any preprocessing valid for all tests here
    //
  }

  static boolean isInTopHalf(Pair p) {
    return p.y.signum() > 0 || (p.y.signum() == 0 && p.x.signum() > 0);
  }

  static void single(int testId) throws Exception {
    // add code here
    //
    int n = ni();
    Pair[] p = new Pair[n];

    for (int i = 0; i < n; i++) {
      int x = ni();
      int y = ni();
      p[i] = new Pair(i + 1, toBI(x), toBI(y));
    }

    Arrays.sort(p, (a, b) -> {
      boolean aInTop = isInTopHalf(a);
      boolean bInTop = isInTopHalf(b);
      if (aInTop == bInTop) {
        return -cross(a, b).signum();
      }
      if (aInTop)
        return -1;
      return 1;
    });

    //  for (Pair q: p) {
    //    printf("%d %s %s\n", q.id, q.x, q.y);
    //  }

    Pair r1 = p[n - 1], r2 = p[0];
    for (int i = 0; i < n - 1; i++) {
      int j = (i + 1) % n;
      Pair a = new Pair(0, dot(r1, r2), cross(r1, r2).abs());
      Pair b = new Pair(0, dot(p[i], p[j]), cross(p[i], p[j]).abs());
      if (cross(b, a).signum() > 0) {
        r1 = p[i];
        r2 = p[j];
      }
    }
    printf("%d %d\n", r1.id, r2.id);
  }

  static void multiple() throws Exception {
    // multiple tests in single file
    int T = ni();
    for (int t = 0; t < T; t++) {
      single(t);
    }
  }

  static void printf(String format, Object... args) {
    out.printf(format, args);
  }

  static void println(String string) {
    out.println(string);
  }

  static long toL(String s) {
    return Long.parseLong(s);
  }

  static int toI(String s) {
    return Integer.parseInt(s);
  }

  static double toD(String s) {
    return Double.parseDouble(s);
  }

  static long toL(BigInteger n) {
    return n.longValue();
  }

  static BigInteger toBI(long n) {
    return BigInteger.valueOf(n);
  }

  static List<Integer> newli() {
    return new ArrayList<Integer>();
  }

  static List<Long> newll() {
    return new ArrayList<Long>();
  }

  static void nia(int[] a, int n) throws Exception {
    for (var i = 0; i < n; i++) {
      a[i] = ni();
    }
  }

  static void nla(long[] a, int n) throws Exception {
    for (var i = 0; i < n; i++) {
      a[i] = nl();
    }
  }

  static void nia(List<Integer> a, int n) throws Exception {
    for (var i = 0; i < n; i++) {
      a.add(ni());
    }
  }

  static void nla(List<Long> a, int n) throws Exception {
    for (var i = 0; i < n; i++) {
      a.add(nl());
    }
  }

  static int ni() throws Exception {
    while (stk == null || !stk.hasMoreTokens()) {
      stk = new StringTokenizer(in.readLine());
    }
    return Integer.parseInt(stk.nextToken());
  }

  static long nl() throws Exception {
    while (stk == null || !stk.hasMoreTokens()) {
      stk = new StringTokenizer(in.readLine());
    }
    return Long.parseLong(stk.nextToken());
  }

  static double nd() throws Exception {
    while (stk == null || !stk.hasMoreTokens()) {
      stk = new StringTokenizer(in.readLine());
    }
    return Double.parseDouble(stk.nextToken());
  }

  static String ns() throws Exception {
    while (stk == null || !stk.hasMoreTokens()) {
      stk = new StringTokenizer(in.readLine());
    }
    return stk.nextToken();
  }

  static int min(int a, int b) {
    return a < b ? a : b;
  }

  static int max(int a, int b) {
    return a > b ? a : b;
  }

  static long min(long a, long b) {
    return a < b ? a : b;
  }

  static long max(long a, long b) {
    return a > b ? a : b;
  }

  static double min(double a, double b) {
    return a < b ? a : b;
  }

  static double max(double a, double b) {
    return a > b ? a : b;
  }

  static int gcd(int a, int b) {
    if (b == 0) {
      return a;
    }
    return gcd(b, a % b);
  }

  static long gcd(long a, long b) {
    if (b == 0) {
      return a;
    }
    return gcd(b, a % b);
  }
}