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.*;
import java.util.stream.*;

@SuppressWarnings("unchecked")
public class P598C {

  public class Vector implements Comparable<Vector> {
    final BigDecimal ONE_HALF = BigDecimal.valueOf(0.5D);
    final MathContext MC = MathContext.DECIMAL128;
    int n, x, y;
    BigDecimal nx, ny;

    public Vector(int n, int x, int y) {
      this.n = n;
      this.x = x;
      this.y = y;
      BigDecimal x2y2 = BigDecimal.valueOf(x).multiply(BigDecimal.valueOf(x))
                                  .add(BigDecimal.valueOf(y).multiply(BigDecimal.valueOf(y)));
      BigDecimal vl = BigDecimal.valueOf(Math.sqrt(x * x + y * y));
      vl = vl.add(x2y2.divide(vl, MC)).multiply(ONE_HALF);
      nx = BigDecimal.valueOf(x).divide(vl, MC);
      ny = BigDecimal.valueOf(y).divide(vl, MC);
    }

    BigDecimal edge(Vector v) {
      BigDecimal dx = nx.subtract(v.nx);
      BigDecimal dy = ny.subtract(v.ny);
      
      return (dx.multiply(dx).add(dy.multiply(dy)));
    }

    @Override
    public int compareTo(Vector v) {
      if ((y >= 0) && (v.y < 0)) {
        return -1;
      } else if ((y < 0) && (v.y >= 0)) {
        return 1;
      } else {
        return ((y >= 0) ? ((nx.compareTo(v.nx) >= 0) ? -1 : 1) : ((nx.compareTo(v.nx) >= 0) ? 1 : -1));
      }
    }
  }

  public void run() throws Exception {
    ArrayList<Vector> v = new ArrayList();

    for (int n = nextInt(); n > 0; n--) {
      v.add(new Vector(v.size() + 1, nextInt(), nextInt()));
    }

    v.sort(null);
    v.add(new Vector(v.get(0).n, v.get(0).x, v.get(0).y));

    int mi = 0;
    BigDecimal me = BigDecimal.TEN;
    for (int i = 0; i < (v.size() - 1); i++) {
      BigDecimal e = v.get(i).edge(v.get(i + 1));
      if (e.compareTo(me) < 0) {
        me = e;
        mi = i;
      }
    }

    println(v.get(mi).n + " " + v.get(mi + 1).n);
  }

  public static void main(String... args) throws Exception {
    br = new BufferedReader(new InputStreamReader(System.in));
    pw = new PrintWriter(new BufferedOutputStream(System.out));
    new P598C().run();
    br.close();
    pw.close();
    System.err.println("\n[Time : " + (System.currentTimeMillis() - startTime) + " ms]");
  }

  static long startTime = System.currentTimeMillis();
  static BufferedReader br;
  static PrintWriter pw;
  StringTokenizer stok;

  String nextToken() throws IOException {
    while (stok == null || !stok.hasMoreTokens()) {
      String s = br.readLine();
      if (s == null) { return null; }
      stok = new StringTokenizer(s);
    }
    return stok.nextToken();
  }

  void print(byte b) { print("" + b); }
  void print(int i) { print("" + i); }
  void print(long l) { print("" + l); }
  void print(double d) { print("" + d); }
  void print(char c) { print("" + c); }
  void print(Object o) {
    if (o instanceof int[]) { print(Arrays.toString((int [])o));
    } else if (o instanceof long[]) { print(Arrays.toString((long [])o));
    } else if (o instanceof char[]) { print(Arrays.toString((char [])o));
    } else if (o instanceof byte[]) { print(Arrays.toString((byte [])o));
    } else if (o instanceof short[]) { print(Arrays.toString((short [])o));
    } else if (o instanceof boolean[]) { print(Arrays.toString((boolean [])o));
    } else if (o instanceof float[]) { print(Arrays.toString((float [])o));
    } else if (o instanceof double[]) { print(Arrays.toString((double [])o));
    } else if (o instanceof Object[]) { print(Arrays.toString((Object [])o));
    } else { print("" + o); }
  }
  void print(String s) { pw.print(s); }
  void println() { println(""); }
  void println(byte b) { println("" + b); }
  void println(int i) { println("" + i); }
  void println(long l) { println("" + l); }
  void println(double d) { println("" + d); }
  void println(char c) { println("" + c); }
  void println(Object o) { print(o); println(); }
  void println(String s) { pw.println(s); }
  int nextInt() throws IOException { return Integer.parseInt(nextToken()); }
  long nextLong() throws IOException { return Long.parseLong(nextToken()); }
  double nextDouble() throws IOException { return Double.parseDouble(nextToken()); }
  char nextChar() throws IOException { return (char) (br.read()); }
  String next() throws IOException { return nextToken(); }
  String nextLine() throws IOException { return br.readLine(); }
  int [] readInt(int size) throws IOException {
    int [] array = new int [size];
    for (int i = 0; i < size; i++) { array[i] = nextInt(); }
    return array;
  }
  long [] readLong(int size) throws IOException {
    long [] array = new long [size];
    for (int i = 0; i < size; i++) { array[i] = nextLong(); }
    return array;
  }
  double [] readDouble(int size) throws IOException {
    double [] array = new double [size];
    for (int i = 0; i < size; i++) { array[i] = nextDouble(); }
    return array;
  }
  String [] readLines(int size) throws IOException {
    String [] array = new String [size];
    for (int i = 0; i < size; i++) { array[i] = nextLine(); }
    return array;
  }
}