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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Reader;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.StringTokenizer;

// Educational Codeforces Round 1
// Nearest vectors
public class Problem_598_C {


  public static void main(String[] args)
  {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    PrintWriter out = new PrintWriter(outputStream);
    Problem_598_C solver = new Problem_598_C();
    solver.solve(1, new InputStreamReader(inputStream), out);
    out.close();
  }

  static class Angle implements Comparable<Angle>{
    long x;
    long y;
    int index;

    Angle(long x, long y, int i)
    {
      this.x = x;
      this.y = y;
      index = i;
    }

    @Override
    public int compareTo(Angle o)
    {
      long ax = x, ay = y;
      long bx = o.x, by = o.y;
      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;
      int v = Long.compare(ay*bx, ax*by);
      if(v != 0) return v;
      return index - o.index;
    }

    @Override
    public String toString()
    {
      return "(" + index + "," + x + ","+ y + ")";
    }
  }
  
  public static long dot(Angle a, Angle b)
  { 
    return a.x*b.x+a.y*b.y; 
  }

  public void solve(int test, Reader input, PrintWriter out)
  {
    MyScanner in = new MyScanner(input);

    int n = in.nextInt();

    Angle[] angles = new Angle[n];

    for(int i = 0; i < n; i++) {
      int dx = in.nextInt();
      int dy = in.nextInt();
      angles[i] = new Angle(dx, dy, i+1);
    }

    Arrays.sort(angles);

    BigInteger bnum = BigInteger.TEN.negate();
    BigInteger bden = BigInteger.ONE;
    int argi = -1;
    for(int i = 0, j = 1;i < n;i++,j++){
      if(j == n)j = 0;
      long d = dot(angles[i], angles[j]);
      long ni = dot(angles[i], angles[i]);
      long nj = dot(angles[j], angles[j]);
      BigInteger num = BigInteger.valueOf(d*d);
      if(d < 0)num = num.negate();
      BigInteger den = BigInteger.valueOf(ni*nj);
      // bnum/bden < num/den
      if(bnum.multiply(den).compareTo(num.multiply(bden)) < 0){
        argi = i;
        bden = den;
        bnum = num;
      }
    }
    out.println(angles[argi].index + " " + (angles[(argi+1)%n].index));
  }

  //-----------MyScanner class for faster input----------
  public static class MyScanner {
    BufferedReader br;
    StringTokenizer st;

    public MyScanner(Reader reader) {
      br = new BufferedReader(reader);
    }

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

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

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

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

    String nextLine(){
      String str = "";
      try {
        str = br.readLine();
      } catch (IOException e) {
        e.printStackTrace();
      }
      return str;
    }

  }
  //--------------------------------------------------------

}