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:
/*************************************************************************
  >         File: Main.java
  >       Author: Riho.Yoshioka
  >         Mail: riho.yoshioka@yandex.com
  > Created Time: Sun 31 Jul 2016 02:24:56 PM CST
*************************************************************************/
import java.io.*;
import java.util.*;
import java.math.*;

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);
    
    TaskC solver = new TaskC();
    solver.solve(1, in, out);
    out.close();
  }

  static class TaskC {
    Point[] p;

    public void solve(int testNumber, InputReader in, PrintWriter out) {
      int n = in.nextInt();
      p = new Point[n];
      for (int i = 0; i < n; i++) {
        int x = in.nextInt(); 
        int y = in.nextInt();
        p[i] = new Point(x, y, i + 1);
      }
      Arrays.sort(p, new Comparator<Point> () {
        public int compare(Point lhs, Point rhs) {
          if (lhs.dim() == rhs.dim()) {
            return Point.det(lhs, rhs) < 0 ? 1 : -1;
          }
          else {
            return lhs.dim() < rhs.dim() ? 1 : -1;
          }
        }
      });
      BigDecimal ans = new BigDecimal("-100.0");
      int best = -1;
      for (int i = 0; i < n; i++) {
        BigDecimal angle = calc(i, (i + 1) % n);
        if (angle.compareTo(ans) > 0) {
          best = i;
          ans = angle;
        }
      }
      //out.println(ans);
      out.println(p[best].idx + " " + p[(best + 1) % n].idx);
    }

    private BigDecimal sqrt(BigDecimal x, final int scale) {
      BigDecimal x0 = new BigDecimal("0");
      BigDecimal x1 = new BigDecimal(Math.sqrt(x.doubleValue()));
      while (!x0.equals(x1)) {
        x0 = x1;
        x1 = x.divide(x0, scale, BigDecimal.ROUND_HALF_UP);
        x1 = x1.add(x0);
        x1 = x1.divide(new BigDecimal("2"), scale, BigDecimal.ROUND_HALF_UP);
      }
      return x1;
    }

    private BigDecimal calc(int x, int y) {
      Point np = new Point(p[x].x - p[y].x, p[x].y - p[y].y, 0);
      BigDecimal up = new BigDecimal(p[x].norm() + p[y].norm() - np.norm());
      BigDecimal down = new BigDecimal("2");
      down = down.multiply(sqrt(new BigDecimal(p[x].norm()), 50));
      down = down.multiply(sqrt(new BigDecimal(p[y].norm()), 50));
      return up.divide(down, 50, BigDecimal.ROUND_HALF_UP);
    }
  }

  static final class Point implements Comparator<Point> {
    public long x, y;
    public int idx;

    public Point(long a, long b, int c) {
      x = a; y = b;
      idx = c;
    }

    public long norm() {
      return x * x + y * y;
    }

    public int dim() {
      return x < 0 || (x == 0 && y < 0) ? 1 : 0;
    }

    public int compare(Point lhs, Point rhs) {
      if (lhs.dim() == rhs.dim()) {
        return det(lhs, rhs) < 0 ? 1 : -1;
      }
      else {
        return lhs.dim() < rhs.dim() ? 1 : -1;
      }
    }

    static long det(Point a, Point b) {
      return a.x * b.y - a.y * b.x;
    }
  }

  static class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
      reader = new BufferedReader(new InputStreamReader(stream), 32768);
      tokenizer = null;
    }

    public String next() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          tokenizer = new StringTokenizer(reader.readLine());
        } catch (IOException e) {
          throw new RuntimeException(e);
        }
      }
      return tokenizer.nextToken();
    }

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

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

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