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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Ruins He
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    OutputWriter out = new OutputWriter(outputStream);
    TaskC solver = new TaskC();
    solver.solve(1, in, out);
    out.close();
  }

  static class TaskC {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
      int n = in.nextInt();
      Point[] points = new Point[n];
      Integer[] idx = new Integer[n];
      for (int i = 0; i < n; i++) {
        long x = in.nextLong();
        long y = in.nextLong();
        points[i] = new Point(x, y);
        idx[i] = i;
      }
      Geos.VectorPolarComparator comparator = new Geos.VectorPolarComparator();
      Arrays.sort(idx, (a, b) -> comparator.compare(points[a], points[b]));
      BigInteger rA = BigInteger.valueOf(points[idx[0]].dotProduct(points[idx[n - 1]]));
      rA = BigInteger.valueOf(rA.signum()).multiply(rA.multiply(rA));
      BigInteger rB = BigInteger.valueOf(points[idx[0]].norm() * points[idx[n - 1]].norm());
      if (rB.signum() < 0) {
        rA = rA.negate();
        rB = rB.negate();
      }
      int a = idx[n - 1], b = idx[0];
      for (int i = 1; i < n; i++) {
        BigInteger cA = BigInteger.valueOf(points[idx[i]].dotProduct(points[idx[i - 1]]));
        cA = BigInteger.valueOf(cA.signum()).multiply(cA.multiply(cA));
        BigInteger cB = BigInteger.valueOf(points[idx[i - 1]].norm() * points[idx[i]].norm());
        if (cB.signum() < 0) {
          cA = cA.negate();
          cB = cB.negate();
        }
        if (cA.multiply(rB).compareTo(rA.multiply(cB)) > 0) {
          rA = cA;
          rB = cB;
          a = idx[i - 1];
          b = idx[i];
        }
      }
      out.printObjects(a + 1, b + 1);
    }

  }

  static class InputReader {
    public final BufferedReader reader;
    public StringTokenizer tokenizer = null;

    public InputReader(Reader reader) {
      this.reader = new BufferedReader(reader, 32767);
    }

    public InputReader(InputStream inputStream) {
      this(new InputStreamReader(inputStream));
    }

    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());
    }

  }

  static class Point {
    public long x;
    public long y;

    public Point(long x, long y) {
      this.x = x;
      this.y = y;
    }

    public long crossProduct(Point p) {
      return x * p.y - y * p.x;
    }

    public long dotProduct(Point p) {
      return x * p.x + y * p.y;
    }

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


    public String toString() {
      return String.format("(%d, %d @ %.4f)", x, y, Math.atan2(y, x));
    }

  }

  static class Geos {
    private Geos() {
    }

    public static class VectorPolarComparator implements Comparator<Point> {

      public int compare(Point a, Point b) {
        int fa = getQuadrantId(a);
        int fb = getQuadrantId(b);
        return fa != fb ? Integer.compare(fa, fb) : Long.compare(0, a.crossProduct(b));
      }

      private static int getQuadrantId(Point point) {
        if (point.y == 0) return point.x < 0 ? 0 : 4;
        else if (point.x == 0) return point.y < 0 ? 2 : 6;
        else if (point.y < 0) return point.x < 0 ? 1 : 3;
        else return point.x > 0 ? 5 : 7;
      }

    }

  }

  static class OutputWriter {
    private final PrintWriter writer;

    private OutputWriter(Writer writer, boolean autoFlush) {
      this.writer = new PrintWriter(new BufferedWriter(writer, 32767), autoFlush);
    }

    public OutputWriter(Writer writer) {
      this(writer, true);
    }

    public OutputWriter(OutputStream outputStream) {
      this(new OutputStreamWriter(outputStream), false);
    }

    public OutputWriter println() {
      writer.println();
      return this;
    }

    public OutputWriter printObjects(Object... values) {
      return printObjects(" ", values);
    }

    public OutputWriter printObjects(String s, Object... values) {
      for (int i = 0; i < values.length; i++) {
        if (i > 0) print(s);
        print(values[i]);
      }
      println();
      return this;
    }

    public void print(Object object) {
      writer.print(object);
    }

    public void close() {
      writer.close();
    }

  }
}