import java.util.*;
import java.util.zip.*;
import java.util.List;
import java.util.regex.*;
import java.util.concurrent.*;
import java.util.concurrent.atomic.*;
import java.util.concurrent.locks.*;
import java.util.function.*;
import javax.swing.*;
import javax.swing.event.*;
import javax.swing.text.*;
import javax.swing.table.*;
import java.io.*;
import java.net.*;
import java.lang.reflect.*;
import java.lang.ref.*;
import java.lang.management.*;
import java.security.*;
import java.security.spec.*;
import java.awt.*;
import java.awt.event.*;
import java.awt.image.*;
import java.awt.geom.*;
import javax.imageio.*;
import java.math.*;
import java.time.Duration;
// We store the angle in clockwise radians for more efficient
// calculations.
// So 0=right, pi=down etc.

class main {

static class Angle {
  Angle() {}
  double radians;
  
  Angle(double radians) {
  this.radians = radians;}
  
  // Create angle from x/y ratio
  Angle(double x, double y) { radians = atan2(x, y); }
  
  static Angle fromRadians(double radians) { return new Angle(radians); }
  static Angle fromDegrees(double degrees) { return new Angle(degreesToRadians(degrees)); }

  double radians() { return radians; }
  double degrees() { return radiansToDegrees(radians); }
  
  double x() { return cos(radians); }
  double y() { return sin(radians); }
  
  public String toString() { return formatDouble(degrees(), 1) + "°"; }
}
static double atan2(double x, double y) {
  return Math.atan2(x, y);
}


static double degreesToRadians(double deg) {
  return degreeToRadian(deg);
}


static double radiansToDegrees(double rad) {
  return radianToDegree(rad);
}


static double cos(double x) {
  return Math.cos(x);
}


static double sin(double x) {
  return Math.sin(x);
}


static String formatDouble(double d, int digits) {
  String format = digits <= 0 ? "0" : "0." + rep(digits, '#');
  return decimalFormatEnglish(format, d);
}

static String formatDouble(double d) {
  return str(d);
}






static double degreeToRadian(double deg) {
  return deg*(pi()/180);
}


static double radianToDegree(double rad) {
  return rad*(180/pi());
}


static String rep(int n, char c) {
  return repeat(c, n);
}

static String rep(char c, int n) {
  return repeat(c, n);
}

static <A> List<A> rep(A a, int n) {
  return repeat(a, n);
}

static <A> List<A> rep(int n, A a) {
  return repeat(n, a);
}



static String decimalFormatEnglish(String format, double d) {
  return decimalFormatEnglish(format).format(d);
}

static java.text.DecimalFormat decimalFormatEnglish(String format) {
  return new java.text.DecimalFormat(format, new java.text.DecimalFormatSymbols(Locale.ENGLISH));
}


static String str(Object o) {
  return o == null ? "null" : o.toString();
}

static String str(char[] c) {
  return new String(c);
}

static String str(char[] c, int offset, int count) {
  return new String(c, offset, count);
}




static double pi() {
  return Math.PI;
}


static String repeat(char c, int n) {
  n = Math.max(n, 0);
  char[] chars = new char[n];
  for (int i = 0; i < n; i++)
    chars[i] = c;
  return new String(chars);
}

static <A> List<A> repeat(A a, int n) {
  n = Math.max(n, 0);
  List<A> l = new ArrayList(n);
  for (int i = 0; i < n; i++)
    l.add(a);
  return l;
}

static <A> List<A> repeat(int n, A a) {
  return repeat(a, n);
}



}