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 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 javax.imageio.*;
import java.math.*;
class main {


public static void main(final String[] args) throws Exception {
  List l = ll("hello", "world");
  assertEquals(2, l(new SynchronizedList(l)));
}


static <A> List<A> ll(A... a) {
  return litlist(a);
}
static Map<Thread, Boolean> _registerThread_threads = Collections.synchronizedMap(new WeakHashMap());

static Thread _registerThread(Thread t) {
  _registerThread_threads.put(t, true);
  return t;
}

static void _registerThread() { _registerThread(Thread.currentThread()); }
static <A> A assertEquals(Object x, A y) {
  return assertEquals(null, x, y);
}

static <A> A assertEquals(String msg, Object x, A y) {
  if (!(x == null ? y == null : x.equals(y)))
    throw fail((msg != null ? msg + ": " : "") + y + " != " + x);
  return y;
}
static int l(Object[] a) { return a == null ? 0 : a.length; }
static int l(boolean[] a) { return a == null ? 0 : a.length; }
static int l(byte[] a) { return a == null ? 0 : a.length; }
static int l(int[] a) { return a == null ? 0 : a.length; }
static int l(float[] a) { return a == null ? 0 : a.length; }
static int l(char[] a) { return a == null ? 0 : a.length; }
static int l(Collection c) { return c == null ? 0 : c.size(); }
static int l(Map m) { return m == null ? 0 : m.size(); }
static int l(CharSequence s) { return s == null ? 0 : s.length(); } static long l(File f) { return f == null ? 0 : f.length(); }

static int l(Object o) {
  return o instanceof String ? l((String) o)
    : o instanceof Map ? l((Map) o)
    : l((Collection) o); // incomplete
}






static RuntimeException fail() {
  throw new RuntimeException("fail");
}

static RuntimeException fail(Throwable e) {
  throw asRuntimeException(e);
}

static RuntimeException fail(Object msg) {
  throw new RuntimeException(String.valueOf(msg));
}

static RuntimeException fail(String msg) {
  throw new RuntimeException(unnull(msg));
}
 
static RuntimeException fail(String msg, Throwable innerException) {
  throw new RuntimeException(msg, innerException);
}

static <A> ArrayList<A> litlist(A... a) {
  return new ArrayList<A>(Arrays.asList(a));
}


static RuntimeException asRuntimeException(Throwable t) {
  return t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
}
static String unnull(String s) {
  return s == null ? "" : s;
}

static <A> List<A> unnull(List<A> l) {
  return l == null ? emptyList() : l;
}

static <A> Iterable<A> unnull(Iterable<A> i) {
  return i == null ? emptyList() : i;
}

static Object[] unnull(Object[] a) {
  return a == null ? new Object[0] : a;
}

static BitSet unnull(BitSet b) {
  return b == null ? new BitSet() : b;
}


static List emptyList() {
  return new ArrayList();
  //ret Collections.emptyList();
}


static class SynchronizedList<E> extends SynchronizedCollection<E> implements List<E> {
  final List<E> list;

  SynchronizedList(List<E> list) {
      super(list);
      this.list = list;
  }
  SynchronizedList(List<E> list, Object mutex) {
      super(list, mutex);
      this.list = list;
  }

  public boolean equals(Object o) {
      if (this == o)
          return true;
      synchronized (mutex) {return list.equals(o);}
  }
  public int hashCode() {
      synchronized (mutex) {return list.hashCode();}
  }

  public E get(int index) {
      synchronized (mutex) {return list.get(index);}
  }
  public E set(int index, E element) {
      synchronized (mutex) {return list.set(index, element);}
  }
  public void add(int index, E element) {
      synchronized (mutex) {list.add(index, element);}
  }
  public E remove(int index) {
      synchronized (mutex) {return list.remove(index);}
  }

  public int indexOf(Object o) {
      synchronized (mutex) {return list.indexOf(o);}
  }
  public int lastIndexOf(Object o) {
      synchronized (mutex) {return list.lastIndexOf(o);}
  }

  public boolean addAll(int index, Collection<? extends E> c) {
      synchronized (mutex) {return list.addAll(index, c);}
  }

  public ListIterator<E> listIterator() {
      return list.listIterator(); // Must be manually synched by user
  }

  public ListIterator<E> listIterator(int index) {
      return list.listIterator(index); // Must be manually synched by user
  }

  public List<E> subList(int fromIndex, int toIndex) {
      synchronized (mutex) {
          return new SynchronizedList<>(list.subList(fromIndex, toIndex),
                                      mutex);
      }
  }

  /*public void replaceAll(UnaryOperator<E> operator) {
      synchronized (mutex) {list.replaceAll(operator);}
  }*/
  
  public void sort(Comparator<? super E> c) {
      synchronized (mutex) {list.sort(c);}
  }
}

static <A> List<A> subList(List<A> l, int startIndex) {
  return subList(l, startIndex, l(l));
}

static <A> List<A> subList(List<A> l, int startIndex, int endIndex) {
  startIndex = max(0, min(l(l), startIndex));
  endIndex = max(0, min(l(l), endIndex));
  if (startIndex > endIndex) return litlist();
  return l.subList(startIndex, endIndex);
}


static void set(Object o, String field, Object value) {
  if (o instanceof Class) set((Class) o, field, value);
  else try {
    Field f = set_findField(o.getClass(), field);
    smartSet(f, o, value);
  } catch (Exception e) {
    throw new RuntimeException(e);
  }
}

static void set(Class c, String field, Object value) {
  try {
    Field f = set_findStaticField(c, field);
    smartSet(f, null, value);
  } catch (Exception e) {
    throw new RuntimeException(e);
  }
}
  
static Field set_findStaticField(Class<?> c, String field) {
  Class _c = c;
  do {
    for (Field f : _c.getDeclaredFields())
      if (f.getName().equals(field) && (f.getModifiers() & Modifier.STATIC) != 0)
        return f;
    _c = _c.getSuperclass();
  } while (_c != null);
  throw new RuntimeException("Static field '" + field + "' not found in " + c.getName());
}

static Field set_findField(Class<?> c, String field) {
  Class _c = c;
  do {
    for (Field f : _c.getDeclaredFields())
      if (f.getName().equals(field))
        return f;
    _c = _c.getSuperclass();
  } while (_c != null);
  throw new RuntimeException("Field '" + field + "' not found in " + c.getName());
}
static <A> void remove(List<A> l, int i) {
  if (l != null && i >= 0 && i < l(l))
    l.remove(i);
}
static <A> void addAll(Collection<A> c, Collection<A> b) {
  if (c != null && b != null) c.addAll(b);
}

static <A> void addAll(Collection<A> c, A... b) {
  if (c != null) c.addAll(Arrays.asList(b));
}
static boolean equals(Object a, Object b) {
  return a == null ? b == null : a.equals(b);
}
// get purpose 1: access a list/array/map (safer version of x.get(y))

static <A> A get(List<A> l, int idx) {
  return l != null && idx >= 0 && idx < l(l) ? l.get(idx) : null;
}

// seems to conflict with other signatures
/*static <A, B> B get(Map<A, B> map, A key) {
  ret map != null ? map.get(key) : null;
}*/

static <A> A get(A[] l, int idx) {
  return idx >= 0 && idx < l(l) ? l[idx] : null;
}

// default to false
static boolean get(boolean[] l, int idx) {
  return idx >= 0 && idx < l(l) ? l[idx] : false;
}

// get purpose 2: access a field by reflection or a map

static Object get(Object o, String field) {
  try {
    if (o instanceof Class) return get((Class) o, field);
    
    if (o instanceof Map)
      return ((Map) o).get(field);
      
    Field f = getOpt_findField(o.getClass(), field);
    if (f != null) {
      f.setAccessible(true);
      return f.get(o);
    }
      
    
  } catch (Exception e) {
    throw asRuntimeException(e);
  }
  throw new RuntimeException("Field '" + field + "' not found in " + o.getClass().getName());
}

static Object get_raw(Object o, String field) {
  try {
    Field f = get_findField(o.getClass(), field);
    f.setAccessible(true);
    return f.get(o);
  } catch (Exception e) {
    throw new RuntimeException(e);
  }
}

static Object get(Class c, String field) {
  try {
    Field f = get_findStaticField(c, field);
    f.setAccessible(true);
    return f.get(null);
  } catch (Exception e) {
    throw new RuntimeException(e);
  }
}

static Field get_findStaticField(Class<?> c, String field) {
  Class _c = c;
  do {
    for (Field f : _c.getDeclaredFields())
      if (f.getName().equals(field) && (f.getModifiers() & Modifier.STATIC) != 0)
        return f;
    _c = _c.getSuperclass();
  } while (_c != null);
  throw new RuntimeException("Static field '" + field + "' not found in " + c.getName());
}

static Field get_findField(Class<?> c, String field) {
  Class _c = c;
  do {
    for (Field f : _c.getDeclaredFields())
      if (f.getName().equals(field))
        return f;
    _c = _c.getSuperclass();
  } while (_c != null);
  throw new RuntimeException("Field '" + field + "' not found in " + c.getName());
}



static int max(int a, int b) { return Math.max(a, b); }
static int max(int a, int b, int c) { return max(max(a, b), c); }
static long max(int a, long b) { return Math.max((long) a, b); }
static long max(long a, long b) { return Math.max(a, b); }
static double max(int a, double b) { return Math.max((double) a, b); }
static float max(float a, float b) { return Math.max(a, b); }

static int max(Collection<Integer> c) {
  int x = Integer.MIN_VALUE;
  for (int i : c) x = max(x, i);
  return x;
}

static double max(double[] c) {
  if (c.length == 0) return Double.MIN_VALUE;
  double x = c[0];
  for (int i = 1; i < c.length; i++) x = Math.max(x, c[i]);
  return x;
}

static float max(float[] c) {
  if (c.length == 0) return Float.MAX_VALUE;
  float x = c[0];
  for (int i = 1; i < c.length; i++) x = Math.max(x, c[i]);
  return x;
}

static byte max(byte[] c) {
  byte x = -128;
  for (byte d : c) if (d > x) x = d;
  return x;
}

static short max(short[] c) {
  short x = -0x8000;
  for (short d : c) if (d > x) x = d;
  return x;
}
static void smartSet(Field f, Object o, Object value) throws Exception {
  f.setAccessible(true);
  
  // take care of common case (long to int)
  if (f.getType() == int.class && value instanceof Long)
    value = ((Long) value).intValue();
    
  try {
    f.set(o, value);
  } catch (Exception e) {
    
    throw e;
  }
}
static int min(int a, int b) {
  return Math.min(a, b);
}

static long min(long a, long b) {
  return Math.min(a, b);
}

static float min(float a, float b) { return Math.min(a, b); }
static float min(float a, float b, float c) { return min(min(a, b), c); }

static double min(double a, double b) {
  return Math.min(a, b);
}

static double min(double[] c) {
  double x = Double.MAX_VALUE;
  for (double d : c) x = Math.min(x, d);
  return x;
}

static float min(float[] c) {
  float x = Float.MAX_VALUE;
  for (float d : c) x = Math.min(x, d);
  return x;
}

static byte min(byte[] c) {
  byte x = 127;
  for (byte d : c) if (d < x) x = d;
  return x;
}

static short min(short[] c) {
  short x = 0x7FFF;
  for (short d : c) if (d < x) x = d;
  return x;
}
static Field getOpt_findField(Class<?> c, String field) {
  Class _c = c;
  do {
    for (Field f : _c.getDeclaredFields())
      if (f.getName().equals(field))
        return f;
    _c = _c.getSuperclass();
  } while (_c != null);
  return null;
}


static class SynchronizedCollection<E> implements Collection<E> {
  final Collection<E> c;  // Backing Collection
  final Object mutex;     // Object on which to synchronize

  SynchronizedCollection(Collection<E> c) {
      this.c = Objects.requireNonNull(c);
      mutex = this;
  }

  SynchronizedCollection(Collection<E> c, Object mutex) {
      this.c = Objects.requireNonNull(c);
      this.mutex = Objects.requireNonNull(mutex);
  }

  public int size() {
      synchronized (mutex) {return c.size();}
  }
  public boolean isEmpty() {
      synchronized (mutex) {return c.isEmpty();}
  }
  public boolean contains(Object o) {
      synchronized (mutex) {return c.contains(o);}
  }
  public Object[] toArray() {
      synchronized (mutex) {return c.toArray();}
  }
  public <T> T[] toArray(T[] a) {
      synchronized (mutex) {return c.toArray(a);}
  }

  public Iterator<E> iterator() {
      return c.iterator(); // Must be manually synched by user!
  }

  public boolean add(E e) {
      synchronized (mutex) {return c.add(e);}
  }
  public boolean remove(Object o) {
      synchronized (mutex) {return c.remove(o);}
  }

  public boolean containsAll(Collection<?> coll) {
      synchronized (mutex) {return c.containsAll(coll);}
  }
  public boolean addAll(Collection<? extends E> coll) {
      synchronized (mutex) {return c.addAll(coll);}
  }
  public boolean removeAll(Collection<?> coll) {
      synchronized (mutex) {return c.removeAll(coll);}
  }
  public boolean retainAll(Collection<?> coll) {
      synchronized (mutex) {return c.retainAll(coll);}
  }
  public void clear() {
      synchronized (mutex) {c.clear();}
  }
  public String toString() {
      synchronized (mutex) {return c.toString();}
  }
  
  /*public void forEach(Consumer<? super E> consumer) {
      synchronized (mutex) {c.forEach(consumer);}
  }*/
 
  /*public boolean removeIf(Predicate<? super E> filter) {
      synchronized (mutex) {return c.removeIf(filter);}
  }*/
  @Override
  public Spliterator<E> spliterator() {
      return c.spliterator(); // Must be manually synched by user!
  }
  
  /*public Stream<E> stream() {
      return c.stream(); // Must be manually synched by user!
  }*/
  
  /*public Stream<E> parallelStream() {
      return c.parallelStream(); // Must be manually synched by user!
  }*/
}

// union-type entry
static class E {
  String q, a, state;
  boolean test; // not used anymore probably
  String comment; // not checked for comparison
  
  E() {}
  E(String text, String type) {
    if (eq(type, "q")) q = text;
    else if (eq(type, "a")) a = text;
    else state = text;
  }
  
  // does not compare the "test" bit
  boolean eqTo(E y) {
    E x = this;
    return eq/*ic*/(x.q, y.q) && eq/*ic*/(x.a, y.a) && eq/*ic*/(x.state, y.state);
  }
  
  public boolean equals(Object o) {
    return o instanceof E && eqTo((E) o);
  }
  
  public int hashCode() {
    return stdHash(this, "q", "a", "state");
  }
  
  static E state(String state) {
    if (state == null) return null; E e = new E(); e.state = state; return e;
  }
  
  static E q(String q) {
    if (q == null) return null; E e = new E(); e.q = q; return e;
  }
  
  static E a(String a) {
    if (a == null) return null; E e = new E(); e.a = a; return e;
  }
  
  public String toString() {
    return unparsePoemLine(this);
  }
  
  boolean q() { return q != null; }
  boolean a() { return a != null; }
  boolean state() { return state != null; }
  String type() { return q() ? "q" : a() ? "a" : "state"; }
  String text() { return q() ? q : a() ? a : state; }
}

static int stdHash(Object a, String... fields) {
  if (a == null) return 0;
  int hash = getClassName(a).hashCode();
  for (String field : fields)
    hash = hash*2+hashCode(getOpt(a, field));
  return hash;
}
static <A> boolean containsAll(Collection<? extends A> a, Collection<A> b) {
  for (A o : b)
    if (!a.contains(o))
      return false;
  return true;
}
static boolean isEmpty(Collection c) {
  return c == null || c.isEmpty();
}

static boolean isEmpty(CharSequence s) {
  return s == null || s.length() == 0;
}

static boolean isEmpty(Object[] a) {
  return a == null || a.length == 0;
}

static boolean isEmpty(Map map) {
  return map == null || map.isEmpty();
}
static boolean eq(Object a, Object b) {
  return a == null ? b == null : a == b || a.equals(b);
}
static String unparsePoemLine(E e) {
  return trim(unparsePoem(litlist(e)));
}
static boolean contains(Collection c, Object o) {
  return c != null && c.contains(o);
}

static boolean contains(Object[] x, Object o) {
  if (x != null)
    for (Object a : x)
      if (eq(a, o))
        return true;
  return false;
}

static boolean contains(String s, char c) {
  return s != null && s.indexOf(c) >= 0;
}

static boolean contains(String s, String b) {
  return s != null && s.indexOf(b) >= 0;
}


static String unparsePoem(List<E> poem) {
  List<String> l = new ArrayList();
  for (E e : poem) {
    String s;
    if (e.q != null)
      s = "Usr: " + trim(e.q);
    else if (e.a != null)
      s = "Bot: " + trim(e.a);
    else if (e.state != null)
      s = "[" + trim(e.state) + "]";
    else
      s = "?";
    if (e.comment != null)
      s += " // " + e.comment;
    l.add(s);
  }
  return joinLines(l);
}
static String trim(String s) { return s == null ? null : s.trim(); }
static String trim(StringBuilder buf) { return buf.toString().trim(); }
static String trim(StringBuffer buf) { return buf.toString().trim(); }
static int hashCode(Object a) {
  return a == null ? 0 : a.hashCode();
}
static Object getOpt(Object o, String field) {
  return getOpt_cached(o, field);
}

static Object getOpt_raw(Object o, String field) {
  try {
    Field f = getOpt_findField(o.getClass(), field);
    if (f == null) return null;
    f.setAccessible(true);
    return f.get(o);
  } catch (Exception e) {
    throw new RuntimeException(e);
  }
}

static Object getOpt(Class c, String field) {
  try {
    if (c == null) return null;
    Field f = getOpt_findStaticField(c, field);
    if (f == null) return null;
    f.setAccessible(true);
    return f.get(null);
  } catch (Exception e) {
    throw new RuntimeException(e);
  }
}

static Field getOpt_findStaticField(Class<?> c, String field) {
  Class _c = c;
  do {
    for (Field f : _c.getDeclaredFields())
      if (f.getName().equals(field) && (f.getModifiers() & Modifier.STATIC) != 0)
        return f;
    _c = _c.getSuperclass();
  } while (_c != null);
  return null;
}

static String getClassName(Object o) {
  return o == null ? "null" : o.getClass().getName();
}


static String joinLines(List<String> lines) {
  return fromLines(lines);
}

static String joinLines(String glue, String text) {
  return join(glue, toLines(text));
}
static final WeakHashMap<Class, HashMap<String, Field>> getOpt_cache = new WeakHashMap();
static final HashMap getOpt_special = new HashMap(); // just a marker

static {
  getOpt_cache.put(Class.class, getOpt_special);
  getOpt_cache.put(String.class, getOpt_special);
}

static Object getOpt_cached(Object o, String field) { try {
  if (o == null) return null;

  Class c = o.getClass();
  HashMap<String, Field> map;
  synchronized(getOpt_cache) {
    map = getOpt_cache.get(c);
    if (map == null)
      map = getOpt_makeCache(c);
  }
  
  if (map == getOpt_special) {
    if (o instanceof Class)
      return getOpt((Class) o, field);
    /*if (o instanceof S)
      ret getOpt(getBot((S) o), field);*/
    if (o instanceof Map)
      return ((Map) o).get(field);
  }
    
  Field f = map.get(field);
  if (f != null) return f.get(o);
  
  return null;
} catch (Exception __e) { throw rethrow(__e); } }

// used internally - we are in synchronized block
static HashMap<String, Field> getOpt_makeCache(Class c) {
  HashMap<String, Field> map;
  if (isSubtypeOf(c, Map.class))
    map = getOpt_special;
  else {
    map = new HashMap();
    Class _c = c;
    do {
      for (Field f : _c.getDeclaredFields()) {
        f.setAccessible(true);
        String name = f.getName();
        if (!map.containsKey(name))
          map.put(name, f);
      }
      _c = _c.getSuperclass();
    } while (_c != null);
  }
  getOpt_cache.put(c, map);
  return map;
}


// usually L<S>
static String fromLines(Collection lines) {
  StringBuilder buf = new StringBuilder();
  if (lines != null)
    for (Object line : lines)
      buf.append(str(line)).append('\n');
  return buf.toString();
}

static String fromLines(String... lines) {
  return fromLines(asList(lines));
}
static List<String> toLines(File f) {
  return toLines(loadTextFile(f));
}

  public static List<String> toLines(String s) {
    List<String> lines = new ArrayList<String>();
    if (s == null) return lines;
    int start = 0;
    while (true) {
      int i = toLines_nextLineBreak(s, start);
      if (i < 0) {
        if (s.length() > start) lines.add(s.substring(start));
        break;
      }

      lines.add(s.substring(start, i));
      if (s.charAt(i) == '\r' && i+1 < s.length() && s.charAt(i+1) == '\n')
        i += 2;
      else
        ++i;

      start = i;
    }
    return lines;
  }

  private static int toLines_nextLineBreak(String s, int start) {
    for (int i = start; i < s.length(); i++) {
      char c = s.charAt(i);
      if (c == '\r' || c == '\n')
        return i;
    }
    return -1;
  }
  public static String join(String glue, Iterable<String> strings) {
    if (strings == null) return "";
    StringBuilder buf = new StringBuilder();
    Iterator<String> i = strings.iterator();
    if (i.hasNext()) {
      buf.append(i.next());
      while (i.hasNext())
        buf.append(glue).append(i.next());
    }
    return buf.toString();
  }
  
  public static String join(String glue, String[] strings) {
    return join(glue, Arrays.asList(strings));
  }
  
  public static String join(Iterable<String> strings) {
    return join("", strings);
  }
  
  public static String join(String[] strings) {
    return join("", strings);
  }

static boolean isSubtypeOf(Class a, Class b) {
  return b.isAssignableFrom(a); // << always hated that method, let's replace it!
}


static <A> ArrayList<A> asList(A[] a) {
  return new ArrayList<A>(Arrays.asList(a));
}

static ArrayList<Integer> asList(int[] a) {
  ArrayList<Integer> l = new ArrayList();
  for (int i : a) l.add(i);
  return l;
}

static <A> ArrayList<A> asList(Iterable<A> s) {
  if (s instanceof ArrayList) return (ArrayList) s;
  ArrayList l = new ArrayList();
  if (s != null)
    for (A a : s)
      l.add(a);
  return l;
}

static <A> ArrayList<A> asList(Enumeration<A> e) {
  ArrayList l = new ArrayList();
  if (e != null)
    while (e.hasMoreElements())
      l.add(e.nextElement());
  return l;
}
  public static String loadTextFile(String fileName) {
    return loadTextFile(fileName, null);
  }
  
  public static String loadTextFile(String fileName, String defaultContents) {
    try {
      if (!new File(fileName).exists())
        return defaultContents;
  
      FileInputStream fileInputStream = new FileInputStream(fileName);
      InputStreamReader inputStreamReader = new InputStreamReader(fileInputStream, "UTF-8");
      return loadTextFile(inputStreamReader);
    } catch (IOException e) {
      throw new RuntimeException(e);
    }
  }
  
  public static String loadTextFile(File fileName) {
    return loadTextFile(fileName, null);
  }

  public static String loadTextFile(File f, String defaultContents) {
    return f == null ? defaultContents : loadTextFile(f.getPath(), defaultContents);
  }
  
  public static String loadTextFile(Reader reader) throws IOException {
    StringBuilder builder = new StringBuilder();
    try {
      char[] buffer = new char[1024];
      int n;
      while (-1 != (n = reader.read(buffer)))
        builder.append(buffer, 0, n);
        
    } finally {
      reader.close();
    }
    return builder.toString();
  }
static String str(Object o) {
  return o == null ? "null" : o.toString();
}

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


static RuntimeException rethrow(Throwable e) {
  throw asRuntimeException(e);
}

}