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 {
static List<String> l = splitAtSpace("one two three four five six seven eight nine ten!");
static List<Object[]> perm;

public static void main(final String[] args) throws Exception {
  List<String> ll = l;
  print("\nPermutating: " + ll);
  long _startTime_0 = sysNow();  perm = allPermutations_arrays(ll);  done2("Permutating", _startTime_0); 
  print("Have " + n(perm, "permutation"));
  assertEquals(factorial(l(ll)), l(perm));
  assertEquals(l(new HashSet(perm)), l(perm));
  print("\nOK (probably)");
  //pnl(perm);
}
static volatile StringBuffer local_log = new StringBuffer(); // not redirected
static volatile StringBuffer print_log = local_log; // might be redirected, e.g. to main bot

// in bytes - will cut to half that
static volatile int print_log_max = 1024*1024;
static volatile int local_log_max = 100*1024;
//static int print_maxLineLength = 0; // 0 = unset

static boolean print_silent; // total mute if set

static Object print_byThread_lock = new Object();
static volatile ThreadLocal<F1<String, Boolean>> print_byThread; // special handling by thread

static void print() {
  print("");
}

// slightly overblown signature to return original object...
static <A> A print(A o) {
  ping();
  if (print_silent) return o;
  String s = String.valueOf(o) + "\n";
  print_noNewLine(s);
  return o;
}

static void print_noNewLine(String s) {
  if (print_byThread != null) {
    F1<String, Boolean> f = print_byThread.get();
    if (f != null)
      if (isFalse(f.get(s))) return;
  }

  print_raw(s);
}

static void print_raw(String s) {
  s = fixNewLines(s);
  // TODO if (print_maxLineLength != 0)
  StringBuffer loc = local_log;
  StringBuffer buf = print_log;
  int loc_max = print_log_max;
  if (buf != loc && buf != null) {
    print_append(buf, s, print_log_max);
    loc_max = local_log_max;
  }
  if (loc != null) 
    print_append(loc, s, loc_max);
  System.out.print(s);
}

static void print(long l) {
  print(String.valueOf(l));
}

static void print(char c) {
  print(String.valueOf(c));
}

static void print_append(StringBuffer buf, String s, int max) {
  synchronized(buf) {
    buf.append(s);
    max /= 2;
    if (buf.length() > max) try {
      int newLength = max/2;
      int ofs = buf.length()-newLength;
      String newString = buf.substring(ofs);
      buf.setLength(0);
      buf.append("[...] ").append(newString);
    } catch (Exception e) {
      buf.setLength(0);
    }
  }
}
static long sysNow() {
  return System.nanoTime()/1000000;
}
static <A> List<Object[]> allPermutations_arrays(List<A> l) {
  int n = factorial(l(l));
  List<Object[]> out = new ArrayList(n);
  allPermutations_arrays_impl(cloneList(l), l(l), out);
  return out;
}

static <A> void allPermutations_arrays_impl(List<A> l, int n, List<Object[]> out) {
  if (n <= 1) {
    ping();
    out.add(toObjectArray(l));
  } else for(int i = 0; i < n; i++) {
    allPermutations_arrays_impl(l, n-1, out);
    swapElements(l, n % 2 == 0 ? i : 0, n-1);
  }
}
static int done2_minPrint = 10;

static long done2(long startTime, String desc) {
  return done2(startTime, desc, done2_minPrint);
}

static long done2(long startTime, String desc, int minPrint) {
  long time = sysNow()-startTime;
  saveTiming_noPrint(time);
  if (time >= minPrint)
    print(desc + " [" + time + " ms]");
  return time;
}

static long done2(String desc, long startTime) {
  return done2(startTime, desc);
}

static long done2(long startTime) {
  return done2(startTime, "");
}
static List<String> splitAtSpace(String s) {
  return asList(s.split("\\s+"));
}
static int factorial(int i) {
  int n = 1;
  while (i > 1) n *= i--;
  return n;
}
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 String n(long l, String name) {
  return l + " " + trim(l == 1 ? singular(name) : getPlural(name));
}

static String n(Collection l, String name) {
  return n(l(l), name);
}

static String n(Map m, String name) {
  return n(l(m), name);
}

static String n(Object[] a, String name) {
  return n(l(a), name);
}




static String fixNewLines(String s) {
  return s.replace("\r\n", "\n").replace("\r", "\n");
}
static List<String> getPlural_specials = ll("sheep", "fish");

static String getPlural(String s) {
  if (containsIgnoreCase(getPlural_specials, s)) return s;
  if (ewic(s, "y")) return dropSuffixIgnoreCase("y", s) + "ies";
  if (ewic(s, "ss")) return s + "es";
  if (ewic(s, "s")) return s;
  return s + "s";
}
static volatile boolean ping_pauseAll;
static int ping_sleep = 100; // poll pauseAll flag every 100
static volatile boolean ping_anyActions;
static Map<Thread, Object> ping_actions = synchroMap(new WeakHashMap());

// always returns true
static boolean ping() {
  if (ping_pauseAll || ping_anyActions) ping_impl();
  return true;
}

// returns true when it slept
static boolean ping_impl() { try {
  if (ping_pauseAll && !isAWTThread()) {
    do
      Thread.sleep(ping_sleep);
    while (ping_pauseAll);
    return true;
  }
  
  if (ping_anyActions) {
    Object action;
    synchronized(ping_actions) {
      action = ping_actions.get(currentThread());
      if (action instanceof Runnable)
        ping_actions.remove(currentThread());
      if (ping_actions.isEmpty()) ping_anyActions = false;
    }
    
    if (action instanceof Runnable)
      ((Runnable) action).run();
    else if (eq(action, "cancelled"))
      throw fail("Thread cancelled.");
  }
  
  return false;
} catch (Exception __e) { throw rethrow(__e); } }
static <A> List<A> cloneList(Collection<A> l) {
  if (l == null) return new ArrayList();
  // assume collection's mutex is equal to collection, which will be true unless you explicitly pass a mutex to synchronizedList() which no one ever does.
  synchronized(l) {
    return new ArrayList<A>(l);
  }
}
static boolean isFalse(Object o) {
  return eq(false, o);
}
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;
}
static void swapElements(List l, int i, int j) {
  if (i == j) return;
  Object o = l.get(i);
  l.set(i, l.get(j));
  l.set(j, o);
}
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 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 ThreadLocal<Long> saveTiming_last = new ThreadLocal();

static void saveTiming(long ms) {
  print(ms + " ms");
  saveTiming_noPrint(ms);
}

static void saveTiming_noPrint(long ms) {
  saveTiming_last.set(ms);
}
static Object[] toObjectArray(Collection c) {
  List l = asList(c);
  return l.toArray(new Object[l.size()]);
}

static Map<String, String> singular_specials = litmap(
  "children", "child", "images", "image", "chess", "chess");
  
static Set<String> singular_specials2 = litset("time", "machine");

static String singular(String s) {
  if (s == null) return null;
  { String _a_908 = singular_specials.get(s); if (!empty(_a_908)) return _a_908; }
  if (singular_specials2.contains(dropSuffix("s", s)))
    return dropSuffix("s", s);
  if (s.endsWith("ness")) return s;
  if (s.endsWith("ges")) return dropSuffix("s", s);
  s = dropSuffix("es", s);
  s = dropSuffix("s", s);
  return s;
}


static <A> List<A> ll(A... a) {
  return litlist(a);
}
static Map synchroMap() {
  return synchroHashMap();
}

static <A, B> Map<A, B> synchroMap(Map<A, B> map) {
  return Collections.synchronizedMap(map);
}
static String dropSuffixIgnoreCase(String suffix, String s) {
  return ewic(s, suffix) ? s.substring(0, l(s)-l(suffix)) : s;
}
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 boolean empty(Collection c) { return c == null || c.isEmpty(); }
static boolean empty(String s) { return s == null || s.length() == 0; }
static boolean empty(Map map) { return map == null || map.isEmpty(); }
static boolean empty(Object[] o) { return o == null || o.length == 0; }
static boolean empty(Object o) {
  if (o instanceof Collection) return empty((Collection) o);
  if (o instanceof String) return empty((String) o);
  if (o instanceof Map) return empty((Map) o);
  if (o instanceof Object[]) return empty((Object[]) o);
  throw fail("unknown type for 'empty': " + getType(o));
}

static boolean empty(float[] a) { return a == null || a.length == 0; }
static boolean empty(int[] a) { return a == null || a.length == 0; }
static boolean empty(long[] a) { return a == null || a.length == 0; }
static RuntimeException asRuntimeException(Throwable t) {
  return t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
}
// TODO: test if android complains about this
static boolean isAWTThread() {
  if (isAndroid()) return false;
  if (isHeadless()) return false;
  return isAWTThread_awt();
}

static boolean isAWTThread_awt() {
  return SwingUtilities.isEventDispatchThread();
}
static RuntimeException rethrow(Throwable e) {
  throw asRuntimeException(e);
}
static Thread currentThread() {
  return Thread.currentThread();
}
static <A> HashSet<A> litset(A... items) {
  return lithashset(items);
}
static boolean ewic(String a, String b) {
  return endsWithIgnoreCase(a, b);
}
static String dropSuffix(String suffix, String s) {
  return s.endsWith(suffix) ? s.substring(0, l(s)-l(suffix)) : s;
}
static boolean containsIgnoreCase(List<String> l, String s) {
  for (String x : l)
    if (eqic(x, s))
      return true;
  return false;
}

static boolean containsIgnoreCase(String[] l, String s) {
  for (String x : l)
    if (eqic(x, s))
      return true;
  return false;
}

static boolean containsIgnoreCase(String s, char c) {
  return indexOfIgnoreCase(s, String.valueOf(c)) >= 0;
}

static boolean containsIgnoreCase(String a, String b) {
  return indexOfIgnoreCase(a, b) >= 0;
}
static boolean eq(Object a, Object b) {
  return a == null ? b == null : a == b || a.equals(b);
}
static Map litmap(Object... x) {
  TreeMap map = new TreeMap();
  litmap_impl(map, x);
  return map;
}

static void litmap_impl(Map map, Object... x) {
  for (int i = 0; i < x.length-1; i += 2)
    if (x[i+1] != null)
      map.put(x[i], x[i+1]);
}


static Boolean isHeadless_cache;

static boolean isHeadless() {
  if (isHeadless_cache != null) return isHeadless_cache;
  if (GraphicsEnvironment.isHeadless()) return isHeadless_cache = true;
  
  // Also check if AWT actually works.
  // If DISPLAY variable is set but no X server up, this will notice.
  
  try {
    SwingUtilities.isEventDispatchThread();
    return isHeadless_cache = false;
  } catch (Throwable e) { return isHeadless_cache = true; }
}
static <A> HashSet<A> lithashset(A... items) {
  HashSet<A> set = new HashSet();
  for (A a : items) set.add(a);
  return set;
}
static String getType(Object o) {
  return getClassName(o);
}
static boolean endsWithIgnoreCase(String a, String b) {
  return a != null && l(a) >= l(b) && a.regionMatches(true, l(a)-l(b), b, 0, l(b));
}
static List emptyList() {
  return new ArrayList();
  //ret Collections.emptyList();
}

static List emptyList(int capacity) {
  return new ArrayList(capacity);
}

// Try to match capacity
static List emptyList(Iterable l) {
  return l instanceof Collection ? emptyList(((Collection) l).size()) : emptyList();
}
static <A> ArrayList<A> litlist(A... a) {
  return new ArrayList<A>(Arrays.asList(a));
}
static boolean eqic(String a, String b) {
  if ((a == null) != (b == null)) return false;
  if (a == null) return true;
  return a.equalsIgnoreCase(b);
}
static Map synchroHashMap() {
  return Collections.synchronizedMap(new HashMap());
}

// works on lists and strings and null

static int indexOfIgnoreCase(Object a, Object b) {
  if (a == null) return -1;
  if (a instanceof String) {
     Matcher m = Pattern.compile((String) b, Pattern.CASE_INSENSITIVE + Pattern.LITERAL).matcher((String) a);
     if (m.find()) return m.start(); else return -1;
  }
  if (a instanceof List) {
    for (int i = 0; i < ((List) a).size(); i++) {
      Object o = ((List) a).get(i);
      if (o != null && ((String) o).equalsIgnoreCase((String) b))
        return i;
    }
    return -1;
  }
  throw fail("Unknown type: " + a);
}
static int isAndroid_flag;

static boolean isAndroid() {
  if (isAndroid_flag == 0)
    isAndroid_flag = System.getProperty("java.vendor").toLowerCase().indexOf("android") >= 0 ? 1 : -1;
  return isAndroid_flag > 0;
}



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


static abstract class F1<A, B> {
  abstract B get(A a);
}

// 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 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;
}

}