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 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.*;
public class main {


public static void main(String[] args) throws Exception {
  List<List<Long>> bitMap = ll(
    ll(5L, 6L),
    ll(5L, 7L)
  );
  analyzeBitMap(bitMap);
}
// Looks only at the values
static void analyzeBitMap(MultiMap<Long, Long> bitMap) {
  analyzeBitMap(values(bitMap.data));
}

static void analyzeBitMap(Collection<List<Long>> bitMap) {
  if (bitMap.isEmpty()) return;
  
  HashSet<Long> allSeen = new HashSet<Long>();
  for (List<Long> l : bitMap)
    allSeen.addAll(l);
  printStruct("allSeen", allSeen);
  MultiMap<Long, Long> implies = fullSelfMap(allSeen);
  MultiMap<Long, Long> eq = fullSelfMap(allSeen);
  
  for (List<Long> l : bitMap) {
    HashSet<Long> set = new HashSet(l);
    for (Long a : cloneList(implies.keySet())) {
      boolean ax = set.contains(a);
      for (Long b : cloneList(implies.get(a))) {
        boolean bx = set.contains(b);
        if (ax && !bx)
          implies.remove(a, b);
      }
    }
    
    for (Long a : cloneList(eq.keySet())) {
      boolean ax = set.contains(a);
      for (Long b : cloneList(eq.get(a))) {
        boolean bx = set.contains(b);
        if (ax != bx)
          eq.remove(a, b);
      }
    }
  }
  
  printStruct("implies", implies);
  printStruct("eq", eq);
  
  List<List<Long>> clusters = multiMapToClusters(eq);
  for (int i = 0; i < l(clusters); i++)
    print(("Cluster " + (i+1) + ": ") + struct(clusters.get(i)));
}

static MultiMap<Long, Long> fullSelfMap(Collection<Long> l) {
  MultiMap<Long, Long> mm = new MultiMap<Long, Long>();
  for (Long x : l) mm.putAll(x, l);
  return mm;
}

static List<List<Long>> multiMapToClusters(MultiMap<Long, Long> mm) {
  // a cluster is a list of concepts.
  // first, make trivial clusters (one per item).
  
  Map<Long, List<Long>> clusters = new TreeMap<Long, List<Long>>();
  for (Long a : mm.keySet()) {
    if (!clusters.containsKey(a))
      clusters.put(a, ll(a));
  }
  
  // then, merge the clusters.
  
  for (Long a : mm.keySet())
    for (Long b : mm.get(a)) {
      List<Long> c1 = clusters.get(a);
      List<Long> c2 = clusters.get(b);
      if (c1 != c2) // different clusters, need to merge!
        mergeClusters(clusters, c1, c2);
    }
  
  return asList(new HashSet<List<Long>>(clusters.values()));
}

static void mergeClusters(Map<Long, List<Long>> clusters, List<Long> c1, List<Long> c2) {
  for (Long x : c2) {
    clusters.put(x, c1);
    c1.add(x);
  }
} // analyzeBitMap

static <A> List<A> ll(A... a) {
  return litlist(a);
}
static void printStruct(String prefix, Object o) {
  printStructure(prefix, o);
}

static void printStruct(Object o) {
  printStructure(o);
}

static String struct(Object o) {
  return structure(o);
}
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 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) {
  // 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 <A, B> Collection<B> values(Map<A, B> map) {
  return map == null ? emptyList() : map.values();
}

static <A> List<A> cloneList(Collection<A> l) {
  //O mutex = getOpt(l, "mutex");
  /*if (mutex != null)
    synchronized(mutex) {
      ret new ArrayList<A>(l);
    }
  else
    ret new ArrayList<A>(l);*/
  // assume 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 <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 List emptyList() {
  return new ArrayList();
  //ret Collections.emptyList();
}
static <A> ArrayList<A> litlist(A... a) {
  return new ArrayList<A>(Arrays.asList(a));
}
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());

// returns true if it did anything
static boolean ping() {
  if (ping_pauseAll) {
    do
      sleep(ping_sleep);
    while (ping_pauseAll);
    return true;
  }
  
  if (ping_anyActions) {
    Object action;
    synchronized(mc()) {
      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;
}
static String structure(Object o) {
  HashSet refd = new HashSet();
  StringBuilder out = new StringBuilder();
  structure_1(out, o, new structure_Data(refd));
  return structure_2(str(out), refd);
}

// leave to false, unless unstructure() breaks
static boolean structure_allowShortening = false;

static int structure_shareStringsLongerThan = 20;

static class structure_Data {
  int stringSizeLimit;
  IdentityHashMap<Object, Integer> seen = new IdentityHashMap<Object, Integer>();
  HashSet<Integer> refd;
  HashMap<String, Integer> strings = new HashMap<String, Integer>();
  HashSet<String> concepts = new HashSet<String>();
  Class conceptClass = findClass("Concept");
  
  structure_Data(HashSet<Integer> refd) {
  this.refd = refd;}
}

static void structure_1(StringBuilder out, Object o, structure_Data d) {
  if (o == null) { out.append("null"); return; }
  
  // these are never back-referenced (for readability)
  
  if (o instanceof BigInteger) {
    out.append("bigint(").append(o).append(")"); return;
  }
  
  if (o instanceof Double) {
    out.append("d(").append(quote(str(o))).append(")"); return;
  }
    
  if (o instanceof Float) {
    out.append("fl ").append(quote(str(o))); return;
  }
    
  if (o instanceof Long) {
    out.append(o).append("L"); return;
  }
  
  if (o instanceof Integer) {
    out.append(str(o)); return;
  }
    
  if (o instanceof Boolean) {
    out.append(((Boolean) o).booleanValue() ? "t" : "f"); return;
  }
    
  if (o instanceof Character) {
    out.append(quoteCharacter((Character) o)); return;
  }
    
  if (o instanceof File) {
    out.append("File ").append(quote(((File) o).getPath())); return;
  }
    
  // referencable objects follow
  
  Integer ref = null;
  if (!(o instanceof String)) {
    ref = d.seen.get(o);
    if (ref != null) {
      d.refd.add(ref);
      out.append("r").append(ref); return;
    }
  }
  
  if (o instanceof String && (ref = d.strings.get((String) o)) != null) {
    d.refd.add(ref);
    out.append("r").append(ref); return;
  }
  
  ref = d.seen.size()+1;
  d.seen.put(o, ref);
  out.append("m").append(ref).append(" "); // marker

  if (o instanceof String) {
    String s = d.stringSizeLimit != 0 ? shorten((String) o, d.stringSizeLimit) : (String) o;
    if (l(s) >= structure_shareStringsLongerThan)
      d.strings.put(s, ref);
    out.append(quote(s)); return;
  }
    
  String name = o.getClass().getName();

  if (o instanceof HashSet) {
    out.append("hashset ");
    structure_1(out, new ArrayList((Set) o), d);
    return;
  }

  if (o instanceof TreeSet) {
    out.append("treeset ");
    structure_1(out, new ArrayList((Set) o), d);
    return;
  }
  
  if (o instanceof Collection && neq(name, "main$Concept$RefL")) {
    out.append("[");
    int l = out.length();
    for (Object x : (Collection) o) {
      if (out.length() != l) out.append(", ");
      structure_1(out, x, d);
    }
    out.append("]");
    return;
  }
  
  if (o instanceof Map) {
    if (o instanceof HashMap) out.append("hm");
    out.append("{");
    int l = out.length();
    for (Object e : ((Map) o).entrySet()) {
      if (out.length() != l) out.append(", ");
      structure_1(out, ((Map.Entry) e).getKey(), d);
      out.append("=");
      structure_1(out, ((Map.Entry) e).getValue(), d);
    }
    out.append("}");
    return;
  }
  
  if (o.getClass().isArray()) {
    if (o instanceof byte[]) {
      out.append("ba ").append(quote(bytesToHex((byte[]) o))); return;
    }

    int n = Array.getLength(o);

    if (o instanceof boolean[]) {
      String hex = boolArrayToHex((boolean[]) o);
      int i = l(hex);
      while (i > 0 && hex.charAt(i-1) == '0' && hex.charAt(i-2) == '0') i -= 2;
      out.append("boolarray ").append(n).append(" ").append(quote(substring(hex, 0, i))); return;
    }
    
    String atype = "array", sep = ", ";

    if (o instanceof int[]) {
      //ret "intarray " + quote(intArrayToHex((int[]) o));
      atype = "intarray";
      sep = " ";
    }
    
    out.append(atype).append("{");
    for (int i = 0; i < n; i++) {
      if (i != 0) out.append(sep);
      structure_1(out, Array.get(o, i), d);
    }
    out.append("}"); return;
  }

  if (o instanceof Class) {
    out.append("class(").append(quote(((Class) o).getName())).append(")"); return;
  }
    
  if (o instanceof Throwable) {
    out.append("exception(").append(quote(((Throwable) o).getMessage())).append(")"); return;
  }
    
  if (o instanceof BitSet) {
    BitSet bs = (BitSet) o;
    out.append("bitset{");
    int l = out.length();
    for (int i = bs.nextSetBit(0); i >= 0; i = bs.nextSetBit(i+1)) {
      if (out.length() != l) out.append(", ");
      out.append(i);
    }
    out.append("}"); return;
  }
    
  // Need more cases? This should cover all library classes...
  if (name.startsWith("java.") || name.startsWith("javax.")) {
    out.append(str(o)); return;
  }
    
  String shortName = o.getClass().getName().replaceAll("^main\\$", "");
  
  if (shortName.equals("Lisp")) {
    out.append("l(");
    structure_1(out, getOpt(o, "head"), d);
    List args = (List) ( getOpt(o, "args"));
    if (nempty(args))
      for (int i = 0; i < l(args); i++) {
        out.append(", ");
        Object arg = args.get(i);
        
        // sweet shortening
        if (arg != null && eq(arg.getClass().getName(), "main$Lisp") && isTrue(call(arg, "isEmpty")))
          arg = get(arg, "head");
          
        structure_1(out, arg, d);
      }
    out.append(")"); return;
  }
  
  Class c = o.getClass();
  boolean concept = d.conceptClass != null && d.conceptClass.isInstance(o);
  String dynName = shortDynamicClassName(o);
  if (concept && !d.concepts.contains(dynName)) {
    d.concepts.add(dynName);
    out.append("c ");
  }
  
  // serialize an object with fields.
  // first, collect all fields and values in fv.
  
  TreeMap<String, Object> fv = new TreeMap<String, Object>();
  while (c != Object.class) {
    for (Field field : c.getDeclaredFields()) {
      if ((field.getModifiers() & (Modifier.STATIC | Modifier.TRANSIENT)) != 0)
        continue;
      String fieldName = field.getName();
      
      Object value;
      try {
        field.setAccessible(true);
        value = field.get(o);
      } catch (Exception e) {
        value = "?";
      }
      
      // omit field "className" if equal to class's name
      if (concept && eq(fieldName, "className")
        && eq(value, shortName)) value = null;
      
      // put special cases here...
      
      if (value != null)
        fv.put(fieldName, value);
    }
    c = c.getSuperclass();
  }
  
  // Now we have fields & values. Process fieldValues if it's a DynamicObject.
  
  if (o instanceof DynamicObject) {
    fv.putAll((Map) fv.get("fieldValues"));
    fv.remove("fieldValues");
    shortName = dynName;
    fv.remove("className");
  }
  
  String singleField = fv.size() == 1 ? first(fv.keySet()) : null;
  
  // Render this$1 first because unstructure needs it for constructor call.
  
  out.append(shortName).append("(");
  int l = out.length();
  
  if (fv.containsKey("this$1")) {
    out.append("this$1=");
    structure_1(out, fv.get("this$1"), d);
    fv.remove("this$1");
  }
  
  // Render the other fields.

  for (String fieldName : fv.keySet()) {
    if (out.length() != l) out.append(", ");
    out.append(fieldName).append("=");
    structure_1(out, fv.get(fieldName), d);
  }

  /*if (structure_allowShortening && singleField != null)
    b = b.replaceAll("^" + singleField + "=", ""); // drop field name if only one*/
    
  if (out.length() == l) out.setLength(l-1); // drop "("
  else out.append(")");
}

// drop unused markers
static String structure_2(String s, HashSet<Integer> refd) {
  List<String> tok = javaTok(s);
  StringBuilder out = new StringBuilder();
  for (int i = 1; i < l(tok); i += 2) {
    String t = tok.get(i);
    if (t.startsWith("m") && isInteger(t.substring(1))
      && !refd.contains(parseInt(t.substring(1))))
      continue;
    out.append(t).append(tok.get(i+1));
  }
  return str(out);
}

static void printStructure(String prefix, Object o) {
  if (endsWithLetter(prefix)) prefix += ": ";
  print(prefix + structure(o));
}

static void printStructure(Object o) {
  print(structure(o));
}



static Map synchroMap() {
  return synchroHashMap();
}

static <A, B> Map<A, B> synchroMap(Map<A, B> map) {
  return Collections.synchronizedMap(map);
}
// replacement for class JavaTok
// maybe incomplete, might want to add floating point numbers
// todo also: extended multi-line strings

static int javaTok_n, javaTok_elements;
static boolean javaTok_opt;

static List<String> javaTok(String s) {
  return javaTok(s, null);
}

static List<String> javaTok(String s, List<String> existing) {
  ++javaTok_n;
  int nExisting = javaTok_opt && existing != null ? existing.size() : 0;
  List<String> tok = existing != null ? new ArrayList(nExisting) : new ArrayList();
  int l = s.length();
  
  int i = 0, n = 0;
  while (i < l) {
    int j = i;
    char c; String cc;
    
    // scan for whitespace
    while (j < l) {
      c = s.charAt(j);
      cc = s.substring(j, Math.min(j+2, l));
      if (c == ' ' || c == '\t' || c == '\r' || c == '\n')
        ++j;
      else if (cc.equals("/*")) {
        do ++j; while (j < l && !s.substring(j, Math.min(j+2, l)).equals("*/"));
        j = Math.min(j+2, l);
      } else if (cc.equals("//")) {
        do ++j; while (j < l && "\r\n".indexOf(s.charAt(j)) < 0);
      } else
        break;
    }
    
    if (n < nExisting && javaTok_isCopyable(existing.get(n), s, i, j))
      tok.add(existing.get(n));
    else
      tok.add(quickSubstring(s, i, j));
    ++n;
    i = j;
    if (i >= l) break;
    c = s.charAt(i); // cc is not needed in rest of loop body
    cc = s.substring(i, Math.min(i+2, l));

    // scan for non-whitespace
    if (c == '\'' || c == '"') {
      char opener = c;
      ++j;
      while (j < l) {
        if (s.charAt(j) == opener || s.charAt(j) == '\n') { // end at \n to not propagate unclosed string literal errors
          ++j;
          break;
        } else if (s.charAt(j) == '\\' && j+1 < l)
          j += 2;
        else
          ++j;
      }
    } else if (Character.isJavaIdentifierStart(c))
      do ++j; while (j < l && (Character.isJavaIdentifierPart(s.charAt(j)) || "'".indexOf(s.charAt(j)) >= 0)); // for stuff like "don't"
    else if (Character.isDigit(c)) {
      do ++j; while (j < l && Character.isDigit(s.charAt(j)));
      if (j < l && s.charAt(j) == 'L') ++j; // Long constants like 1L
    } else if (cc.equals("[[")) {
      do ++j; while (j+1 < l && !s.substring(j, j+2).equals("]]"));
      j = Math.min(j+2, l);
    } else if (cc.equals("[=") && i+2 < l && s.charAt(i+2) == '[') {
      do ++j; while (j+2 < l && !s.substring(j, j+3).equals("]=]"));
      j = Math.min(j+3, l);
    } else
      ++j;

    if (n < nExisting && javaTok_isCopyable(existing.get(n), s, i, j))
      tok.add(existing.get(n));
    else
      tok.add(quickSubstring(s, i, j));
    ++n;
    i = j;
  }
  
  if ((tok.size() % 2) == 0) tok.add("");
  javaTok_elements += tok.size();
  return tok;
}

static List<String> javaTok(List<String> tok) {
  return javaTok(join(tok), tok);
}

static boolean javaTok_isCopyable(String t, String s, int i, int j) {
  return t.length() == j-i
    && s.regionMatches(i, t, 0, j-i); // << could be left out, but that's brave
}
static String substring(String s, int x) {
  return safeSubstring(s, x);
}

static String substring(String s, int x, int y) {
  return safeSubstring(s, x, y);
}
static void sleep(long ms) {
  ping();
  try {
    Thread.sleep(ms);
  } catch (Exception e) { throw new RuntimeException(e); }
}

static void sleep() { try {
 
  print("Sleeping.");
  synchronized(main.class) { main.class.wait(); }

} catch (Throwable __e) { throw __e instanceof RuntimeException ? (RuntimeException) __e : new RuntimeException(__e); }}
  public static String bytesToHex(byte[] bytes) {
    return bytesToHex(bytes, 0, bytes.length);
  }

  public static String bytesToHex(byte[] bytes, int ofs, int len) {
    StringBuilder stringBuilder = new StringBuilder(len*2);
    for (int i = 0; i < len; i++) {
      String s = "0" + Integer.toHexString(bytes[ofs+i]);
      stringBuilder.append(s.substring(s.length()-2, s.length()));
    }
    return stringBuilder.toString();
  }

static boolean isInteger(String s) {
  return s != null && Pattern.matches("\\-?\\d+", s);
}
static String quote(Object o) {
  if (o == null) return "null";
  String s = str(o);
  return "\"" + s.replace("\\", "\\\\").replace("\"", "\\\"").replace("\r", "\\r").replace("\n", "\\n") + "\"";
}
static String shorten(String s, int max) {
  if (s == null) return "";
  if (max < 0) return s;
  return s.length() <= max ? s : s.substring(0, Math.min(s.length(), max)) + "...";
}
static Object mc() {
  return getMainClass();
}
// get purpose 1: access a list/array (safer version of x.get(y))

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

static Class get_dynamicObject = findClass("DynamicObject");

// 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);
    }
      
    if (get_dynamicObject != null && get_dynamicObject.isInstance(o))
      return call(get_raw(o, "fieldValues"), "get", field);
  } 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 String quoteCharacter(char c) {
  if (c == '\'') return "'\\''";
  if (c == '\\') return "'\\\\'";
  return "'" + c + "'";
}

static boolean neq(Object a, Object b) {
  return !eq(a, b);
}
static String shortDynamicClassName(Object o) {
  return shortenClassName(dynamicClassName(o));
}
static boolean endsWithLetter(String s) {
  return nempty(s) && isLetter(last(s));
}
static Thread currentThread() {
  return Thread.currentThread();
}
static boolean nempty(Collection c) {
  return !isEmpty(c);
}

static boolean nempty(CharSequence s) {
  return !isEmpty(s);
}

static boolean nempty(Object[] o) {
  return !isEmpty(o);
}

static boolean nempty(Map m) {
  return !isEmpty(m);
}

static boolean nempty(Iterator i) {
  return i != null && i.hasNext();
}
// currently finds only inner classes of class "main"
// returns null on not found
// this is the simple version that is not case-tolerant
static Class findClass(String name) {
  if (!isJavaIdentifier(name)) return null;
  try {
    return Class.forName("main$" + name);
  } catch (ClassNotFoundException e) {
    return null;
  }
}
static boolean eq(Object a, Object b) {
  if (a == null) return b == null;
  if (a.equals(b)) return true;
  if (a instanceof BigInteger) {
    if (b instanceof Integer) return a.equals(BigInteger.valueOf((Integer) b));
    if (b instanceof Long) return a.equals(BigInteger.valueOf((Long) b));
  }
  return false;
}
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 int l(Object o) {
  return l((List) o); // incomplete
}

static String str(Object o) {
  return String.valueOf(o);
}
  static Object call(Object o) {
    return callFunction(o);
  }
  
  // varargs assignment fixer for a single string array argument
  static Object call(Object o, String method, String[] arg) {
    return call(o, method, new Object[] {arg});
  }
  
  static Object call(Object o, String method, Object... args) {
    try {
      if (o instanceof Class) {
        Method m = call_findStaticMethod((Class) o, method, args, false);
        m.setAccessible(true);
        return m.invoke(null, args);
      } else {
        Method m = call_findMethod(o, method, args, false);
        m.setAccessible(true);
        return m.invoke(o, args);
      }
    } catch (Exception e) {
      throw e instanceof RuntimeException ? (RuntimeException) e : new RuntimeException(e);
    }
  }

  static Method call_findStaticMethod(Class c, String method, Object[] args, boolean debug) {
    Class _c = c;
    while (c != null) {
      for (Method m : c.getDeclaredMethods()) {
        if (debug)
          System.out.println("Checking method " + m.getName() + " with " + m.getParameterTypes().length + " parameters");;
        if (!m.getName().equals(method)) {
          if (debug) System.out.println("Method name mismatch: " + method);
          continue;
        }

        if ((m.getModifiers() & Modifier.STATIC) == 0 || !call_checkArgs(m, args, debug))
          continue;

        return m;
      }
      c = c.getSuperclass();
    }
    throw new RuntimeException("Method '" + method + "' (static) with " + args.length + " parameter(s) not found in " + _c.getName());
  }

  static Method call_findMethod(Object o, String method, Object[] args, boolean debug) {
    Class c = o.getClass();
    while (c != null) {
      for (Method m : c.getDeclaredMethods()) {
        if (debug)
          System.out.println("Checking method " + m.getName() + " with " + m.getParameterTypes().length + " parameters");;
        if (m.getName().equals(method) && call_checkArgs(m, args, debug))
          return m;
      }
      c = c.getSuperclass();
    }
    throw new RuntimeException("Method '" + method + "' (non-static) with " + args.length + " parameter(s) not found in " + o.getClass().getName());
  }

  private static boolean call_checkArgs(Method m, Object[] args, boolean debug) {
    Class<?>[] types = m.getParameterTypes();
    if (types.length != args.length) {
      if (debug)
        System.out.println("Bad parameter length: " + args.length + " vs " + types.length);
      return false;
    }
    for (int i = 0; i < types.length; i++)
      if (!(args[i] == null || isInstanceX(types[i], args[i]))) {
        if (debug)
          System.out.println("Bad parameter " + i + ": " + args[i] + " vs " + types[i]);
        return false;
      }
    return true;
  }


static int parseInt(String s) {
  return empty(s) ? 0 : Integer.parseInt(s);
}
  static RuntimeException fail() {
    throw new RuntimeException("fail");
  }
  
  static RuntimeException fail(Object msg) {
    throw new RuntimeException(String.valueOf(msg));
  }
  
  static RuntimeException fail(String msg) {
    throw new RuntimeException(unnull(msg));
  }
   
  // disabled for now to shorten some programs 
  /*static RuntimeException fail(S msg, O... args) {
    throw new RuntimeException(format(msg, args));
  }*/
// hmm, this shouldn't call functions really. That was just
// for coroutines.
static boolean isTrue(Object o) {
  if (o instanceof Boolean)
    return ((Boolean) o).booleanValue();
  if (o == null) return false;
  return ((Boolean) callF(o)).booleanValue();
}

static boolean isTrue(Object pred, Object arg) {
  return booleanValue(callF(pred, arg));
}
static Object getOpt(Object o, String field) {
  if (o instanceof String) o = getBot ((String) o);
  if (o == null) return null;
  if (o instanceof Class) return getOpt((Class) o, field);
  
  if (o.getClass().getName().equals("main$DynamicObject"))
    return ((Map) getOpt_raw(o, "fieldValues")).get(field);
  
  if (o instanceof Map) return ((Map) o).get(field);
  
  return getOpt_raw(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 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 String boolArrayToHex(boolean[] a) {
  return bytesToHex(boolArrayToBytes(a));
}
static Object first(Object list) {
  return ((List) list).isEmpty() ? null : ((List) list).get(0);
}

static <A> A first(List<A> list) {
  return list.isEmpty() ? null : list.get(0);
}

static <A> A first(A[] bla) {
  return bla == null || bla.length == 0 ? null : bla[0];
}

static <A> A first(Iterable<A> i) {
  if (i == null) return null;
  Iterator<A> it = i.iterator();
  return it.hasNext() ? it.next() : null;
}



static Object callF(Object f, Object... args) {
  return callFunction(f, args);
}
static Object callFunction(Object f, Object... args) {
  if (f == null) return null;
  if (f instanceof Runnable) {
    ((Runnable) f).run();
    return null;
  } else if (f instanceof String)
    return call(mc(), (String) f, args);
  else
    return call(f, "get", args);
  //else throw fail("Can't call a " + getClassName(f));
}
static boolean empty(Collection c) {
  return isEmpty(c);
}

static boolean empty(String s) {
  return isEmpty(s);
}

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));
}
// hopefully covers all cases :)
static String safeSubstring(String s, int x, int y) {
  if (s == null) return null;
  if (x < 0) x = 0;
  if (x > s.length()) return "";
  if (y < x) y = x;
  if (y > s.length()) y = s.length();
  return s.substring(x, y);
}

static String safeSubstring(String s, int x) {
  return safeSubstring(s, x, l(s));
}

static RuntimeException asRuntimeException(Throwable t) {
  return t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
}
static Object getBot(String botID) {
  return callOpt(getMainBot(), "getBot", botID);
}

  public static String join(String glue, Iterable<String> strings) {
    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 byte[] boolArrayToBytes(boolean[] a) {
  byte[] b = new byte[(l(a)+7)/8];
  for (int i = 0; i < l(a); i++)
    if (a[i])
      b[i/8] |= 1 << (i & 7);
  return b;
}
// extended over Class.isInstance() to handle primitive types
static boolean isInstanceX(Class type, Object arg) {
  if (type == boolean.class) return arg instanceof Boolean;
  if (type == int.class) return arg instanceof Integer;
  if (type == long.class) return arg instanceof Long;
  if (type == float.class) return arg instanceof Float;
  if (type == short.class) return arg instanceof Short;
  if (type == char.class) return arg instanceof Character;
  if (type == byte.class) return arg instanceof Byte;
  if (type == double.class) return arg instanceof Double;
  return type.isInstance(arg);
}
static <A> A last(List<A> l) {
  return l.isEmpty() ? null : l.get(l.size()-1);
}

static char last(String s) {
  return empty(s) ? '#' : s.charAt(l(s)-1);
}
static String shortenClassName(String name) {
  return name == null ? null : substring(name, xIndexOf(name, '$')+1);
}
static boolean booleanValue(Object o) {
  return eq(true, o);
}
static String quickSubstring(String s, int i, int j) {
  if (i == j) return "";
  return s.substring(i, j);
}
static boolean isJavaIdentifier(String s) {
  if (s.length() == 0 || !Character.isJavaIdentifierStart(s.charAt(0)))
    return false;
  for (int i = 1; i < s.length(); i++)
    if (!Character.isJavaIdentifierPart(s.charAt(i)))
      return false;
  return true;
}
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 isLetter(char c) {
  return Character.isLetter(c);
}
static Class getMainClass() { try {
 
  return main.class;

} catch (Throwable __e) { throw __e instanceof RuntimeException ? (RuntimeException) __e : new RuntimeException(__e); }}

static Class getMainClass(Object o) { try {
 
  return (o instanceof Class ? (Class) o : o.getClass()).getClassLoader().loadClass("main");

} catch (Throwable __e) { throw __e instanceof RuntimeException ? (RuntimeException) __e : new RuntimeException(__e); }}
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 String dynamicClassName(Object o) {
  if (o instanceof DynamicObject && ((DynamicObject) o).className != null)
    return "main$" + ((DynamicObject) o).className;
  return className(o);
}
static Map synchroHashMap() {
  return Collections.synchronizedMap(new HashMap());
}



// returns l(s) if not found
static int xIndexOf(String s, String sub, int i) {
  if (s == null) return 0;
  i = s.indexOf(sub, min(i, l(s)));
  return i >= 0 ? i : l(s);
}

static int xIndexOf(String s, String sub) {
  return xIndexOf(s, sub, 0);
}

static int xIndexOf(String s, char c) {
  if (s == null) return 0;
  int i = s.indexOf(c);
  return i >= 0 ? i : l(s);
}
static String getType(Object o) {
  return getClassName(o);
}
static Object callOpt(Object o) {
  if (o == null) return null;
  return callF(o);
}

static Object callOpt(Object o, String method, Object... args) {
  try {
    if (o == null) return null;
    if (o instanceof Class) {
      Method m = callOpt_findStaticMethod((Class) o, method, args, false);
      if (m == null) return null;
      m.setAccessible(true);
      return m.invoke(null, args);
    } else {
      Method m = callOpt_findMethod(o, method, args, false);
      if (m == null) return null;
      m.setAccessible(true);
      return m.invoke(o, args);
    }
  } catch (Exception e) {
    throw new RuntimeException(e);
  }
}

static Method callOpt_findStaticMethod(Class c, String method, Object[] args, boolean debug) {
  Class _c = c;
  while (c != null) {
    for (Method m : c.getDeclaredMethods()) {
      if (debug)
        System.out.println("Checking method " + m.getName() + " with " + m.getParameterTypes().length + " parameters");;
      if (!m.getName().equals(method)) {
        if (debug) System.out.println("Method name mismatch: " + method);
        continue;
      }

      if ((m.getModifiers() & Modifier.STATIC) == 0 || !callOpt_checkArgs(m, args, debug))
        continue;

      return m;
    }
    c = c.getSuperclass();
  }
  return null;
}

static Method callOpt_findMethod(Object o, String method, Object[] args, boolean debug) {
  Class c = o.getClass();
  while (c != null) {
    for (Method m : c.getDeclaredMethods()) {
      if (debug)
        System.out.println("Checking method " + m.getName() + " with " + m.getParameterTypes().length + " parameters");;
      if (m.getName().equals(method) && callOpt_checkArgs(m, args, debug))
        return m;
    }
    c = c.getSuperclass();
  }
  return null;
}

private static boolean callOpt_checkArgs(Method m, Object[] args, boolean debug) {
  Class<?>[] types = m.getParameterTypes();
  if (types.length != args.length) {
    if (debug)
      System.out.println("Bad parameter length: " + args.length + " vs " + types.length);
    return false;
  }
  for (int i = 0; i < types.length; i++)
    if (!(args[i] == null || isInstanceX(types[i], args[i]))) {
      if (debug)
        System.out.println("Bad parameter " + i + ": " + args[i] + " vs " + types[i]);
      return false;
    }
  return true;
}


static String className(Object o) {
  return getClassName(o);
}
static Object mainBot;

static Object getMainBot() {
  return mainBot;
}


static String getClassName(Object o) {
  return o == null ? "null" : o.getClass().getName();
}
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 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 byte min(byte[] c) {
  byte x = 127;
  for (byte d : c) if (d < x) x = d;
  return x;
}


static boolean DynamicObject_loading;

static class DynamicObject {
  String className; // just the name, without the "main$"
  Map<String, Object> fieldValues = new TreeMap<String, Object>();
  
  DynamicObject() {}
  // className = just the name, without the "main$"
  DynamicObject(String className) {
  this.className = className;}
}

static class MultiMap<A,B> {
  Map<A, List<B>> data = new HashMap<A, List<B>>();
  
  MultiMap() {}
  MultiMap(boolean useTreeMap) { if (useTreeMap) data = new TreeMap(); }
  MultiMap(MultiMap<A, B> map) { putAll(map); }

  synchronized void put(A key, B value) {
    List<B> list = data.get(key);
    if (list == null)
      data.put(key, list = new ArrayList<B>());
    list.add(value);
  }

  synchronized void addAll(A key, Collection<B> values) {
    putAll(key, values);
  }
  
  synchronized void addAllIfNotThere(A key, Collection<B> values) {
    for (B value : values)
      setPut(key, value);
  }
  
  synchronized void setPut(A key, B value) {
    if (!containsPair(key, value))
      put(key, value);
  }
  
  synchronized boolean containsPair(A key, B value) {
    return get(key).contains(value);
  }
  
  synchronized void putAll(A key, Collection<B> values) {
    for (B value : values)
      put(key, value);
  }

  synchronized void removeAll(A key, Collection<B> values) {
    for (B value : values)
      remove(key, value);
  }
  
  synchronized List<B> get(A key) {
    List<B> list = data.get(key);
    return list == null ? Collections.<B> emptyList() : list;
  }

  // returns actual mutable live list
  // creates the list if not there
  synchronized List<B> getActual(A key) {
    List<B> list = data.get(key);
    if (list == null)
      data.put(key, list = litlist());
    return list;
  }
 
  synchronized void clean(A key) {
    List<B> list = data.get(key);
    if (list != null && list.isEmpty())
      data.remove(key);
  }

  synchronized Set<A> keySet() {
    return data.keySet();
  }

  synchronized Set<A> keys() {
    return data.keySet();
  }

  synchronized void remove(A key) {
    data.remove(key);
  }

  synchronized void remove(A key, B value) {
    List<B> list = data.get(key);
    if (list != null) {
      list.remove(value);
      if (list.isEmpty())
        data.remove(key);
    }
  }

  synchronized void clear() {
    data.clear();
  }

  synchronized boolean containsKey(A key) {
    return data.containsKey(key);
  }

  synchronized B getFirst(A key) {
    List<B> list = get(key);
    return list.isEmpty() ? null : list.get(0);
  }
  
  synchronized void putAll(MultiMap<A, B> map) {
    for (A key : map.keySet())
      putAll(key, map.get(key));
  }
  
  // note: expensive operation
  synchronized int size() {
    int n = 0;
    for (List l : data.values())
      n += l(l);
    return n;
  }
  
  // expensive operation
  synchronized List<A> reverseGet(B b) {
    List<A> l = new ArrayList<A>();
    for (A key : data.keySet())
      if (data.get(key).contains(b))
        l.add(key);
    return l;
  }
  
  synchronized Map<A, List<B>> asMap() {
    return cloneMap(data);
  }
  
  boolean isEmpty() { return data.isEmpty(); }
}

static <A, B> Set<A> keys(Map<A, B> map) {
  return map.keySet();
}

static Set keys(Object map) {
  return keys((Map) map);
}
static <A, B> Map<A, B> cloneMap(Map<A, B> map) {
  if (map == null) return litmap();
  // assume mutex is equal to collection, which will be true unless you explicitly pass a mutex to synchronizedList() which no one ever does.
  synchronized(map) {
    return new HashMap(map);
  }
}


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]);
}

}