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.*;
// A is node type, B is link type
class main {
static class BreadthFirstPathFinder_withLinkType implements Steppable {
LinkedList queue = new LinkedList();
MultiMap> links = new MultiMap(); // backwards (child -> parent)
IF1>> getChildren; // must set
BreadthFirstPathFinder_withLinkType() {}
BreadthFirstPathFinder_withLinkType(IF1>> getChildren) {
this.getChildren = getChildren;}
BreadthFirstPathFinder_withLinkType(IF1>> getChildren, A startNode) {
this.getChildren = getChildren; add(startNode); }
void add(A a) {
add(a, null, null);
}
void add(A a, A prev, B linkType) {
if (!links.containsKey(a)) {
links.put(a, prev == null ? null : pair(prev, linkType));
queue.add(a);
}
}
public boolean step() {
ping();
if (empty(queue)) return false;
A a = popFirst(queue);
for (Pair link : unnull(getChildren.get(a)))
add(link.a, a, link.b);
return true;
}
boolean nodeReached(A a) {
return links.containsKey(a);
}
Collection getBackLinks(A a) {
return pairsA(links.get(a));
}
Collection> getBackLinksWithTypes(A a) {
return links.get(a);
}
List> examplePathWithTypes(A start, A dest) {
List> path = new ArrayList();
A node = dest;
path.add(pair(node, null)); // dest node has no link type
while (node != start) { ping();
Pair link = first(getBackLinksWithTypes(node));
if (link == null) return null; // no path found
path.add(link);
node = link.a;
}
return reversed(path);
}
}
static void add(BitSet bs, int i) {
bs.set(i);
}
static boolean add(Collection c, A a) {
return c != null && c.add(a);
}
static void add(Container c, Component x) {
addToContainer(c, x);
}
static Pair pair(A a, B b) {
return new Pair(a, b);
}
static Pair pair(A a) {
return new Pair(a, a);
}
//sbool ping_actions_shareable = true;
static volatile boolean ping_pauseAll = false;
static int ping_sleep = 100; // poll pauseAll flag every 100
static volatile boolean ping_anyActions = false;
static Map ping_actions = newWeakHashMap();
static ThreadLocal ping_isCleanUpThread = new ThreadLocal();
// always returns true
static boolean ping() {
if (ping_pauseAll || ping_anyActions) ping_impl(true /* XXX */);
//ifndef LeanMode ping_impl(); endifndef
return true;
}
// returns true when it slept
static boolean ping_impl(boolean okInCleanUp) { try {
if (ping_pauseAll && !isAWTThread()) {
do
Thread.sleep(ping_sleep);
while (ping_pauseAll);
return true;
}
if (ping_anyActions) { // don't allow sharing ping_actions
if (!okInCleanUp && !isTrue(ping_isCleanUpThread.get()))
failIfUnlicensed();
Object action = null;
synchronized(ping_actions) {
if (!ping_actions.isEmpty()) {
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 boolean empty(Collection c) { return c == null || c.isEmpty(); }
static boolean empty(Iterable c) { return c == null || !c.iterator().hasNext(); }
static boolean empty(CharSequence 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);
if (o instanceof byte[]) return empty((byte[]) o);
if (o == null) return true;
throw fail("unknown type for 'empty': " + getType(o));
}
static boolean empty(Iterator i) { return i == null || !i.hasNext(); }
static boolean empty(double[] a) { return a == null || a.length == 0; }
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 boolean empty(byte[] a) { return a == null || a.length == 0; }
static boolean empty(short[] a) { return a == null || a.length == 0; }
static boolean empty(MultiMap mm) { return mm == null || mm.isEmpty(); }
static boolean empty(File f) { return getFileSize(f) == 0; }
static A popFirst(List l) {
if (empty(l)) return null;
A a = first(l);
l.remove(0);
return a;
}
static A popFirst(Collection l) {
if (empty(l)) return null;
A a = first(l);
l.remove(a);
return a;
}
static List popFirst(int n, List l) {
List part = cloneSubList(l, 0, n);
removeSubList(l, 0, n);
return part;
}
static String unnull(String s) {
return s == null ? "" : s;
}
static Collection unnull(Collection l) {
return l == null ? emptyList() : l;
}
static List unnull(List l) { return l == null ? emptyList() : l; }
static int[] unnull(int[] l) { return l == null ? emptyIntArray() : l; }
static char[] unnull(char[] l) { return l == null ? emptyCharArray() : l; }
static double[] unnull(double[] l) { return l == null ? emptyDoubleArray() : l; }
static Map unnull(Map l) {
return l == null ? emptyMap() : l;
}
static Iterable unnull(Iterable i) {
return i == null ? emptyList() : i;
}
static A[] unnull(A[] a) {
return a == null ? (A[]) emptyObjectArray() : a;
}
static BitSet unnull(BitSet b) {
return b == null ? new BitSet() : b;
}
//ifclass Symbol
static Pair unnull(Pair p) {
return p != null ? p : new Pair(null, null);
}
static long unnull(Long l) { return l == null ? 0L : l; }
static List pairsA(Collection> l) {
return firstOfPairs(l);
}
static Object first(Object list) {
return first((Iterable) list);
}
static A first(List list) {
return empty(list) ? null : list.get(0);
}
static A first(A[] bla) {
return bla == null || bla.length == 0 ? null : bla[0];
}
static A first(Iterator i) {
return i == null || !i.hasNext() ? null : i.next();
}
static A first(Iterable i) {
if (i == null) return null;
Iterator it = i.iterator();
return it.hasNext() ? it.next() : null;
}
static Character first(String s) { return empty(s) ? null : s.charAt(0); }
static Character first(CharSequence s) { return empty(s) ? null : s.charAt(0); }
static A first(Pair p) {
return p == null ? null : p.a;
}
static Byte first(byte[] l) {
return empty(l) ? null : l[0];
}
static List reversed(Iterable l) {
return reversedList(l);
}
static List reversed(A[] l) {
return reversedList(asList(l));
}
static String reversed(String s) {
return reversedString(s);
}
static void addToContainer(Container a, Component... b) {
if (a == null) return;
{ swing(new Runnable() { public void run() { try {
for (Component c : unnull(b))
if (c != null)
a.add(c);
} catch (Exception __e) { throw rethrow(__e); } } public String toString() { return "for (Component c : unnull(b))\r\n if (c != null) \r\n a.add(c);"; }}); }
}
static Map newWeakHashMap() {
return _registerWeakMap(synchroMap(new WeakHashMap()));
}
// 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 boolean isTrue(Object o) {
if (o instanceof Boolean)
return ((Boolean) o).booleanValue();
if (o == null) return false;
if (o instanceof ThreadLocal) // TODO: remove this
return isTrue(((ThreadLocal) o).get());
throw fail(getClassName(o));
}
static boolean isTrue(Boolean b) {
return b != null && b.booleanValue();
}
static void failIfUnlicensed() {
assertTrue("license off", licensed());
}
static Thread currentThread() {
return Thread.currentThread();
}
static boolean eq(Object a, Object b) {
return a == b || a != null && b != null && a.equals(b);
}
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(msg == null ? "" : msg); }
static RuntimeException fail(String msg, Throwable innerException) { throw new RuntimeException(msg, innerException); }
static RuntimeException rethrow(Throwable t) {
if (t instanceof Error)
_handleError((Error) t);
throw t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
}
static RuntimeException rethrow(String msg, Throwable t) {
throw new RuntimeException(msg, t);
}
static String getType(Object o) {
return getClassName(o);
}
static long getFileSize(String path) {
return path == null ? 0 : new File(path).length();
}
static long getFileSize(File f) {
return f == null ? 0 : f.length();
}
static List cloneSubList(List l, int startIndex, int endIndex) {
return newSubList(l, startIndex, endIndex);
}
static List cloneSubList(List l, int startIndex) {
return newSubList(l, startIndex);
}
static void removeSubList(List l, int from, int to) {
if (l != null) subList(l, from, to).clear();
}
static void removeSubList(List l, int from) {
if (l != null) subList(l, from).clear();
}
static ArrayList emptyList() {
return new ArrayList();
//ret Collections.emptyList();
}
static ArrayList emptyList(int capacity) {
return new ArrayList(max(0, capacity));
}
// Try to match capacity
static ArrayList emptyList(Iterable l) {
return l instanceof Collection ? emptyList(((Collection) l).size()) : emptyList();
}
static ArrayList emptyList(Object[] l) {
return emptyList(l(l));
}
// get correct type at once
static ArrayList emptyList(Class c) {
return new ArrayList();
}
static int[] emptyIntArray_a = new int[0];
static int[] emptyIntArray() { return emptyIntArray_a; }
static char[] emptyCharArray = new char[0];
static char[] emptyCharArray() { return emptyCharArray; }
static double[] emptyDoubleArray = new double[0];
static double[] emptyDoubleArray() { return emptyDoubleArray; }
static Map emptyMap() {
return new HashMap();
}
static Object[] emptyObjectArray_a = new Object[0];
static Object[] emptyObjectArray() { return emptyObjectArray_a; }
static List firstOfPairs(Collection> l) {
List out = new ArrayList();
for (Pair p : unnull(l)) out.add(firstOfPair(p));
return out;
}
static List reversedList(Iterable l) {
List x = cloneList(l);
Collections.reverse(x);
return x;
}
// unclear semantics as to whether return null on null
static ArrayList asList(A[] a) {
return a == null ? new ArrayList() : new ArrayList(Arrays.asList(a));
}
static ArrayList asList(int[] a) {
if (a == null) return null;
ArrayList l = emptyList(a.length);
for (int i : a) l.add(i);
return l;
}
static ArrayList asList(long[] a) {
if (a == null) return null;
ArrayList l = emptyList(a.length);
for (long i : a) l.add(i);
return l;
}
static ArrayList asList(float[] a) {
if (a == null) return null;
ArrayList l = emptyList(a.length);
for (float i : a) l.add(i);
return l;
}
static ArrayList asList(double[] a) {
if (a == null) return null;
ArrayList l = emptyList(a.length);
for (double i : a) l.add(i);
return l;
}
static ArrayList asList(Iterable 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 ArrayList asList(Enumeration e) {
ArrayList l = new ArrayList();
if (e != null)
while (e.hasMoreElements())
l.add(e.nextElement());
return l;
}
static String reversedString(String s) {
return reverseString(s);
}
static Object swing(Object f) {
return swingAndWait(f);
}
static A swing(F0 f) {
return (A) swingAndWait(f);
}
static A swing(IF0 f) {
return (A) swingAndWait(f);
}
static List _registerWeakMap_preList;
static A _registerWeakMap(A map) {
if (javax() == null) {
// We're in class init
if (_registerWeakMap_preList == null) _registerWeakMap_preList = synchroList();
_registerWeakMap_preList.add(map);
return map;
}
try {
call(javax(), "_registerWeakMap", map);
} catch (Throwable e) {
printException(e);
print("Upgrade JavaX!!");
}
return map;
}
static void _onLoad_registerWeakMap() {
assertNotNull(javax());
if (_registerWeakMap_preList == null) return;
for (Object o : _registerWeakMap_preList)
_registerWeakMap(o);
_registerWeakMap_preList = null;
}
static Map synchroMap() {
return synchroHashMap();
}
static Map synchroMap(Map map) {
return Collections.synchronizedMap(map);
}
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 Boolean isHeadless_cache;
static boolean isHeadless() {
if (isHeadless_cache != null) return isHeadless_cache;
if (isAndroid()) return isHeadless_cache = true;
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 String getClassName(Object o) {
return o == null ? "null" : o instanceof Class ? ((Class) o).getName() : o.getClass().getName();
}
static void assertTrue(Object o) {
if (!(eq(o, true) /*|| isTrue(pcallF(o))*/))
throw fail(str(o));
}
static boolean assertTrue(String msg, boolean b) {
if (!b)
throw fail(msg);
return b;
}
static boolean assertTrue(boolean b) {
if (!b)
throw fail("oops");
return b;
}
static volatile boolean licensed_yes = true;
static boolean licensed() {
if (!licensed_yes) return false;
ping_okInCleanUp();
return true;
}
static void licensed_off() {
licensed_yes = false;
}
static String str(Object o) {
return o == null ? "null" : o.toString();
}
static String str(char[] c) {
return new String(c);
}
static RuntimeException asRuntimeException(Throwable t) {
if (t instanceof Error)
_handleError((Error) t);
return t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
}
static void _handleError(Error e) {
call(javax(), "_handleError", e);
}
static List newSubList(List l, int startIndex, int endIndex) {
return cloneList(subList(l, startIndex, endIndex));
}
static List newSubList(List l, int startIndex) {
return cloneList(subList(l, startIndex));
}
static List subList(List l, int startIndex) {
return subList(l, startIndex, l(l));
}
static List subList(int startIndex, int endIndex, List l) {
return subList(l, startIndex, endIndex);
}
static List subList(List l, int startIndex, int endIndex) {
if (l == null) return null;
int n = l(l);
startIndex = Math.max(0, startIndex);
endIndex = Math.min(n, endIndex);
if (startIndex >= endIndex) return ll();
if (startIndex == 0 && endIndex == n) return l;
return l.subList(startIndex, endIndex);
}
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 double max(double a, double b) { return Math.max(a, b); }
static int max(Collection 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 int max(int[] c) {
int x = Integer.MIN_VALUE;
for (int d : c) if (d > x) x = d;
return x;
}
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(short[] a) { return a == null ? 0 : a.length; }
static int l(long[] 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(double[] 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(Iterator i) { return iteratorCount_int_close(i); } // consumes the iterator && closes it if possible
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 == null ? 0
: o instanceof String ? l((String) o)
: o instanceof Map ? l((Map) o)
: o instanceof Collection ? l((Collection) o)
: o instanceof Object[] ? l((Object[]) o)
: o instanceof boolean[] ? l((boolean[]) o)
: o instanceof byte[] ? l((byte[]) o)
: o instanceof char[] ? l((char[]) o)
: o instanceof short[] ? l((short[]) o)
: o instanceof int[] ? l((int[]) o)
: o instanceof float[] ? l((float[]) o)
: o instanceof double[] ? l((double[]) o)
: o instanceof long[] ? l((long[]) o)
: (Integer) call(o, "size");
}
static A firstOfPair(Pair p) {
return p == null ? null : p.a;
}
static ArrayList cloneList(Iterable l) {
return l instanceof Collection ? cloneList((Collection) l) : asList(l);
}
static ArrayList cloneList(Collection l) {
if (l == null) return new ArrayList();
synchronized(collectionMutex(l)) {
return new ArrayList(l);
}
}
static String reverseString(String s) {
return new StringBuilder(s).reverse().toString();
}
static void swingAndWait(Runnable r) { try {
if (isAWTThread())
r.run();
else
EventQueue.invokeAndWait(addThreadInfoToRunnable(r));
} catch (Exception __e) { throw rethrow(__e); } }
static Object swingAndWait(final Object f) {
if (isAWTThread())
return callF(f);
else {
final Var result = new Var();
swingAndWait(new Runnable() { public void run() { try {
result.set(callF(f));
} catch (Exception __e) { throw rethrow(__e); } } public String toString() { return "result.set(callF(f));"; }});
return result.get();
}
}
static Class javax() {
return getJavaX();
}
static List synchroList() {
return Collections.synchronizedList(new ArrayList());
}
static List synchroList(List l) {
return Collections.synchronizedList(l);
}
static Object call(Object o) {
return callF(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) {
//ret call_cached(o, method, args);
return call_withVarargs(o, method, args);
}
static A printException(A e) {
printStackTrace(e);
return e;
}
static volatile StringBuffer local_log = new StringBuffer(); // not redirected
static volatile Appendable 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 boolean print_silent = false; // total mute if set
static Object print_byThread_lock = new Object();
static volatile ThreadLocal