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 String joinUniqueNemptiesCI(String sep, Object... strings) {
return joinUniqueNemptiesCI(sep, asList(strings));
}
static String joinUniqueNemptiesCI(String sep, Iterable strings) {
return join(sep, uniquifyCI(nempties(allToStrOrNull(strings))));
}
// 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;
}
public static String join(String glue, Iterable strings) {
if (strings == null) return "";
if (strings instanceof Collection) {
if (((Collection) strings).size() == 1) return str(first(((Collection) strings)));
}
StringBuilder buf = new StringBuilder();
Iterator 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));
}
static String join(Iterable strings) {
return join("", strings);
}
static String join(Iterable strings, String glue) {
return join(glue, strings);
}
public static String join(String[] strings) {
return join("", strings);
}
static String join(String glue, Pair p) {
return p == null ? "" : str(p.a) + glue + str(p.b);
}
static List uniquifyCI(Collection l) {
TreeSet set = ciSet();
List out = new ArrayList();
for (String a : unnull(l))
if (set.add(a))
out.add(a);
return out;
}
static List nempties(Collection c) {
return filterNempty(c);
}
static List allToStrOrNull(Iterable c) {
return lmap(__18 -> strOrNull(__18),c);
}
static List allToStrOrNull(Object[] c) {
return lmap(__19 -> strOrNull(__19),c);
}
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 String str(Object o) {
return o == null ? "null" : o.toString();
}
static String str(char[] c) {
return new String(c);
}
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 TreeSet ciSet() {
return caseInsensitiveSet();
}
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 filterNempty(Collection c) {
List l = new ArrayList();
for (String x : unnull(c))
if (nempty(x))
l.add(x);
return l;
}
static List lmap(IF1 f, Iterable l) {
return lambdaMap(f, l);
}
static List lmap(IF1 f, A[] l) {
return lambdaMap(f, l);
}
static String strOrNull(Object o) {
return o == null ? null : str(o);
}
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 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(File f) { return getFileSize(f) == 0; }
static TreeSet caseInsensitiveSet() {
return caseInsensitiveSet_treeSet();
}
static TreeSet caseInsensitiveSet(Collection c) {
return caseInsensitiveSet_treeSet(c);
}
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 boolean nempty(Collection c) {
return !empty(c);
}
static boolean nempty(CharSequence s) {
return !empty(s);
}
static boolean nempty(Object[] o) { return !empty(o); }
static boolean nempty(byte[] o) { return !empty(o); }
static boolean nempty(int[] o) { return !empty(o); }
static boolean nempty(Map m) {
return !empty(m);
}
static boolean nempty(Iterator i) {
return i != null && i.hasNext();
}
static boolean nempty(Object o) { return !empty(o); }
static List lambdaMap(IF1 f, Iterable l) {
return map(l, f);
}
static List lambdaMap(IF1 f, A[] l) {
return map(l, f);
}
static int iteratorCount_int_close(Iterator i) { try {
int n = 0;
if (i != null) while (i.hasNext()) { i.next(); ++n; }
if (i instanceof AutoCloseable) ((AutoCloseable) i).close();
return n;
} catch (Exception __e) { throw rethrow(__e); } }
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 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 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 TreeSet caseInsensitiveSet_treeSet() {
return new TreeSet(caseInsensitiveComparator());
}
static TreeSet caseInsensitiveSet_treeSet(Collection c) {
return toCaseInsensitiveSet_treeSet(c);
}
static List map(Iterable l, Object f) { return map(f, l); }
static List map(Object f, Iterable l) {
List x = emptyList(l);
if (l != null) for (Object o : l)
x.add(callF(f, o));
return x;
}
static List map(Iterable l, F1 f) { return map(f, l); }
static List map(F1 f, Iterable l) {
List x = emptyList(l);
if (l != null) for (A o : l)
x.add(callF(f, o));
return x;
}
static List map(IF1 f, Iterable l) { return map(l, f); }
static List map(Iterable l, IF1 f) {
List x = emptyList(l);
if (l != null) for (A o : l)
x.add(f.get(o));
return x;
}
static List map(IF1 f, A[] l) { return map(l, f); }
static List map(A[] l, IF1 f) {
List x = emptyList(l);
if (l != null) for (A o : l)
x.add(f.get(o));
return x;
}
static List map(Object f, Object[] l) { return map(f, asList(l)); }
static List map(Object[] l, Object f) { return map(f, l); }
static List map(Object f, Map map) {
return map(map, f);
}
// map: func(key, value) -> list element
static List map(Map map, Object f) {
List x = new ArrayList();
if (map != null) for (Object _e : map.entrySet()) {
Map.Entry e = (Map.Entry) _e;
x.add(callF(f, e.getKey(), e.getValue()));
}
return x;
}
static List map(Map map, IF2 f) {
return map(map, (Object) f);
}
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 Map> callF_cache = newDangerousWeakHashMap();
static B callF(F1 f, A a) {
return f == null ? null : f.get(a);
}
static B callF(IF1 f, A a) {
return f == null ? null : f.get(a);
}
static C callF(IF2 f, A a, B b) {
return f == null ? null : f.get(a, b);
}
static void callF(VF1 f, A a) {
if (f != null) f.get(a);
}
static Object callF(Object f, Object... args) {
if (f instanceof String)
return callMCWithVarArgs((String) f, args); // possible SLOWDOWN over callMC
return safeCallF(f, args);
}
static Object safeCallF(Object f, Object... args) {
if (f instanceof Runnable) {
((Runnable) f).run();
return null;
}
if (f == null) return null;
Class c = f.getClass();
ArrayList methods;
synchronized(callF_cache) {
methods = callF_cache.get(c);
if (methods == null)
methods = callF_makeCache(c);
}
int n = l(methods);
if (n == 0) {
throw fail("No get method in " + getClassName(c));
}
if (n == 1) return invokeMethod(methods.get(0), f, args);
for (int i = 0; i < n; i++) {
Method m = methods.get(i);
if (call_checkArgs(m, args, false))
return invokeMethod(m, f, args);
}
throw fail("No matching get method in " + getClassName(c));
}
// used internally
static ArrayList callF_makeCache(Class c) {
ArrayList l = new ArrayList();
Class _c = c;
do {
for (Method m : _c.getDeclaredMethods())
if (m.getName().equals("get")) {
makeAccessible(m);
l.add(m);
}
if (!l.isEmpty()) break;
_c = _c.getSuperclass();
} while (_c != null);
callF_cache.put(c, l);
return l;
}
static Object call_withVarargs(Object o, String method, Object... args) { try {
if (o == null) return null;
if (o instanceof Class) {
Class c = (Class) o;
_MethodCache cache = callOpt_getCache(c);
Method me = cache.findStaticMethod(method, args);
if (me != null)
return invokeMethod(me, null, args);
// try varargs
List methods = cache.cache.get(method);
if (methods != null) methodSearch: for (Method m : methods) {
{ if (!(m.isVarArgs())) continue; }
{ if (!(isStaticMethod(m))) continue; }
Object[] newArgs = massageArgsForVarArgsCall(m, args);
if (newArgs != null)
return invokeMethod(m, null, newArgs);
}
throw fail("Method " + c.getName() + "." + method + "(" + joinWithComma(classNames(args)) + ") not found");
} else {
Class c = o.getClass();
_MethodCache cache = callOpt_getCache(c);
Method me = cache.findMethod(method, args);
if (me != null)
return invokeMethod(me, o, args);
// try varargs
List methods = cache.cache.get(method);
if (methods != null) methodSearch: for (Method m : methods) {
{ if (!(m.isVarArgs())) continue; }
Object[] newArgs = massageArgsForVarArgsCall(m, args);
if (newArgs != null)
return invokeMethod(m, o, newArgs);
}
throw fail("Method " + c.getName() + "." + method + "(" + joinWithComma(classNames(args)) + ") not found");
}
} catch (Exception __e) { throw rethrow(__e); } }
static RuntimeException asRuntimeException(Throwable t) {
if (t instanceof Error)
_handleError((Error) t);
return t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
}
static String getClassName(Object o) {
return o == null ? "null" : o instanceof Class ? ((Class) o).getName() : o.getClass().getName();
}
static Comparator caseInsensitiveComparator() {
return betterCIComparator();
}
static TreeSet toCaseInsensitiveSet_treeSet(Iterable c) {
if (isCISet(c)) return (TreeSet) c;
TreeSet set = caseInsensitiveSet_treeSet();
addAll(set, c);
return set;
}
static TreeSet toCaseInsensitiveSet_treeSet(String... x) {
TreeSet set = caseInsensitiveSet_treeSet();
addAll(set, x);
return set;
}
static void _handleError(Error e) {
call(javax(), "_handleError", e);
}
static Map newDangerousWeakHashMap() {
return _registerDangerousWeakMap(synchroMap(new WeakHashMap()));
}
// initFunction: voidfunc(Map) - is called initially, and after clearing the map
static Map newDangerousWeakHashMap(Object initFunction) {
return _registerDangerousWeakMap(synchroMap(new WeakHashMap()), initFunction);
}
static Object callMCWithVarArgs(String method, Object... args) {
return call_withVarargs(mc(), method, args);
}
static Object invokeMethod(Method m, Object o, Object... args) { try {
try {
return m.invoke(o, args);
} catch (InvocationTargetException e) {
throw rethrow(getExceptionCause(e));
} catch (IllegalArgumentException e) {
throw new IllegalArgumentException(e.getMessage() + " - was calling: " + m + ", args: " + joinWithSpace(classNames(args)));
}
} catch (Exception __e) { throw rethrow(__e); } }
static boolean call_checkArgs(Method m, Object[] args, boolean debug) {
Class>[] types = m.getParameterTypes();
if (types.length != args.length) {
if (debug)
print("Bad parameter length: " + args.length + " vs " + types.length);
return false;
}
for (int i = 0; i < types.length; i++) {
Object arg = args[i];
if (!(arg == null ? !types[i].isPrimitive()
: isInstanceX(types[i], arg))) {
if (debug)
print("Bad parameter " + i + ": " + arg + " vs " + types[i]);
return false;
}
}
return true;
}
static Field makeAccessible(Field f) {
try {
f.setAccessible(true);
} catch (Throwable e) {
// Note: The error reporting only works with Java VM option --illegal-access=deny
vmBus_send("makeAccessible_error",e, f);
}
return f;
}
static Method makeAccessible(Method m) {
try {
m.setAccessible(true);
} catch (Throwable e) {
vmBus_send("makeAccessible_error",e, m);
}
return m;
}
static Constructor makeAccessible(Constructor c) {
try {
c.setAccessible(true);
} catch (Throwable e) {
vmBus_send("makeAccessible_error",e, c);
}
return c;
}
static final Map callOpt_cache = newDangerousWeakHashMap();
static Object callOpt_cached(Object o, String methodName, Object... args) { try {
if (o == null) return null;
if (o instanceof Class) {
Class c = (Class) o;
_MethodCache cache = callOpt_getCache(c);
// TODO: (super-rare) case where method exists static and non-static
// with different args
Method me = cache.findMethod(methodName, args);
if (me == null || (me.getModifiers() & Modifier.STATIC) == 0) return null;
return invokeMethod(me, null, args);
} else {
Class c = o.getClass();
_MethodCache cache = callOpt_getCache(c);
Method me = cache.findMethod(methodName, args);
if (me == null) return null;
return invokeMethod(me, o, args);
}
} catch (Exception __e) { throw rethrow(__e); } }
static _MethodCache callOpt_getCache(Class c) {
synchronized(callOpt_cache) {
_MethodCache cache = callOpt_cache.get(c);
if (cache == null)
callOpt_cache.put(c, cache = new _MethodCache(c));
return cache;
}
}
static boolean isStaticMethod(Method m) {
return methodIsStatic(m);
}
static Object[] massageArgsForVarArgsCall(Method m, Object[] args) {
Class>[] types = m.getParameterTypes();
int n = types.length-1, nArgs = args.length;
if (nArgs < n) return null;
for (int i = 0; i < n; i++)
if (!argumentCompatibleWithType(args[i], types[i]))
return null;
Class varArgType = types[n].getComponentType();
for (int i = n; i < nArgs; i++)
if (!argumentCompatibleWithType(args[i], varArgType))
return null;
Object[] newArgs = new Object[n+1];
arraycopy(args, 0, newArgs, 0, n);
Object[] varArgs = arrayOfType(varArgType, nArgs-n);
arraycopy(args, n, varArgs, 0, nArgs-n);
newArgs[n] = varArgs;
return newArgs;
}
static String joinWithComma(Collection c) {
return join(", ", c);
}
static String joinWithComma(String... c) {
return join(", ", c);
}
static String joinWithComma(Pair p) {
return p == null ? "" : joinWithComma(str(p.a), str(p.b));
}
static List classNames(Collection l) {
return getClassNames(l);
}
static List classNames(Object[] l) {
return getClassNames(Arrays.asList(l));
}
static betterCIComparator_C betterCIComparator_instance;
static betterCIComparator_C betterCIComparator() {
if (betterCIComparator_instance == null)
betterCIComparator_instance = new betterCIComparator_C();
return betterCIComparator_instance;
}
final static class betterCIComparator_C implements Comparator {
public int compare(String s1, String s2) {
if (s1 == null) return s2 == null ? 0 : -1;
if (s2 == null) return 1;
int n1 = s1.length();
int n2 = s2.length();
int min = Math.min(n1, n2);
for (int i = 0; i < min; i++) {
char c1 = s1.charAt(i);
char c2 = s2.charAt(i);
if (c1 != c2) {
c1 = Character.toUpperCase(c1);
c2 = Character.toUpperCase(c2);
if (c1 != c2) {
c1 = Character.toLowerCase(c1);
c2 = Character.toLowerCase(c2);
if (c1 != c2) {
// No overflow because of numeric promotion
return c1 - c2;
}
}
}
}
return n1 - n2;
}
}
static boolean isCISet(Iterable l) {
return l instanceof TreeSet && ((TreeSet) l).comparator() == caseInsensitiveComparator();
}
static void addAll(Collection c, Iterable b) {
if (c != null && b != null) for (A a : b) c.add(a);
}
static boolean addAll(Collection c, Collection b) {
return c != null && b != null && c.addAll(b);
}
static boolean addAll(Collection c, B... b) {
return c != null && b != null && c.addAll(Arrays.asList(b));
}
static Map addAll(Map a, Map extends A,? extends B> b) {
if (a != null) a.putAll(b);
return a;
}
static Class javax() {
return getJavaX();
}
static List _registerDangerousWeakMap_preList;
static A _registerDangerousWeakMap(A map) {
return _registerDangerousWeakMap(map, null);
}
static A _registerDangerousWeakMap(A map, Object init) {
callF(init, map);
if (init instanceof String) {
final String f = (String) init;
init = new VF1