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 takeRandom(int n, List l) {
return takeFirst(n, shuffledIterator(l));
}
static List takeFirst(List l, int n) {
return l(l) <= n ? l : newSubListOrSame(l, 0, n);
}
static List takeFirst(int n, List l) {
return takeFirst(l, n);
}
static String takeFirst(int n, String s) { return substring(s, 0, n); }
static String takeFirst(String s, int n) { return substring(s, 0, n); }
static List takeFirst(int n, Iterable i) {
List l = new ArrayList();
Iterator it = i.iterator();
for (int _repeat_52 = 0; _repeat_52 < n; _repeat_52++) { if (it.hasNext()) l.add(it.next()); else break; }
return l;
}
static IterableIterator shuffledIterator(final List l) {
return new IterableIterator() {
int n = l(l);
int i = 0;
Map shuffled = new HashMap();
public boolean hasNext() { return i < n; }
public A next() {
int j = random(i, n);
A a = get(i), b = get(j);
shuffled.put(j, a);
shuffled.remove(i);
++i;
return b;
}
A get(int i) {
return shuffled.containsKey(i) ? shuffled.get(i) : l.get(i);
}
};
}
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(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 List newSubListOrSame(List l, int startIndex) {
return newSubListOrSame(l, startIndex, l(l));
}
static List newSubListOrSame(List l, int startIndex, int endIndex) {
if (l == null) return null;
int n = l(l);
startIndex = max(0, startIndex);
endIndex = min(n, endIndex);
if (startIndex >= endIndex) return ll();
if (startIndex == 0 && endIndex == n) return l;
return cloneList(l.subList(startIndex, endIndex));
}
static String substring(String s, int x) {
return substring(s, x, strL(s));
}
static String substring(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 Random random_random = new Random();
static int random(int n) {
return n <= 0 ? 0 : random_random.nextInt(n);
}
static double random(double max) {
return random()*max;
}
static double random() {
return random_random.nextInt(100001)/100000.0;
}
static double random(double min, double max) {
return min+random()*(max-min);
}
// min <= value < max
static int random(int min, int max) {
return min+random(max-min);
}
static A random(List l) {
return oneOf(l);
}
static A random(Collection c) {
if (c instanceof List) return random((List) c);
int i = random(l(c));
return collectionGet(c, i);
}
// get purpose 1: access a list/array/map (safer version of x.get(y))
static A get(List l, int idx) {
return l != null && idx >= 0 && idx < l(l) ? l.get(idx) : null;
}
// seems to conflict with other signatures
/*static B get(Map map, A key) {
ret map != null ? map.get(key) : null;
}*/
static 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 == null) return null;
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() & java.lang.reflect.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 Object get(String field, Object o) {
return get(o, field);
}
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 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 min(int a, int b) {
return Math.min(a, b);
}
static long min(long a, long b) {
return Math.min(a, b);
}
static float min(float a, float b) { return Math.min(a, b); }
static float min(float a, float b, float c) { return min(min(a, b), c); }
static double min(double a, double b) {
return Math.min(a, b);
}
static double min(double[] c) {
double x = Double.MAX_VALUE;
for (double d : c) x = Math.min(x, d);
return x;
}
static float min(float[] c) {
float x = Float.MAX_VALUE;
for (float d : c) x = Math.min(x, d);
return x;
}
static byte min(byte[] c) {
byte x = 127;
for (byte d : c) if (d < x) x = d;
return x;
}
static short min(short[] c) {
short x = 0x7FFF;
for (short d : c) if (d < x) x = d;
return x;
}
static int min(int[] c) {
int x = Integer.MAX_VALUE;
for (int d : c) if (d < x) x = d;
return x;
}
static List ll(A... a) {
ArrayList l = new ArrayList(a.length);
if (a != null) for (A x : a) l.add(x);
return l;
}
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 int strL(String s) {
return s == null ? 0 : s.length();
}
static A oneOf(List l) {
return l.isEmpty() ? null : l.get(new Random().nextInt(l.size()));
}
static char oneOf(String s) {
return empty(s) ? '?' : s.charAt(random(l(s)));
}
static String oneOf(String... l) {
return oneOf(asList(l));
}
static A collectionGet(Collection c, int idx) {
if (c == null || idx < 0 || idx >= l(c)) return null;
if (c instanceof List) return listGet((List) c, idx);
Iterator it = c.iterator();
for (int i = 0; i < idx; i++) if (it.hasNext()) it.next(); else return null;
return it.hasNext() ? it.next() : 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 RuntimeException asRuntimeException(Throwable t) {
if (t instanceof Error)
_handleError((Error) t);
return t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
}
static Map> callF_cache = newDangerousWeakHashMap();
static void callF(VF1 f, A a) {
if (f != null) f.get(a);
}
static Object callF(Object f, Object... args) { try {
if (f instanceof String)
return callMC((String) f, 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));
} catch (Exception __e) { throw rethrow(__e); } }
// 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")) {
m.setAccessible(true);
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 in " + c);
}
} catch (Exception __e) { throw rethrow(__e); } }
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(float[] a) {
if (a == null) return null;
ArrayList l = emptyList(a.length);
for (float 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 Object collectionMutex(Object o) {
String c = className(o);
if (eq(c, "java.util.TreeMap$KeySet"))
c = className(o = getOpt(o, "m"));
else if (eq(c, "java.util.HashMap$KeySet"))
c = className(o = get_raw(o, "this$0"));
if (eqOneOf(c, "java.util.TreeMap$AscendingSubMap", "java.util.TreeMap$DescendingSubMap"))
c = className(o = get_raw(o, "m"));
return o;
}
static boolean empty(Collection c) { return c == null || c.isEmpty(); }
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(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(File f) { return getFileSize(f) == 0; }
static A listGet(List l, int idx) {
return l != null && idx >= 0 && idx < l(l) ? l.get(idx) : null;
}
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 HashMap> callMC_cache = new HashMap();
static String callMC_key;
static Method callMC_value;
// varargs assignment fixer for a single string array argument
static Object callMC(String method, String[] arg) {
return callMC(method, new Object[] {arg});
}
static Object callMC(String method, Object... args) { try {
Method me;
if (callMC_cache == null) callMC_cache = new HashMap(); // initializer time workaround
synchronized(callMC_cache) {
me = method == callMC_key ? callMC_value : null;
}
if (me != null) try {
return invokeMethod(me, null, args);
} catch (IllegalArgumentException e) {
throw new RuntimeException("Can't call " + me + " with arguments " + classNames(args), e);
}
List m;
synchronized(callMC_cache) {
m = callMC_cache.get(method);
}
if (m == null) {
if (callMC_cache.isEmpty()) {
callMC_makeCache();
m = callMC_cache.get(method);
}
if (m == null) throw fail("Method named " + method + " not found in main");
}
int n = m.size();
if (n == 1) {
me = m.get(0);
synchronized(callMC_cache) {
callMC_key = method;
callMC_value = me;
}
try {
return invokeMethod(me, null, args);
} catch (IllegalArgumentException e) {
throw new RuntimeException("Can't call " + me + " with arguments " + classNames(args), e);
}
}
for (int i = 0; i < n; i++) {
me = m.get(i);
if (call_checkArgs(me, args, false))
return invokeMethod(me, null, args);
}
throw fail("No method called " + method + " with matching arguments found in main");
} catch (Exception __e) { throw rethrow(__e); } }
static void callMC_makeCache() {
synchronized(callMC_cache) {
callMC_cache.clear();
Class _c = (Class) mc(), c = _c;
while (c != null) {
for (Method m : c.getDeclaredMethods())
if ((m.getModifiers() & java.lang.reflect.Modifier.STATIC) != 0) {
m.setAccessible(true);
multiMapPut(callMC_cache, m.getName(), m);
}
c = c.getSuperclass();
}
}
}
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 getClassName(Object o) {
return o == null ? "null" : o instanceof Class ? ((Class) o).getName() : o.getClass().getName();
}
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 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 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 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 className(Object o) {
return getClassName(o);
}
static boolean eq(Object a, Object b) {
return a == null ? b == null : a == b || b != null && a.equals(b);
}
static Object getOpt(Object o, String field) {
return getOpt_cached(o, field);
}
static Object getOpt(String field, Object o) {
return getOpt_cached(o, field);
}
static Object getOpt_raw(Object o, String field) { try {
Field f = getOpt_findField(o.getClass(), field);
if (f == null) return null;
f.setAccessible(true);
return f.get(o);
} catch (Exception __e) { throw rethrow(__e); } }
// access of static fields is not yet optimized
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 rethrow(__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() & java.lang.reflect.Modifier.STATIC) != 0)
return f;
_c = _c.getSuperclass();
} while (_c != null);
return null;
}
static boolean eqOneOf(Object o, Object... l) {
for (Object x : l) if (eq(o, x)) return true; return false;
}
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 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