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 class LCSortedPairIndex {
long[] pairs;
int[] index;
int ofs; // added to every result
LCSortedPairIndex(long[] pairs, int ofs) {
this(pairs);
this.ofs = ofs;
}
LCSortedPairIndex(long[] pairs) {
this(pairs, null);
}
// primer is destroyed in the process
LCSortedPairIndex(long[] pairs, LCSortedPairIndex primer) {
this.pairs = pairs;
int[] primerData = primer == null ? null : primer.index;
if (primer != null) primer.pairs = null;
index = lc_sortedPairIndex(pairs, primerData);
}
int get(long pair) {
int i = intArrayBinarySearchWithGeneralizedComparator(index, a -> {
int x = cmp(pairs[a], pair);
return x;
});
return i >= 0 ? index[i]+ofs : -1;
}
}
// if primer is not null, it must contain a shuffled version of the list [0, 1, ...] (of any length)
// primer is used to speed up the sort
static int[] lc_sortedPairIndex(long[] pairs) { return lc_sortedPairIndex(pairs, null); }
static int[] lc_sortedPairIndex(long[] pairs, int[] primer) {
int n = pairs.length;
int[] idx = new int[n];
copyIntArray(primer, idx);
for (int i = l(primer); i < n; i++) idx[i] = i;
timSortIntArrayWithComparator(idx, (a, b) -> cmp(pairs[a], pairs[b]));
return idx;
}
static int intArrayBinarySearchWithGeneralizedComparator(int[] a, IF1_IntToInt comparator) {
return intArrayBinarySearchWithGeneralizedComparator(a, 0, a.length, comparator);
}
static int intArrayBinarySearchWithGeneralizedComparator(int[] a, int fromIndex, int toIndex, IF1_IntToInt comparator) {
int low = fromIndex;
int high = toIndex - 1;
while (low <= high) {
int mid = (low + high) >>> 1;
int midVal = a[mid];
int cmp = comparator.get(midVal);
if (cmp < 0)
low = mid + 1;
else if (cmp > 0)
high = mid - 1;
else
return mid; // key found
}
return -(low + 1); // key not found.
}
static int cmp(Number a, Number b) {
return a == null ? b == null ? 0 : -1 : cmp(a.doubleValue(), b.doubleValue());
}
static int cmp(double a, double b) {
return a < b ? -1 : a == b ? 0 : 1;
}
static int cmp(int a, int b) {
return a < b ? -1 : a == b ? 0 : 1;
}
static int cmp(long a, long b) {
return a < b ? -1 : a == b ? 0 : 1;
}
static int cmp(Object a, Object b) {
if (a == null) return b == null ? 0 : -1;
if (b == null) return 1;
return ((Comparable) a).compareTo(b);
}
static void copyIntArray(int[] a, int[] b) {
if (a != null && b != null)
arraycopy(a, 0, b, 0, Math.min(a.length, b.length));
}
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");
}
// not actually Timsort, but works well
// This code has been contributed by 29AjayKumar
// from: https://www.geeksforgeeks.org/timsort/
static final int timSortIntArrayWithComparator_RUN = 32;
// this function sorts array from left index to
// to right index which is of size atmost RUN
static void timSortIntArrayWithComparator_insertionSort(int[] arr, IntComparator comparator, int left, int right) {
for (int i = left + 1; i <= right; i++)
{
int temp = arr[i];
int j = i - 1;
while (j >= left && comparator.compare(arr[j], temp) > 0)
{
arr[j + 1] = arr[j];
j--;
}
arr[j + 1] = temp;
}
}
// merge function merges the sorted runs
static void timSortIntArrayWithComparator_merge(int[] arr, IntComparator comparator, int l, int m, int r) {
// original array is broken in two parts
// left and right array
int len1 = m - l + 1, len2 = r - m;
int[] left = new int[len1];
int[] right = new int[len2];
for (int x = 0; x < len1; x++)
{
left[x] = arr[l + x];
}
for (int x = 0; x < len2; x++)
{
right[x] = arr[m + 1 + x];
}
int i = 0;
int j = 0;
int k = l;
// after comparing, we merge those two array
// in larger sub array
while (i < len1 && j < len2)
{
if (comparator.compare(left[i], right[j]) <= 0)
{
arr[k] = left[i];
i++;
}
else
{
arr[k] = right[j];
j++;
}
k++;
}
// copy remaining elements of left, if any
while (i < len1)
{
arr[k] = left[i];
k++;
i++;
}
// copy remaining element of right, if any
while (j < len2)
{
arr[k] = right[j];
k++;
j++;
}
}
// iterative Timsort function to sort the
// array[0...n-1] (similar to merge sort)
static void timSortIntArrayWithComparator(int[] arr, IntComparator comparator) { timSortIntArrayWithComparator(arr, lIntArray(arr), comparator); }
static void timSortIntArrayWithComparator(int[] arr, int n, IntComparator comparator) {
// Sort individual subarrays of size RUN
for (int i = 0; i < n; i += timSortIntArrayWithComparator_RUN)
{
timSortIntArrayWithComparator_insertionSort(arr, comparator, i, Math.min((i + 31), (n - 1)));
}
// start merging from size RUN (or 32). It will merge
// to form size 64, then 128, 256 and so on ....
for (int size = timSortIntArrayWithComparator_RUN; size < n; size = 2 * size)
{
// pick starting point of left sub array. We
// are going to merge arr[left..left+size-1]
// and arr[left+size, left+2*size-1]
// After every merge, we increase left by 2*size
for (int left = 0; left < n; left += 2 * size)
{
// find ending point of left sub array
// mid+1 is starting point of right sub array
int mid = Math.min(left + size - 1, n - 1);
int right = Math.min(left + 2 * size - 1, n - 1);
// merge sub array arr[left.....mid] &
// arr[mid+1....right]
timSortIntArrayWithComparator_merge(arr, comparator, left, mid, right);
}
}
}
static void arraycopy(Object[] a, Object[] b) {
if (a != null && b != null)
arraycopy(a, 0, b, 0, Math.min(a.length, b.length));
}
static void arraycopy(Object src, int srcPos, Object dest, int destPos, int n) {
if (n != 0)
System.arraycopy(src, srcPos, dest, destPos, n);
}
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 int lIntArray(int[] a) {
return a == null ? 0 : a.length;
}
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 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 callMCWithVarArgs((String) f, args); // possible SLOWDOWN over callMC
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")) {
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 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 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 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 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