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 java.util.function.*; 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 java.awt.geom.*; import javax.imageio.*; import java.math.*; import java.time.Duration; import java.lang.invoke.VarHandle; import java.lang.invoke.MethodHandles; class main { static long[] cloneSubLongArray(long[] b, int start, int end) { start = max(start, 0); end = min(end, l(b)); if (start >= end) return new long[0]; long[] x = new long[end-start]; System.arraycopy(b, start, x, 0, end-start); return x; } 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 > A max (Iterable l) { A max = null; var it = iterator(l); if (it.hasNext()) { max = it.next(); while (it.hasNext()) { A a = it.next(); if (cmp(a, max) > 0) max = a; } } return max; } /*Nah. static int max(Collection c) { int x = Integer.MIN_VALUE; for (int i : c) x = max(x, i); ret 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 > A max(A a, A b) { return cmp(a, b) >= 0 ? a : b; } 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 > A min(A a, A b) { return cmp(a, b) <= 0 ? a : b; } 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 Iterator iterator(Iterable c) { return c == null ? emptyIterator() : c.iterator(); } 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 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 Iterator emptyIterator() { return Collections.emptyIterator(); } 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 void _handleError(Error e) { //call(javax(), '_handleError, e); } }