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.*; class main { static Dimension maxDimension(Dimension a, Dimension b) { return a == null ? b : b == null ? a : new Dimension(max(a.width, b.width), max(a.height, b.height)); } 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 > A max(A a, A b) { return cmp(a, b) >= 0 ? a : b; } 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); } }