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 int maxX(Iterable l) { int max = Integer.MIN_VALUE; for (Pt p : unnullForIteration(l)) max = max(max, p.x); return max; } static String unnullForIteration(String s) { return s == null ? "" : s; } static Collection unnullForIteration(Collection l) { return l == null ? immutableEmptyList() : l; } static List unnullForIteration(List l) { return l == null ? immutableEmptyList() : l; } static int[] unnullForIteration(int[] l) { return l == null ? emptyIntArray() : l; } static char[] unnullForIteration(char[] l) { return l == null ? emptyCharArray() : l; } static double[] unnullForIteration(double[] l) { return l == null ? emptyDoubleArray() : l; } static Map unnullForIteration(Map l) { return l == null ? immutableEmptyMap() : l; } static Iterable unnullForIteration(Iterable i) { return i == null ? immutableEmptyList() : i; } static A[] unnullForIteration(A[] a) { return a == null ? (A[]) emptyObjectArray() : a; } static BitSet unnullForIteration(BitSet b) { return b == null ? new BitSet() : b; } static Pt unnullForIteration(Pt p) { return p == null ? new Pt() : p; } //ifclass Symbol static long unnullForIteration(Long l) { return l == null ? 0L : l; } 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 List immutableEmptyList() { return Collections.emptyList(); } 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 immutableEmptyMap() { return Collections.emptyMap(); } static Object[] emptyObjectArray_a = new Object[0]; static Object[] emptyObjectArray() { return emptyObjectArray_a; } static class Pt implements Comparable { int x, y; Pt() {} Pt(Point p) { x = p.x; y = p.y; } Pt(int x, int y) { this.y = y; this.x = x;} Point getPoint() { return new Point(x, y); } public boolean equals(Object o) { return o instanceof Pt && x == ((Pt) o).x && y == ((Pt) o).y; } public int hashCode() { return boostHashCombine(x, y); } // compare in scan order public int compareTo(Pt p) { if (y != p.y) return cmp(y, p.y); return cmp(x, p.x); } public String toString() { return x + ", " + y; } } static int boostHashCombine(int a, int b) { return a ^ (b + 0x9e3779b9 + (a << 6) + (a >> 2)); } 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); } }