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 boolean containsPt(int x1, int y1, int w, int h, Pt p) { return p.x >= x1 && p.y >= y1 && p.x < x1+w && p.y < y1+h; } static boolean containsPt(Rect a, int x, int y) { return a != null && a.contains(x, y); } static boolean containsPt(Rect a, Pt p) { return a != null && p != null && a.contains(p.x, p.y); } final static class Rect implements IFieldsToList{ static final String _fieldOrder = "x y w h"; int x; int y; int w; int h; Rect() {} Rect(int x, int y, int w, int h) { this.h = h; this.w = w; this.y = y; this.x = x;} public boolean equals(Object o) { if (!(o instanceof Rect)) return false; Rect __1 = (Rect) o; return x == __1.x && y == __1.y && w == __1.w && h == __1.h; } public int hashCode() { int h = 2543108; h = boostHashCombine(h, _hashCode(x)); h = boostHashCombine(h, _hashCode(y)); h = boostHashCombine(h, _hashCode(w)); h = boostHashCombine(h, _hashCode(h)); return h; } public Object[] _fieldsToList() { return new Object[] {x, y, w, h}; } Rect(Rectangle r) { x = r.x; y = r.y; w = r.width; h = r.height; } Rect(Pt p, int w, int h) { this.h = h; this.w = w; x = p.x; y = p.y; } Rect(Rect r) { x = r.x; y = r.y; w = r.w; h = r.h; } Rectangle getRectangle() { return new Rectangle(x, y, w, h); } public String toString() { return x + "," + y + " / " + w + "," + h; } int x1() { return x; } int y1() { return y; } int x2() { return x + w; } int y2() { return y + h; } boolean contains(Pt p) { return contains(p.x, p.y); } boolean contains(int _x, int _y) { return _x >= x && _y >= y && _x < x+w && _y < y+h; } boolean empty() { return w <= 0 || h <= 0; } } 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 interface IFieldsToList { Object[] _fieldsToList(); } static int boostHashCombine(int a, int b) { return a ^ (b + 0x9e3779b9 + (a << 6) + (a >> 2)); } static int _hashCode(Object a) { return a == null ? 0 : a.hashCode(); } static boolean contains(Collection c, Object o) { return c != null && c.contains(o); } static boolean contains(Object[] x, Object o) { if (x != null) for (Object a : x) if (eq(a, o)) return true; return false; } static boolean contains(String s, char c) { return s != null && s.indexOf(c) >= 0; } static boolean contains(String s, String b) { return s != null && s.indexOf(b) >= 0; } static boolean contains(BitSet bs, int i) { return bs != null && bs.get(i); } 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 boolean eq(Object a, Object b) { return a == b || a != null && b != null && a.equals(b); } static String str(Object o) { return o == null ? "null" : o.toString(); } static String str(char[] c) { return new String(c); } }