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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 Pt topRightCorner(Rect r) {
return r == null ? null : pt(r.x2(), r.y1());
}
static Pt pt(int x, int y) {
return new Pt(x, y);
}
static Pt pt(int x) {
return new Pt(x, x);
}
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(Iterable it, Object a) {
if (it != null)
for (Object o : it)
if (eq(a, o))
return true;
return false;
}
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);
}
}