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; class main { static LineThroughPoint perpendicularBisector(IDoublePt a, IDoublePt b) { DoublePt midpoint = doublePt((a.x_double()+b.x_double())/2, (a.y_double()+b.y_double())/2); double angle = atan2(b.y_double()-a.y_double(), a.x_double()-b.x_double()); return new LineThroughPoint(midpoint, angle); } static DoublePt doublePt(double x) { return doublePt(x, x); } static DoublePt doublePt(double x, double y) { return new DoublePt(x, y); } static double atan2(double x, double y) { return Math.atan2(x, y); } // line that goes through x, y at specified angle // angle is in radians static class LineThroughPoint implements IFieldsToList{ static final String _fieldOrder = "x y angle"; double x; double y; double angle; LineThroughPoint() {} LineThroughPoint(double x, double y, double angle) { this.angle = angle; this.y = y; this.x = x;} public String toString() { return shortClassName_dropNumberPrefix(this) + "(" + x + ", " + y + ", " + angle + ")"; } public boolean equals(Object o) { if (!(o instanceof LineThroughPoint)) return false; LineThroughPoint __1 = (LineThroughPoint) o; return x == __1.x && y == __1.y && angle == __1.angle; } public int hashCode() { int h = -2021865473; h = boostHashCombine(h, _hashCode(x)); h = boostHashCombine(h, _hashCode(y)); h = boostHashCombine(h, _hashCode(angle)); return h; } public Object[] _fieldsToList() { return new Object[] {x, y, angle}; } LineThroughPoint(IDoublePt p, double angle) { this.angle = angle; x = p.x_double(); y = p.y_double(); } } static class DoublePt implements IDoublePt { double x, y; DoublePt() {} DoublePt(Point p) { x = p.x; y = p.y; } DoublePt(double x, double y) { this.y = y; this.x = x;} public boolean equals(Object p) { if (p instanceof DoublePt) { return x == ((DoublePt) p).x && y == ((DoublePt) p).y; } return false; } public int hashCode() { return boostHashCombine(main.hashCode(x), main.hashCode(y)); } public String toString() { return x + ", " + y; } double length() { return sqrt(x*x+y*y); } public double x_double() { return x; } public double y_double() { return y; } } interface IDoublePt { public double x_double(); public double y_double(); } static interface IFieldsToList { Object[] _fieldsToList(); } static String shortClassName_dropNumberPrefix(Object o) { return dropNumberPrefix(shortClassName(o)); } static int boostHashCombine(int a, int b) { return a ^ (b + 0x9e3779b9 + (a << 6) + (a >>> 2)); // OLD (changed) 2022/3/10: ret a ^ (b + 0x9e3779b9 + (a << 6) + (a >> 2)); } static int _hashCode(Object a) { return a == null ? 0 : a.hashCode(); } static int hashCode(Object a) { return a == null ? 0 : a.hashCode(); } static int hashCode(long l) { return Long.hashCode(l); } static int hashCode(double d) { return Double.hashCode(d); } static double sqrt(double x) { return Math.sqrt(x); } static String dropNumberPrefix(String s) { return dropFirst(s, indexOfNonDigit(s)); } static String shortClassName(Object o) { if (o == null) return null; Class c = o instanceof Class ? (Class) o : o.getClass(); String name = c.getName(); return shortenClassName(name); } static String[] dropFirst(int n, String[] a) { return drop(n, a); } static String[] dropFirst(String[] a) { return drop(1, a); } static Object[] dropFirst(Object[] a) { return drop(1, a); } static List dropFirst(List l) { return dropFirst(1, l); } static List dropFirst(int n, Iterable i) { return dropFirst(n, toList(i)); } static List dropFirst(Iterable i) { return dropFirst(toList(i)); } static List dropFirst(int n, List l) { return n <= 0 ? l : new ArrayList(l.subList(Math.min(n, l.size()), l.size())); } static List dropFirst(List l, int n) { return dropFirst(n, l); } static String dropFirst(int n, String s) { return substring(s, n); } static String dropFirst(String s, int n) { return substring(s, n); } static String dropFirst(String s) { return substring(s, 1); } static int indexOfNonDigit(String s) { int n = l(s); for (int i = 0; i < n; i++) if (!isDigit(s.charAt(i))) return i; return -1; } static String shortenClassName(String name) { if (name == null) return null; int i = lastIndexOf(name, "$"); if (i < 0) i = lastIndexOf(name, "."); return i < 0 ? name : substring(name, i+1); } static String[] drop(int n, String[] a) { n = Math.min(n, a.length); String[] b = new String[a.length-n]; System.arraycopy(a, n, b, 0, b.length); return b; } static Object[] drop(int n, Object[] a) { n = Math.min(n, a.length); Object[] b = new Object[a.length-n]; System.arraycopy(a, n, b, 0, b.length); return b; } static ArrayList toList(A[] a) { return asList(a); } static ArrayList toList(int[] a) { return asList(a); } static ArrayList toList(Set s) { return asList(s); } static ArrayList toList(Iterable s) { return asList(s); } static String substring(String s, int x) { return substring(s, x, strL(s)); } static String substring(String s, int x, int y) { if (s == null) return null; if (x < 0) x = 0; int n = s.length(); if (y < x) y = x; if (y > n) y = n; if (x >= y) return ""; return s.substring(x, y); } // convenience method for quickly dropping a prefix static String substring(String s, CharSequence l) { return substring(s, lCharSequence(l)); } 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 boolean isDigit(char c) { return Character.isDigit(c); } static int lastIndexOf(String a, String b) { return a == null || b == null ? -1 : a.lastIndexOf(b); } static int lastIndexOf(String a, char b) { return a == null ? -1 : a.lastIndexOf(b); } // starts searching from i-1 static int lastIndexOf(List l, int i, A a) { if (l == null) return -1; for (i = min(l(l), i)-1; i >= 0; i--) if (eq(l.get(i), a)) return i; return -1; } static int lastIndexOf(List l, A a) { if (l == null) return -1; for (int i = l(l)-1; i >= 0; i--) if (eq(l.get(i), a)) return i; return -1; } // unclear semantics as to whether return null on null static ArrayList asList(A[] a) { return a == null ? new ArrayList() : new ArrayList(Arrays.asList(a)); } static ArrayList asList(int[] a) { if (a == null) return null; ArrayList l = emptyList(a.length); for (int i : a) l.add(i); return l; } static ArrayList asList(long[] a) { if (a == null) return null; ArrayList l = emptyList(a.length); for (long i : a) l.add(i); return l; } static ArrayList asList(float[] a) { if (a == null) return null; ArrayList l = emptyList(a.length); for (float i : a) l.add(i); return l; } static ArrayList asList(double[] a) { if (a == null) return null; ArrayList l = emptyList(a.length); for (double i : a) l.add(i); return l; } static ArrayList asList(short[] a) { if (a == null) return null; ArrayList l = emptyList(a.length); for (short i : a) l.add(i); return l; } static ArrayList asList(Iterator it) { ArrayList l = new ArrayList(); if (it != null) while (it.hasNext()) l.add(it.next()); return l; } // disambiguation static ArrayList asList(IterableIterator s) { return asList((Iterator) s); } static ArrayList asList(Iterable s) { if (s instanceof ArrayList) return (ArrayList) s; ArrayList l = new ArrayList(); if (s != null) for (A a : s) l.add(a); return l; } static ArrayList asList(Enumeration e) { ArrayList l = new ArrayList(); if (e != null) while (e.hasMoreElements()) l.add(e.nextElement()); return l; } static int strL(String s) { return s == null ? 0 : s.length(); } static int lCharSequence(CharSequence s) { return s == null ? 0 : s.length(); } 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 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 boolean eq(Object a, Object b) { return a == b || a != null && b != null && a.equals(b); } static ArrayList emptyList() { return new ArrayList(); //ret Collections.emptyList(); } static ArrayList emptyList(int capacity) { return new ArrayList(max(0, capacity)); } // Try to match capacity static ArrayList emptyList(Iterable l) { return l instanceof Collection ? emptyList(((Collection) l).size()) : emptyList(); } static ArrayList emptyList(Object[] l) { return emptyList(l(l)); } // get correct type at once static ArrayList emptyList(Class c) { return new ArrayList(); } static List ll(A... a) { ArrayList l = new ArrayList(a.length); if (a != null) for (A x : a) l.add(x); return l; } 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 String str(Object o) { return o == null ? "null" : o.toString(); } static String str(char[] c) { return new String(c); } static String str(char[] c, int offset, int count) { return new String(c, offset, count); } 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 void _handleError(Error e) { //call(javax(), '_handleError, e); } 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 Iterator emptyIterator() { return Collections.emptyIterator(); } // you still need to implement hasNext() and next() static abstract class IterableIterator implements Iterator, Iterable { public Iterator iterator() { return this; } public void remove() { unsupportedOperation(); } } static UnsupportedOperationException unsupportedOperation() { throw new UnsupportedOperationException(); } }