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; import java.lang.invoke.VarHandle; import java.lang.invoke.MethodHandles; class main { static Pt ptFromPixelIndex(int index, int w) { return pt(index % w, index / w); } static Pt pt(int x, int y) { return new Pt(x, y); } static Pt pt(int x) { return new Pt(x, x); } static class Pt implements Comparable, IDoublePt { 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; } double length() { return sqrt(x*x+y*y); } public Pt minus(Pt p) { return ptMinus(this, p); } public double x_double() { return x; } public double y_double() { return y; } } interface IDoublePt { public double x_double(); public double y_double(); } 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 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 double sqrt(double x) { return Math.sqrt(x); } static Pt ptMinus(Pt a, Pt b) { if (b == null) return a; return new Pt(a.x-b.x, a.y-b.y); } }