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 class SynchronizedSet<E>
      extends SynchronizedCollection<E>
      implements Set<E> {
  SynchronizedSet() {}
    SynchronizedSet(Set<E> s) {
        super(s);
    }
    SynchronizedSet(Set<E> s, Object mutex) {
        super(s, mutex);
    }

    public boolean equals(Object o) {
        if (this == o)
            return true;
        synchronized (mutex) {return c.equals(o);}
    }
    public int hashCode() {
        synchronized (mutex) {return c.hashCode();}
    }
}
static class SynchronizedCollection<E> implements Collection<E>, Serializable {
  SynchronizedCollection() {}
    @java.io.Serial
    private static final long serialVersionUID = 3053995032091335093L;

    @SuppressWarnings("serial") // Conditionally serializable
    /*final*/ Collection<E> c;  // Backing Collection
    @SuppressWarnings("serial") // Conditionally serializable
    /*final*/ Object mutex;     // Object on which to synchronize

    SynchronizedCollection(Collection<E> c) {
        this.c = Objects.requireNonNull(c);
        mutex = this;
    }

    SynchronizedCollection(Collection<E> c, Object mutex) {
        this.c = Objects.requireNonNull(c);
        this.mutex = Objects.requireNonNull(mutex);
    }

    public int size() {
        synchronized (mutex) {return c.size();}
    }
    public boolean isEmpty() {
        synchronized (mutex) {return c.isEmpty();}
    }
    public boolean contains(Object o) {
        synchronized (mutex) {return c.contains(o);}
    }
    public Object[] toArray() {
        synchronized (mutex) {return c.toArray();}
    }
    public <T> T[] toArray(T[] a) {
        synchronized (mutex) {return c.toArray(a);}
    }
    public <T> T[] toArray(java.util.function.IntFunction<T[]> f) {
        synchronized (mutex) {return c.toArray(f);}
    }

    public Iterator<E> iterator() {
        return c.iterator(); // Must be manually synched by user!
    }

    public boolean add(E e) {
        synchronized (mutex) {return c.add(e);}
    }
    public boolean remove(Object o) {
        synchronized (mutex) {return c.remove(o);}
    }

    public boolean containsAll(Collection<?> coll) {
        synchronized (mutex) {return c.containsAll(coll);}
    }
    public boolean addAll(Collection<? extends E> coll) {
        synchronized (mutex) {return c.addAll(coll);}
    }
    public boolean removeAll(Collection<?> coll) {
        synchronized (mutex) {return c.removeAll(coll);}
    }
    public boolean retainAll(Collection<?> coll) {
        synchronized (mutex) {return c.retainAll(coll);}
    }
    public void clear() {
        synchronized (mutex) {c.clear();}
    }
    public String toString() {
        synchronized (mutex) {return c.toString();}
    }
    // Override default methods in Collection
    @Override
    public void forEach(java.util.function.Consumer<? super E> consumer) {
        synchronized (mutex) {c.forEach(consumer);}
    }
    @Override
    public boolean removeIf(java.util.function.Predicate<? super E> filter) {
        synchronized (mutex) {return c.removeIf(filter);}
    }
    @Override
    public Spliterator<E> spliterator() {
        return c.spliterator(); // Must be manually synched by user!
    }
    @Override
    public java.util.stream.Stream<E> stream() {
        return c.stream(); // Must be manually synched by user!
    }
    @Override
    public java.util.stream.Stream<E> parallelStream() {
        return c.parallelStream(); // Must be manually synched by user!
    }
    @java.io.Serial
    private void writeObject(ObjectOutputStream s) throws IOException {
        synchronized (mutex) {s.defaultWriteObject();}
    }
}


static <A> Iterator<A> iterator(Iterable<A> c) {
  return c == null ? emptyIterator() : c.iterator();
}



static Iterator emptyIterator() {
  return Collections.emptyIterator();
}


}