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 Steppable iteratorToSteppable(Iterator it) {
  return it == null ? null : new Steppable() {
    public boolean step() {
      if (!it.hasNext()) return false;
      it.next();
      return true;
    }
  };
}
// Note for implementors: It is allowed to call step() again
// after it returned false (usually it should just return false again)
static interface Steppable {
  public boolean step(); // return false if done
}

}