/*
 * Copyright (C) 2002-2022 Sebastiano Vigna
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */


package PACKAGE;

import java.util.Collection;
import java.util.Comparator;
import java.util.Iterator;
import java.util.SortedSet;
import java.util.NoSuchElementException;

/** A type-specific AVL tree set with a fast, small-footprint implementation.
 *
 * <p>The iterators provided by this class are type-specific {@link
 * it.unimi.dsi.fastutil.BidirectionalIterator bidirectional iterators}.
 * Moreover, the iterator returned by {@code iterator()} can be safely cast
 * to a type-specific {@linkplain java.util.ListIterator list iterator}.
 */

public class AVL_TREE_SET KEY_GENERIC extends ABSTRACT_SORTED_SET KEY_GENERIC implements java.io.Serializable, Cloneable, SORTED_SET KEY_GENERIC {

	/** A reference to the root entry. */
	protected transient Entry KEY_GENERIC tree;

	/** Number of elements in this set. */
	protected int count;

	/** The entry of the first element of this set. */
	protected transient Entry KEY_GENERIC firstEntry;

	/** The entry of the last element of this set. */
	protected transient Entry KEY_GENERIC lastEntry;

	/** This set's comparator, as provided in the constructor. */
	protected Comparator<? super KEY_GENERIC_CLASS> storedComparator;

	/** This set's actual comparator; it may differ from {@link #storedComparator} because it is
		always a type-specific comparator, so it could be derived from the former by wrapping. */
	protected transient KEY_COMPARATOR KEY_SUPER_GENERIC actualComparator;

	private static final long serialVersionUID = -7046029254386353130L;

	{
		allocatePaths();
	}

	/** Creates a new empty tree set.
	 */

	public AVL_TREE_SET() {
		tree = null;
		count = 0;
	}

	/** Generates the comparator that will be actually used.
	 *
	 * <p>When a given {@link Comparator} is specified and stored in {@link
	 * #storedComparator}, we must check whether it is type-specific.  If it is
	 * so, we can used directly, and we store it in {@link #actualComparator}. Otherwise,
	 * we adapt it using a helper static method.
	 */
	private void setActualComparator() {
#if KEY_CLASS_Object
		actualComparator = storedComparator;
#else
		actualComparator = COMPARATORS.AS_KEY_COMPARATOR(storedComparator);
#endif
	}


	/** Creates a new empty tree set with the given comparator.
	 *
	 * @param c a {@link Comparator} (even better, a type-specific comparator).
	 */

	public AVL_TREE_SET(final Comparator<? super KEY_GENERIC_CLASS> c) {
		this();
		storedComparator = c;
		setActualComparator();
	}


	/** Creates a new tree set copying a given set.
	 *
	 * @param c a collection to be copied into the new tree set.
	 */

	public AVL_TREE_SET(final Collection<? extends KEY_GENERIC_CLASS> c) {
		this();
		addAll(c);
	}

	/** Creates a new tree set copying a given sorted set (and its {@link Comparator}).
	 *
	 * @param s a {@link SortedSet} to be copied into the new tree set.
	 */

	public AVL_TREE_SET(final SortedSet <KEY_GENERIC_CLASS> s) {
		this(s.comparator());
		addAll(s);
	}

	/** Creates a new tree set copying a given type-specific collection.
	 *
	 * @param c a type-specific collection to be copied into the new tree set.
	 */

	public AVL_TREE_SET(final COLLECTION KEY_EXTENDS_GENERIC c) {
		this();
		addAll(c);
	}

	/** Creates a new tree set copying a given type-specific sorted set (and its {@link Comparator}).
	 *
	 * @param s a type-specific sorted set to be copied into the new tree set.
	 */

	public AVL_TREE_SET(final SORTED_SET KEY_GENERIC s) {
		this(s.comparator());
		addAll(s);
	}


	/** Creates a new tree set using elements provided by a type-specific iterator.
	 *
	 * @param i a type-specific iterator whose elements will fill the set.
	 */

	public AVL_TREE_SET(final STD_KEY_ITERATOR KEY_EXTENDS_GENERIC i) {
		while(i.hasNext()) add(i.NEXT_KEY());
	}

#if KEYS_PRIMITIVE

	/** Creates a new tree set using elements provided by an iterator.
	 *
	 * @param i an iterator whose elements will fill the set.
	 */

	SUPPRESS_WARNINGS_KEY_UNCHECKED
	public AVL_TREE_SET(final Iterator<?> i) {
		this(ITERATORS.AS_KEY_ITERATOR(i));
	}

#endif

	/** Creates a new tree set and fills it with the elements of a given array using a given {@link Comparator}.
	 *
	 * @param a an array whose elements will be used to fill the set.
	 * @param offset the first element to use.
	 * @param length the number of elements to use.
	 * @param c a {@link Comparator} (even better, a type-specific comparator).
	 */

	public AVL_TREE_SET(final KEY_GENERIC_TYPE[] a, final int offset, final int length, final Comparator<? super KEY_GENERIC_CLASS> c) {
		this(c);
		ARRAYS.ensureOffsetLength(a, offset, length);
		for(int i = 0; i < length; i++) add(a[offset + i]);
	}


	/** Creates a new tree set and fills it with the elements of a given array.
	 *
	 * @param a an array whose elements will be used to fill the set.
	 * @param offset the first element to use.
	 * @param length the number of elements to use.
	 */

	public AVL_TREE_SET(final KEY_GENERIC_TYPE[] a, final int offset, final int length) {
		this(a, offset, length, null);
	}


	/** Creates a new tree set copying the elements of an array.
	 *
	 * @param a an array to be copied into the new tree set.
	 */

	public AVL_TREE_SET(final KEY_GENERIC_TYPE[] a) {
		this();
		int i = a.length;
		while(i-- != 0) add(a[i]);
	}


	/** Creates a new tree set copying the elements of an array using a given {@link Comparator}.
	 *
	 * @param a an array to be copied into the new tree set.
	 * @param c a {@link Comparator} (even better, a type-specific comparator).
	 */

	public AVL_TREE_SET(final KEY_GENERIC_TYPE[] a, final Comparator<? super KEY_GENERIC_CLASS> c) {
		this(c);
		int i = a.length;
		while(i-- != 0) add(a[i]);
	}




	/*
	 * The following methods implements some basic building blocks used by
	 * all accessors.  They are (and should be maintained) identical to those used in AVLTreeMap.drv.
	 *
	 * The add()/remove() code is derived from Ben Pfaff's GNU libavl
	 * (https://adtinfo.org/). If you want to understand what's
	 * going on, you should have a look at the literate code contained therein
	 * first.
	 */


	/** Compares two keys in the right way.
	 *
	 * <p>This method uses the {@link #actualComparator} if it is non-{@code null}.
	 * Otherwise, it resorts to primitive type comparisons or to {@link Comparable#compareTo(Object) compareTo()}.
	 *
	 * @param k1 the first key.
	 * @param k2 the second key.
	 * @return a number smaller than, equal to or greater than 0, as usual
	 * (i.e., when k1 &lt; k2, k1 = k2 or k1 &gt; k2, respectively).
	 */

	SUPPRESS_WARNINGS_KEY_UNCHECKED
	final int compare(final KEY_GENERIC_TYPE k1, final KEY_GENERIC_TYPE k2) {
		return actualComparator == null ? KEY_CMP(k1, k2) : actualComparator.compare(k1, k2);
	}



	/** Returns the entry corresponding to the given key, if it is in the tree; {@code null}, otherwise.
	 *
	 * @param k the key to search for.
	 * @return the corresponding entry, or {@code null} if no entry with the given key exists.
	 */

	private Entry KEY_GENERIC findKey(final KEY_GENERIC_TYPE k) {
		Entry KEY_GENERIC e = tree;
		int cmp;

		while (e != null && (cmp = compare(k, e.key)) != 0)
			e = cmp < 0 ? e.left() : e.right();

		return e;
	}

	/** Locates a key.
	 *
	 * @param k a key.
	 * @return the last entry on a search for the given key; this will be
	 * the given key, if it present; otherwise, it will be either the smallest greater key or the greatest smaller key.
	 */

	final Entry KEY_GENERIC locateKey(final KEY_GENERIC_TYPE k) {
		Entry KEY_GENERIC e = tree, last = tree;
		int cmp = 0;

		while (e != null && (cmp = compare(k, e.key)) != 0) {
			last = e;
			e = cmp < 0 ? e.left() : e.right();
		}

		return cmp == 0 ? e : last;
	}


	/** This vector remembers the path followed during the current insertion. It suffices for
		about 2<sup>32</sup> entries. */
	private transient boolean dirPath[];

	private void allocatePaths() {
		dirPath = new boolean[48];
	}


	@Override
	public boolean add(final KEY_GENERIC_TYPE k) {
		REQUIRE_KEY_NON_NULL(k)

		if (tree == null) { // The case of the empty tree is treated separately.
			count++;
			tree = lastEntry = firstEntry = new Entry KEY_GENERIC_DIAMOND(k);
		}
		else {
			Entry KEY_GENERIC p = tree, q = null, y = tree, z = null, e = null, w = null;
			int cmp, i = 0;

			while(true) {
				if ((cmp = compare(k, p.key)) == 0) return false;

				if (p.balance() != 0) {
					i = 0;
					z = q;
					y = p;
				}

				if (dirPath[i++] = cmp > 0) {
					if (p.succ()) {
						count++;
						e = new Entry KEY_GENERIC_DIAMOND(k);

						if (p.right == null) lastEntry = e;

						e.left = p;
						e.right = p.right;

						p.right(e);

						break;
					}

					q = p;
					p = p.right;
				}
				else {
					if (p.pred()) {
						count++;
						e = new Entry KEY_GENERIC_DIAMOND(k);

						if (p.left == null) firstEntry = e;

						e.right = p;
						e.left = p.left;

						p.left(e);

						break;
					}

					q = p;
					p = p.left;
				}
			}

			p = y;
			i = 0;

			while(p != e) {
				if (dirPath[i]) p.incBalance();
				else p.decBalance();

				p = dirPath[i++] ? p.right : p.left;
			}

			if (y.balance() == -2) {
				Entry KEY_GENERIC x = y.left;

				if (x.balance() == -1) {
					w = x;
					if (x.succ()) {
						x.succ(false);
						y.pred(x);
					}
					else y.left = x.right;

					x.right = y;
					x.balance(0);
					y.balance(0);
				}
				else {
					assert x.balance() == 1;

					w = x.right;
					x.right = w.left;
					w.left = x;
					y.left = w.right;
					w.right = y;
					if (w.balance() == -1) {
						x.balance(0);
						y.balance(1);
					}
					else if (w.balance() == 0) {
						x.balance(0);
						y.balance(0);
					}
					else {
						x.balance(-1);
						y.balance(0);
					}
					w.balance(0);


					if (w.pred()) {
						x.succ(w);
						w.pred(false);
					}
					if (w.succ()) {
						y.pred(w);
						w.succ(false);
					}

				}
			}
			else if (y.balance() == +2) {
				Entry KEY_GENERIC x = y.right;

				if (x.balance() == 1) {
					w = x;
					if (x.pred()) {
						x.pred(false);
						y.succ(x);
					}
					else y.right = x.left;

					x.left = y;
					x.balance(0);
					y.balance(0);
				}
				else {
					assert x.balance() == -1;

					w = x.left;
					x.left = w.right;
					w.right = x;
					y.right = w.left;
					w.left = y;
					if (w.balance() == 1) {
						x.balance(0);
						y.balance(-1);
					}
					else if (w.balance() == 0) {
						x.balance(0);
						y.balance(0);
					}
					else {
						x.balance(1);
						y.balance(0);
					}
					w.balance(0);


					if (w.pred()) {
						y.succ(w);
						w.pred(false);
					}
					if (w.succ()) {
						x.pred(w);
						w.succ(false);
					}

				}
			}
			else return true;

			if (z == null) tree = w;
			else {
				if (z.left == y) z.left = w;
				else z.right = w;
			}
		}

		return true;
	}




	/** Finds the parent of an entry.
	 *
	 * @param e a node of the tree.
	 * @return the parent of the given node, or {@code null} for the root.
	 */

	private Entry KEY_GENERIC parent(final Entry KEY_GENERIC e) {
		if (e == tree) return null;

		Entry KEY_GENERIC x, y, p;
		x = y = e;

		while(true) {
			if (y.succ()) {
				p = y.right;
				if (p == null || p.left != e) {
					while(! x.pred()) x = x.left;
					p = x.left;
				}
				return p;
			}
			else if (x.pred()) {
				p = x.left;
				if (p == null || p.right != e) {
					while(! y.succ()) y = y.right;
					p = y.right;
				}
				return p;
			}

			x = x.left;
			y = y.right;
		}
	}


	SUPPRESS_WARNINGS_KEY_UNCHECKED
	@Override
	public boolean remove(final KEY_TYPE k) {
		if (tree == null) return false;

		int cmp;
		Entry KEY_GENERIC p = tree, q = null;
		boolean dir = false;
		final KEY_GENERIC_TYPE kk = KEY_GENERIC_CAST k;

		while(true) {
			if ((cmp = compare(kk, p.key)) == 0) break;
			else if (dir = cmp > 0) {
				q = p;
				if ((p = p.right()) == null) return false;
			}
			else {
				q = p;
				if ((p = p.left()) == null) return false;
			}
		}

		if (p.left == null) firstEntry = p.next();
		if (p.right == null) lastEntry = p.prev();

		if (p.succ()) {
			if (p.pred()) {
				if (q != null) {
					if (dir) q.succ(p.right);
					else q.pred(p.left);
				}
				else tree = dir ? p.right : p.left;
			}
			else {
				p.prev().right = p.right;

				if (q != null) {
					if (dir) q.right = p.left;
					else q.left = p.left;
				}
				else tree = p.left;
			}
		}
		else {
			Entry KEY_GENERIC r = p.right;

			if (r.pred()) {
				r.left = p.left;
				r.pred(p.pred());
				if (! r.pred()) r.prev().right = r;
				if (q != null) {
					if (dir) q.right = r;
					else q.left = r;
				}
				else tree = r;

				r.balance(p.balance());
				q = r;
				dir = true;

			}
			else {
				Entry KEY_GENERIC s;

				while(true) {
					s = r.left;
					if (s.pred()) break;
					r = s;
				}

				if (s.succ()) r.pred(s);
				else r.left = s.right;

				s.left = p.left;

				if (! p.pred()) {
					p.prev().right = s;
					s.pred(false);
				}

				s.right = p.right;
				s.succ(false);

				if (q != null) {
					if (dir) q.right = s;
					else q.left = s;
				}
				else tree = s;

				s.balance(p.balance());
				q = r;
				dir = false;
			}
		}

		Entry KEY_GENERIC y;

		while(q != null) {
			y = q;
			q = parent(y);

			if (! dir) {
				dir = q != null && q.left != y;
				y.incBalance();

				if (y.balance() == 1) break;
				else if (y.balance() == 2) {

					Entry KEY_GENERIC x = y.right;
					assert x != null;

					if (x.balance() == -1) {
						Entry KEY_GENERIC w;

						assert x.balance() == -1;

						w = x.left;
						x.left = w.right;
						w.right = x;
						y.right = w.left;
						w.left = y;

						if (w.balance() == 1) {
							x.balance(0);
							y.balance(-1);
						}
						else if (w.balance() == 0) {
							x.balance(0);
							y.balance(0);
						}
						else {
							assert w.balance() == -1;

							x.balance(1);
							y.balance(0);
						}

						w.balance(0);

						if (w.pred()) {
							y.succ(w);
							w.pred(false);
						}
						if (w.succ()) {
							x.pred(w);
							w.succ(false);
						}

						if (q != null) {
							if (dir) q.right = w;
							else q.left = w;
						}
						else tree = w;
					}
					else {
						if (q != null) {
							if (dir) q.right = x;
							else q.left = x;
						}
						else tree = x;

						if (x.balance() == 0) {
							y.right = x.left;
							x.left = y;
							x.balance(-1);
							y.balance(+1);
							break;
						}

						assert x.balance() == 1;

						if (x.pred()) {
							y.succ(true);
							x.pred(false);
						}
						else y.right = x.left;

						x.left = y;
						y.balance(0);
						x.balance(0);
					}
				}
			}
			else {
				dir = q != null && q.left != y;
				y.decBalance();

				if (y.balance() == -1) break;
				else if (y.balance() == -2) {

					Entry KEY_GENERIC x = y.left;
					assert x != null;

					if (x.balance() == 1) {
						Entry KEY_GENERIC w;

						assert x.balance() == 1;

						w = x.right;
						x.right = w.left;
						w.left = x;
						y.left = w.right;
						w.right = y;

						if (w.balance() == -1) {
							x.balance(0);
							y.balance(1);
						}
						else if (w.balance() == 0) {
							x.balance(0);
							y.balance(0);
						}
						else {
							assert w.balance() == 1;

							x.balance(-1);
							y.balance(0);
						}

						w.balance(0);

						if (w.pred()) {
							x.succ(w);
							w.pred(false);
						}
						if (w.succ()) {
							y.pred(w);
							w.succ(false);
						}

						if (q != null) {
							if (dir) q.right = w;
							else q.left = w;
						}
						else tree = w;
					}
					else {
						if (q != null) {
							if (dir) q.right = x;
							else q.left = x;
						}
						else tree = x;

						if (x.balance() == 0) {
							y.left = x.right;
							x.right = y;
							x.balance(+1);
							y.balance(-1);
							break;
						}

						assert x.balance() == -1;

						if (x.succ()) {
							y.pred(true);
							x.succ(false);
						}
						else y.left = x.right;

						x.right = y;
						y.balance(0);
						x.balance(0);
					}
				}
			}
		}

		count--;
		return true;
	}

	SUPPRESS_WARNINGS_KEY_UNCHECKED
	@Override
	public boolean contains(final KEY_TYPE k) {
		return findKey(KEY_GENERIC_CAST k) != null;
	}

#if KEY_CLASS_Object
	SUPPRESS_WARNINGS_KEY_UNCHECKED
	public K get(final KEY_TYPE k) {
		final Entry KEY_GENERIC entry = findKey(KEY_GENERIC_CAST k);
		return entry == null ? null : entry.key;
	}
#endif

	@Override
	public void clear() {
		count = 0;
		tree = null;
		firstEntry = lastEntry = null;
	}


	/** This class represent an entry in a tree set.
	 *
	 * <p>We use the only "metadata", i.e., {@link Entry#info}, to store
	 * information about balance, predecessor status and successor status.
	 *
	 * <p>Note that since the class is recursive, it can be
	 * considered equivalently a tree.
	 */

	private static final class Entry KEY_GENERIC implements Cloneable {
		/** If the bit in this mask is true, {@link #right} points to a successor. */
		private static final int SUCC_MASK = 1 << 31;
		/** If the bit in this mask is true, {@link #left} points to a predecessor. */
		private static final int PRED_MASK = 1 << 30;
		/** The bits in this mask hold the node balance info. You can get it just by casting to byte. */
		private static final int BALANCE_MASK = 0xFF;
		/** The key of this entry. */
		KEY_GENERIC_TYPE key;
		/** The pointers to the left and right subtrees. */
		Entry KEY_GENERIC left, right;
		/** This integers holds different information in different bits (see {@link #SUCC_MASK}, {@link #PRED_MASK} and {@link #BALANCE_MASK}). */
		int info;

		Entry() {}

		/** Creates a new entry with the given key.
		 *
		 * @param k a key.
		 */
		Entry(final KEY_GENERIC_TYPE k) {
			this.key = k;
			info = SUCC_MASK | PRED_MASK;
		}

		/** Returns the left subtree.
		 *
		 * @return the left subtree ({@code null} if the left
		 * subtree is empty).
		 */
		Entry KEY_GENERIC left() {
			return (info & PRED_MASK) != 0 ? null : left;
		}

		/** Returns the right subtree.
		 *
		 * @return the right subtree ({@code null} if the right
		 * subtree is empty).
		 */
		Entry KEY_GENERIC right() {
			return (info & SUCC_MASK) != 0 ? null : right;
		}

		/** Checks whether the left pointer is really a predecessor.
		 * @return true if the left pointer is a predecessor.
		 */
		boolean pred() {
			return (info & PRED_MASK) != 0;
		}

		/** Checks whether the right pointer is really a successor.
		 * @return true if the right pointer is a successor.
		 */
		boolean succ() {
			return (info & SUCC_MASK) != 0;
		}

		/** Sets whether the left pointer is really a predecessor.
		 * @param pred if true then the left pointer will be considered a predecessor.
		 */
		void pred(final boolean pred) {
			if (pred) info |= PRED_MASK;
			else info &= ~PRED_MASK;
		}

		/** Sets whether the right pointer is really a successor.
		 * @param succ if true then the right pointer will be considered a successor.
		 */
		void succ(final boolean succ) {
			if (succ) info |= SUCC_MASK;
			else info &= ~SUCC_MASK;
		}

		/** Sets the left pointer to a predecessor.
		 * @param pred the predecessr.
		 */
		void pred(final Entry KEY_GENERIC pred) {
			info |= PRED_MASK;
			left = pred;
		}

		/** Sets the right pointer to a successor.
		 * @param succ the successor.
		 */
		void succ(final Entry KEY_GENERIC succ) {
			info |= SUCC_MASK;
			right = succ;
		}

		/** Sets the left pointer to the given subtree.
		 * @param left the new left subtree.
		 */
		void left(final Entry KEY_GENERIC left) {
			info &= ~PRED_MASK;
			this.left = left;
		}

		/** Sets the right pointer to the given subtree.
		 * @param right the new right subtree.
		 */
		void right(final Entry KEY_GENERIC right) {
			info &= ~SUCC_MASK;
			this.right = right;
		}

		/** Returns the current level of the node.
		 * @return the current level of this node.
		 */
		int balance() {
			return (byte)info;
		}

		/** Sets the level of this node.
		 * @param level the new level of this node.
		 */
		void balance(int level) {
			info &= ~BALANCE_MASK;
			info |= (level & BALANCE_MASK);
		}

		/** Increments the level of this node. */
		void incBalance() {
			info = info & ~BALANCE_MASK | ((byte)info + 1) & 0xFF;
		}

		/** Decrements the level of this node. */
		protected	void decBalance() {
			info = info & ~BALANCE_MASK | ((byte)info - 1) & 0xFF;
		}

		/** Computes the next entry in the set order.
		 *
		 * @return the next entry ({@code null}) if this is the last entry).
		 */

		Entry KEY_GENERIC next() {
			Entry KEY_GENERIC next = this.right;
			if ((info & SUCC_MASK) == 0) while ((next.info & PRED_MASK) == 0) next = next.left;
			return next;
		}

		/** Computes the previous entry in the set order.
		 *
		 * @return the previous entry ({@code null}) if this is the first entry).
		 */

		Entry KEY_GENERIC prev() {
			Entry KEY_GENERIC prev = this.left;
			if ((info & PRED_MASK) == 0) while ((prev.info & SUCC_MASK) == 0) prev = prev.right;
			return prev;
		}

		@Override
		SUPPRESS_WARNINGS_KEY_UNCHECKED
		public Entry KEY_GENERIC clone() {
			Entry KEY_GENERIC c;
			try {
				c = (Entry KEY_GENERIC)super.clone();
			}
			catch(CloneNotSupportedException cantHappen) {
				throw new InternalError();
			}

			c.key = key;
			c.info = info;

			return c;
		}

		@Override
		public boolean equals(final Object o) {
			if (!(o instanceof Entry)) return false;
			Entry KEY_GENERIC_WILDCARD e = (Entry KEY_GENERIC_WILDCARD)o;

			return KEY_EQUALS(key, e.key);
		}

		@Override
		public int hashCode() {
			return KEY2JAVAHASH_NOT_NULL(key);
		}

		@Override
		public String toString() {
			return String.valueOf(key);
		}

		/*
		  public void prettyPrint() {
		  prettyPrint(0);
		  }

		  public void prettyPrint(int level) {
		  if (pred()) {
		  for (int i = 0; i < level; i++)
		  System.err.print("  ");
		  System.err.println("pred: " + left);
		  }
		  else if (left != null)
		  left.prettyPrint(level +1);
		  for (int i = 0; i < level; i++)
		  System.err.print("  ");
		  System.err.println(key + " (" + level() + ")");
		  if (succ()) {
		  for (int i = 0; i < level; i++)
		  System.err.print("  ");
		  System.err.println("succ: " + right);
		  }
		  else if (right != null)
		  right.prettyPrint(level + 1);
		  }
		*/
	}

	/*
	  public void prettyPrint() {
	  System.err.println("size: " + count);
	  if (tree != null) tree.prettyPrint();
	  }
	*/

	@Override
	public int size() {
		return count;
	}

	@Override
	public boolean isEmpty() {
		return count == 0;
	}

	@Override
	public KEY_GENERIC_TYPE FIRST() {
		if (tree == null) throw new NoSuchElementException();
		return firstEntry.key;
	}

	@Override
	public KEY_GENERIC_TYPE LAST() {
		if (tree == null) throw new NoSuchElementException();
		return lastEntry.key;
	}


	/** An iterator on the whole range.
	 *
	 * <p>This class can iterate in both directions on a threaded tree.
	 */

	private class SetIterator implements KEY_LIST_ITERATOR KEY_GENERIC {
		/** The entry that will be returned by the next call to {@link java.util.ListIterator#previous()} (or {@code null} if no previous entry exists). */
		Entry KEY_GENERIC prev;
		/** The entry that will be returned by the next call to {@link java.util.ListIterator#next()} (or {@code null} if no next entry exists). */
		Entry KEY_GENERIC next;
		/** The last entry that was returned (or {@code null} if we did not iterate or used {@link #remove()}). */
		Entry KEY_GENERIC curr;
		/** The current index (in the sense of a {@link java.util.ListIterator}). Note that this value is not meaningful when this {@link SetIterator} has been created using the nonempty constructor.*/
		int index = 0;

		SetIterator() {
			next = firstEntry;
		}

		SetIterator(final KEY_GENERIC_TYPE k) {
			if ((next = locateKey(k)) != null) {
				if (compare(next.key, k) <= 0) {
					prev = next;
					next = next.next();
				}
				else prev = next.prev();
			}
		}

		@Override
		public boolean hasNext() { return next != null; }
		@Override
		public boolean hasPrevious() { return prev != null; }

		void updateNext() { next = next.next(); }

		Entry KEY_GENERIC nextEntry() {
			if (! hasNext()) throw new NoSuchElementException();
			curr = prev = next;
			index++;
			updateNext();
			return curr;
		}

		@Override
		public KEY_GENERIC_TYPE NEXT_KEY() { return nextEntry().key; }
		@Override
		public KEY_GENERIC_TYPE PREV_KEY() { return previousEntry().key; }

		void updatePrevious() { prev = prev.prev(); }

		Entry KEY_GENERIC previousEntry() {
			if (! hasPrevious()) throw new NoSuchElementException();
			curr = next = prev;
			index--;
			updatePrevious();
			return curr;
		}

		@Override
		public int nextIndex() { return index; }

		@Override
		public int previousIndex() { return index - 1; }

		@Override
		public void remove() {
			if (curr == null) throw new IllegalStateException();
			/* If the last operation was a next(), we are removing an entry that preceeds
			   the current index, and thus we must decrement it. */
			if (curr == prev) index--;
			next = prev = curr;
			updatePrevious();
			updateNext();
			AVL_TREE_SET.this.remove(curr.key);
			curr = null;
		}
	}

	@Override
	public KEY_BIDI_ITERATOR KEY_GENERIC iterator() { return new SetIterator(); }

	@Override
	public KEY_BIDI_ITERATOR KEY_GENERIC iterator(final KEY_GENERIC_TYPE from) { return new SetIterator(from); }

	@Override
	public KEY_COMPARATOR KEY_SUPER_GENERIC comparator() { return actualComparator; }

	@Override
	public SORTED_SET KEY_GENERIC headSet(final KEY_GENERIC_TYPE to) { return new Subset(KEY_NULL, true, to, false); }

	@Override
	public SORTED_SET KEY_GENERIC tailSet(final KEY_GENERIC_TYPE from) { return new Subset(from, false, KEY_NULL, true); }

	@Override
	public SORTED_SET KEY_GENERIC subSet(final KEY_GENERIC_TYPE from, final KEY_GENERIC_TYPE to) { return new Subset(from, false, to, false); }

	/** A subset with given range.
	 *
	 * <p>This class represents a subset. One has to specify the left/right
	 * limits (which can be set to -&infin; or &infin;). Since the subset is a
	 * view on the set, at a given moment it could happen that the limits of
	 * the range are not any longer in the main set. Thus, things such as
	 * {@link java.util.SortedSet#first()} or {@link java.util.SortedSet#size()} must be always computed
	 * on-the-fly.
	 */
	private final class Subset extends ABSTRACT_SORTED_SET KEY_GENERIC implements java.io.Serializable, SORTED_SET KEY_GENERIC {
		private static final long serialVersionUID = -7046029254386353129L;

		/** The start of the subset range, unless {@link #bottom} is true. */
		KEY_GENERIC_TYPE from;
		/** The end of the subset range, unless {@link #top} is true. */
		KEY_GENERIC_TYPE to;
		/** If true, the subset range starts from -&infin;. */
		boolean bottom;
		/** If true, the subset range goes to &infin;. */
		boolean top;

		/** Creates a new subset with given key range.
		 *
		 * @param from the start of the subset range.
		 * @param bottom if true, the first parameter is ignored and the range starts from -&infin;.
		 * @param to the end of the subset range.
		 * @param top if true, the third parameter is ignored and the range goes to &infin;.
		 */
		public Subset(final KEY_GENERIC_TYPE from, final boolean bottom, final KEY_GENERIC_TYPE to, final boolean top) {
			if (! bottom && ! top && AVL_TREE_SET.this.compare(from, to) > 0) throw new IllegalArgumentException("Start element (" + from  + ") is larger than end element (" + to + ")");

			this.from = from;
			this.bottom = bottom;
			this.to = to;
			this.top = top;
		}

		@Override
		public void clear() {
			final SubsetIterator i = new SubsetIterator();
			while(i.hasNext()) {
				i.NEXT_KEY();
				i.remove();
			}
		}

		/** Checks whether a key is in the subset range.
		 * @param k a key.
		 * @return true if is the key is in the subset range.
		 */
		final boolean in(final KEY_GENERIC_TYPE k) {
			return (bottom || AVL_TREE_SET.this.compare(k, from) >= 0) &&
				(top || AVL_TREE_SET.this.compare(k, to) < 0);
		}

		SUPPRESS_WARNINGS_KEY_UNCHECKED
		@Override
		public boolean contains(final KEY_TYPE k) {
			return in(KEY_GENERIC_CAST k) && AVL_TREE_SET.this.contains(k);
		}

		@Override
		public boolean add(final KEY_GENERIC_TYPE  k) {
			if (! in(k)) throw new IllegalArgumentException("Element (" + k + ") out of range [" + (bottom ? "-" : String.valueOf(from)) + ", " + (top ? "-" : String.valueOf(to)) + ")");
			return AVL_TREE_SET.this.add(k);
		}

		SUPPRESS_WARNINGS_KEY_UNCHECKED
		@Override
		public boolean remove(final KEY_TYPE k) {
			if (! in(KEY_GENERIC_CAST k)) return false;
			return AVL_TREE_SET.this.remove(k);
		}

		@Override
		public int size() {
			final SubsetIterator i = new SubsetIterator();
			int n = 0;

			while(i.hasNext()) {
				n++;
				i.NEXT_KEY();
			}

			return n;
		}

		@Override
		public boolean isEmpty() { return ! new SubsetIterator().hasNext(); }

		@Override
		public KEY_COMPARATOR KEY_SUPER_GENERIC comparator() { return actualComparator; }

		@Override
		public KEY_BIDI_ITERATOR KEY_GENERIC iterator() { return new SubsetIterator(); }

		@Override
		public KEY_BIDI_ITERATOR KEY_GENERIC iterator(final KEY_GENERIC_TYPE from) { return new SubsetIterator(from); }

		@Override
		public SORTED_SET KEY_GENERIC headSet(final KEY_GENERIC_TYPE to) {
			if (top) return new Subset(from, bottom, to, false);
			return compare(to, this.to) < 0 ? new Subset(from, bottom, to, false) : this;
		}

		@Override
		public SORTED_SET KEY_GENERIC tailSet(final KEY_GENERIC_TYPE from) {
			if (bottom) return new Subset(from, false, to, top);
			return compare(from, this.from) > 0 ? new Subset(from, false, to, top) : this;
		}

		@Override
		public SORTED_SET KEY_GENERIC subSet(KEY_GENERIC_TYPE from, KEY_GENERIC_TYPE to) {
			if (top && bottom) return new Subset(from, false, to, false);
			if (! top) to = compare(to, this.to) < 0 ? to : this.to;
			if (! bottom) from = compare(from, this.from) > 0 ? from : this.from;
		    if (! top && ! bottom && from == this.from && to == this.to) return this;
			return new Subset(from, false, to, false);
		}

		/** Locates the first entry.
		 *
		 * @return the first entry of this subset, or {@code null} if the subset is empty.
		 */
		public AVL_TREE_SET.Entry KEY_GENERIC firstEntry() {
			if (tree == null) return null;
			// If this subset goes to -infinity, we return the main set first entry; otherwise, we locate the start of the set.
			AVL_TREE_SET.Entry KEY_GENERIC e;
			if (bottom) e = firstEntry;
			else {
				e = locateKey(from);
				// If we find either the start or something greater we're OK.
				if (compare(e.key, from) < 0) e = e.next();
			}
			// Finally, if this subset doesn't go to infinity, we check that the resulting key isn't greater than the end.
			if (e == null || ! top && compare(e.key, to) >= 0) return null;
			return e;
		}

		/** Locates the last entry.
		 *
		 * @return the last entry of this subset, or {@code null} if the subset is empty.
		 */
		public AVL_TREE_SET.Entry KEY_GENERIC lastEntry() {
			if (tree == null) return null;
			// If this subset goes to infinity, we return the main set last entry; otherwise, we locate the end of the set.
			AVL_TREE_SET.Entry KEY_GENERIC e;
			if (top) e = lastEntry;
			else {
				e = locateKey(to);
				// If we find something smaller than the end we're OK.
				if (compare(e.key, to) >= 0) e = e.prev();
			}
			// Finally, if this subset doesn't go to -infinity, we check that the resulting key isn't smaller than the start.
			if (e == null || ! bottom && compare(e.key, from) < 0) return null;
			return e;
		}

		@Override
		public KEY_GENERIC_TYPE FIRST() {
			AVL_TREE_SET.Entry KEY_GENERIC e = firstEntry();
			if (e == null) throw new NoSuchElementException();
			return e.key;
		}

		@Override
		public KEY_GENERIC_TYPE LAST() {
			AVL_TREE_SET.Entry KEY_GENERIC e = lastEntry();
			if (e == null) throw new NoSuchElementException();
			return e.key;
		}

		/** An iterator for subranges.
		 *
		 * <p>This class inherits from {@link SetIterator}, but overrides the methods that
		 * update the pointer after a {@link java.util.ListIterator#next()} or {@link java.util.ListIterator#previous()}. If we would
		 * move out of the range of the subset we just overwrite the next or previous
		 * entry with {@code null}.
		 */
		private final class SubsetIterator extends SetIterator {
			SubsetIterator() {
				next = firstEntry();
			}

			SubsetIterator(final KEY_GENERIC_TYPE k) {
				this();

				if (next != null) {
					if (! bottom && compare(k, next.key) < 0) prev = null;
					else if (! top && compare(k, (prev = lastEntry()).key) >= 0) next = null;
					else {
						next = locateKey(k);

						if (compare(next.key, k) <= 0) {
							prev = next;
							next = next.next();
						}
						else prev = next.prev();
					}
				}
			}

			@Override
			void updatePrevious() {
				prev = prev.prev();
				if (! bottom && prev != null && AVL_TREE_SET.this.compare(prev.key, from) < 0) prev = null;
			}

			@Override
			void updateNext() {
				next = next.next();
				if (! top && next != null && AVL_TREE_SET.this.compare(next.key, to) >= 0) next = null;
			}
		}
	}

	/** Returns a deep copy of this tree set.
	 *
	 * <p>This method performs a deep copy of this tree set; the data stored in the
	 * set, however, is not cloned. Note that this makes a difference only for object keys.
	 *
	 * @return a deep copy of this tree set.
	 */

	@Override
	SUPPRESS_WARNINGS_KEY_UNCHECKED
	public Object clone() {
		AVL_TREE_SET KEY_GENERIC c;
		try {
			c = (AVL_TREE_SET KEY_GENERIC)super.clone();
		}
		catch(CloneNotSupportedException cantHappen) {
			throw new InternalError();
		}

		c.allocatePaths();

		if (count != 0) {
			// Also this apparently unfathomable code is derived from GNU libavl.
			Entry KEY_GENERIC e, p, q, rp = new Entry KEY_GENERIC_DIAMOND(), rq = new Entry KEY_GENERIC_DIAMOND();

			p = rp;
			rp.left(tree);

			q = rq;
			rq.pred(null);

			while(true) {
				if (! p.pred()) {
					e = p.left.clone();
					e.pred(q.left);
					e.succ(q);
					q.left(e);

					p = p.left;
					q = q.left;
				}
				else {
					while(p.succ()) {
						p = p.right;

						if (p == null) {
							q.right = null;
							c.tree = rq.left;

							c.firstEntry = c.tree;
							while(c.firstEntry.left != null) c.firstEntry = c.firstEntry.left;
							c.lastEntry = c.tree;
							while(c.lastEntry.right != null) c.lastEntry = c.lastEntry.right;

							return c;
						}
						q = q.right;
					}

					p = p.right;
					q = q.right;
				}

				if (! p.succ()) {
					e = p.right.clone();
					e.succ(q.right);
					e.pred(q);
					q.right(e);
				}
			}
		}

		return c;
	}


	private void writeObject(java.io.ObjectOutputStream s) throws java.io.IOException {
		int n = count;
		SetIterator i = new SetIterator();

		s.defaultWriteObject();
		while(n-- != 0) s.WRITE_KEY(i.NEXT_KEY());
	}


	/** Reads the given number of entries from the input stream, returning the corresponding tree.
	 *
	 * @param s the input stream.
	 * @param n the (positive) number of entries to read.
	 * @param pred the entry containing the key that preceeds the first key in the tree.
	 * @param succ the entry containing the key that follows the last key in the tree.
	 */
	SUPPRESS_WARNINGS_KEY_UNCHECKED
	private Entry KEY_GENERIC readTree(final java.io.ObjectInputStream s, final int n, final Entry KEY_GENERIC pred, final Entry KEY_GENERIC succ) throws java.io.IOException, ClassNotFoundException {
		if (n == 1) {
			final Entry KEY_GENERIC top = new Entry KEY_GENERIC_DIAMOND(KEY_GENERIC_CAST s.READ_KEY());
			top.pred(pred);
			top.succ(succ);

			return top;
		}

		if (n == 2) {
			/* We handle separately this case so that recursion will
			 *always* be on nonempty subtrees. */
			final Entry KEY_GENERIC top = new Entry KEY_GENERIC_DIAMOND(KEY_GENERIC_CAST s.READ_KEY());
			top.right(new Entry KEY_GENERIC_DIAMOND(KEY_GENERIC_CAST s.READ_KEY()));
			top.right.pred(top);
			top.balance(1);
			top.pred(pred);
			top.right.succ(succ);

			return top;
		}

		// The right subtree is the largest one.
		final int rightN = n / 2, leftN = n - rightN - 1;

		final Entry KEY_GENERIC top = new Entry KEY_GENERIC_DIAMOND();

		top.left(readTree(s, leftN, pred, top));

		top.key = KEY_GENERIC_CAST s.READ_KEY();

		top.right(readTree(s, rightN, top, succ));

		if (n == (n & -n)) top.balance(1); // Quick test for determining whether n is a power of 2.

		return top;
	}


	private void readObject(java.io.ObjectInputStream s) throws java.io.IOException, ClassNotFoundException {
		s.defaultReadObject();
		/* The storedComparator is now correctly set, but we must restore
		   on-the-fly the actualComparator. */
		setActualComparator();
		allocatePaths();

		if (count != 0) {
			tree = readTree(s, count, null, null);
			Entry KEY_GENERIC e;

			e = tree;
			while(e.left() != null) e = e.left();
			firstEntry = e;

			e = tree;
			while(e.right() != null) e = e.right();
			lastEntry = e;
		}
	}

#ifdef ASSERTS_CODE
	private static KEY_GENERIC int checkTree(Entry KEY_GENERIC e) {
		if (e == null) return 0;

		final int leftN = checkTree(e.left()), rightN = checkTree(e.right());
		if (leftN + e.balance() != rightN)
			throw new AssertionError("Mismatch between left tree size (" + leftN + "), right tree size (" + rightN + ") and balance (" + e.balance() + ")");

		return Math.max(leftN , rightN) + 1;
	}
#endif

#ifdef TEST

	private static long seed = System.currentTimeMillis();
	private static java.util.Random r = new java.util.Random(seed);

	private static KEY_TYPE genKey() {
#if KEY_CLASS_Byte || KEY_CLASS_Short || KEY_CLASS_Character
		return (KEY_TYPE)(r.nextInt());
#elif KEYS_PRIMITIVE
		return r.NEXT_KEY();
#else
		return Integer.toBinaryString(r.nextInt());
#endif
	}

	private static java.text.NumberFormat format = new java.text.DecimalFormat("#,###.00");
	private static java.text.FieldPosition p = new java.text.FieldPosition(0);

	private static String format(double d) {
		StringBuffer s = new StringBuffer();
		return format.format(d, s, p).toString();
	}

	private static void speedTest(int n, boolean comp) {
		int i, j;
		AVL_TREE_SET m;
		java.util.TreeSet t;
		KEY_TYPE k[] = new KEY_TYPE[n];
		KEY_TYPE nk[] = new KEY_TYPE[n];
		long ms;

		for(i = 0; i < n; i++) {
			k[i] = genKey();
			nk[i] = genKey();
		}

		double totAdd = 0, totYes = 0, totNo = 0, totIterFor = 0, totIterBack = 0, totRemYes = 0, d, dd;

		if (comp) {
			for(j = 0; j < 20; j++) {

				t = new java.util.TreeSet();

				/* We first add all pairs to t. */
				for(i = 0; i < n;  i++) t.add(KEY2OBJ(k[i]));

				/* Then we remove the first half and put it back. */
				for(i = 0; i < n/2;  i++) t.remove(KEY2OBJ(k[i]));

				ms = System.currentTimeMillis();
				for(i = 0; i < n/2;  i++) t.add(KEY2OBJ(k[i]));
				d = System.currentTimeMillis() - ms;

				/* Then we remove the other half and put it back again. */
				ms = System.currentTimeMillis();
				for(i = n/2; i < n;  i++) t.remove(KEY2OBJ(k[i]));
				dd = System.currentTimeMillis() - ms ;

				ms = System.currentTimeMillis();
				for(i = n/2; i < n;  i++) t.add(KEY2OBJ(k[i]));
				d += System.currentTimeMillis() - ms;
				if (j > 2) totAdd += n/d;
				System.out.print("Add: " + format(n/d) +" K/s ");

				/* Then we remove again the first half. */
				ms = System.currentTimeMillis();
				for(i = 0; i < n/2;  i++) t.remove(KEY2OBJ(k[i]));
				dd += System.currentTimeMillis() - ms ;
				if (j > 2) totRemYes += n/dd;
				System.out.print("RemYes: " + format(n/dd) +" K/s ");

				/* And then we put it back. */
				for(i = 0; i < n/2;  i++) t.add(KEY2OBJ(k[i]));

				/* We check for pairs in t. */
				ms = System.currentTimeMillis();
				for(i = 0; i < n;  i++) t.contains(KEY2OBJ(k[i]));
				d = 1.0 * n / (System.currentTimeMillis() - ms);
				if (j > 2) totYes += d;
				System.out.print("Yes: " + format(d) +" K/s ");

				/* We check for pairs not in t. */
				ms = System.currentTimeMillis();
				for(i = 0; i < n;  i++) t.contains(KEY2OBJ(nk[i]));
				d = 1.0 * n / (System.currentTimeMillis() - ms);
				if (j > 2) totNo += d;
				System.out.print("No: " + format(d) +" K/s ");

				/* We iterate on t. */
				ms = System.currentTimeMillis();
				for(Iterator it = t.iterator(); it.hasNext(); it.next());
				d = 1.0 * n / (System.currentTimeMillis() - ms);
				if (j > 2) totIterFor += d;
				System.out.print("IterFor: " + format(d) +" K/s ");

				System.out.println();
			}

			System.out.println();
			System.out.println("java.util Add: " + format(totAdd/(j-3)) + " K/s RemYes: " + format(totRemYes/(j-3)) + " K/s Yes: " + format(totYes/(j-3)) + " K/s No: " + format(totNo/(j-3)) + " K/s IterFor: " + format(totIterFor/(j-3))  + " K/s");

			System.out.println();

			totAdd = totYes = totNo = totIterFor = totIterBack = totRemYes = 0;

		}

		for(j = 0; j < 20; j++) {

			m = new AVL_TREE_SET();

			/* We first add all pairs to m. */
			for(i = 0; i < n;  i++) m.add(k[i]);

			/* Then we remove the first half and put it back. */
			for(i = 0; i < n/2;  i++) m.remove(k[i]);

			ms = System.currentTimeMillis();
			for(i = 0; i < n/2;  i++) m.add(k[i]);
			d = System.currentTimeMillis() - ms;

			/* Then we remove the other half and put it back again. */
			ms = System.currentTimeMillis();
			for(i = n/2; i < n;  i++) m.remove(k[i]);
			dd = System.currentTimeMillis() - ms ;

			ms = System.currentTimeMillis();
			for(i = n/2; i < n;  i++) m.add(k[i]);
			d += System.currentTimeMillis() - ms;
			if (j > 2) totAdd += n/d;
			System.out.print("Add: " + format(n/d) +" K/s ");

			/* Then we remove again the first half. */
			ms = System.currentTimeMillis();
			for(i = 0; i < n/2;  i++) m.remove(k[i]);
			dd += System.currentTimeMillis() - ms ;
			if (j > 2) totRemYes += n/dd;
			System.out.print("RemYes: " + format(n/dd) +" K/s ");

			/* And then we put it back. */
			for(i = 0; i < n/2;  i++) m.add(k[i]);

			/* We check for pairs in m. */
			ms = System.currentTimeMillis();
			for(i = 0; i < n;  i++) m.contains(k[i]);
			d = 1.0 * n / (System.currentTimeMillis() - ms);
			if (j > 2) totYes += d;
			System.out.print("Yes: " + format(d) +" K/s ");

			/* We check for pairs not in m. */
			ms = System.currentTimeMillis();
			for(i = 0; i < n;  i++) m.contains(nk[i]);
			d = 1.0 * n / (System.currentTimeMillis() - ms);
			if (j > 2) totNo += d;
			System.out.print("No: " + format(d) +" K/s ");

			/* We iterate on m. */
			KEY_LIST_ITERATOR it = (KEY_LIST_ITERATOR)m.iterator();
			ms = System.currentTimeMillis();
			for(; it.hasNext(); it.NEXT_KEY());
			d = 1.0 * n / (System.currentTimeMillis() - ms);
			if (j > 2) totIterFor += d;
			System.out.print("IterFor: " + format(d) +" K/s ");

			/* We iterate back on m. */
			ms = System.currentTimeMillis();
			for(; it.hasPrevious(); it.PREV_KEY());
			d = 1.0 * n / (System.currentTimeMillis() - ms);
			if (j > 2) totIterBack += d;
			System.out.print("IterBack: " + format(d) +" K/s ");

			System.out.println();
		}


		System.out.println();
		System.out.println("fastutil  Add: " + format(totAdd/(j-3)) + " K/s RemYes: " + format(totRemYes/(j-3)) + " K/s Yes: " + format(totYes/(j-3)) + " K/s No: " + format(totNo/(j-3)) + " K/s IterFor: " + format(totIterFor/(j-3))  + " K/s IterBack: " + format(totIterBack/(j-3)) + "K/s");

		System.out.println();
	}


	private static boolean valEquals(Object o1, Object o2) {
		return o1 == null ? o2 == null : o1.equals(o2);
	}

	private static void fatal(String msg) {
		throw new AssertionError(msg);
	}

	private static void ensure(boolean cond, String msg) {
		if (cond) return;
		fatal(msg);
	}

	private static Object[] k, v, nk;
	private static KEY_TYPE kt[];
	private static KEY_TYPE nkt[];
	private static AVL_TREE_SET topSet;

	protected static void testSets(SORTED_SET m, SortedSet t, int n, int level) throws Exception {
		long ms;
		boolean mThrowsIllegal, tThrowsIllegal, mThrowsNoElement, tThrowsNoElement;
		boolean rt = false, rm = false;

		if (level > 4) return;


		/* Now we check that both sets agree on first/last keys. */

		mThrowsNoElement = mThrowsIllegal = tThrowsNoElement = tThrowsIllegal = false;

		try {
			m.first();
		}
		catch (NoSuchElementException e) { mThrowsNoElement = true; }
		try {
			t.first();
		}
		catch (NoSuchElementException e) { tThrowsNoElement = true; }

		ensure(mThrowsNoElement == tThrowsNoElement, "Error (" + level + ", " + seed + "): first() divergence at start in NoSuchElementException  (" + mThrowsNoElement + ", " + tThrowsNoElement + ")");
		if (! mThrowsNoElement) ensure(t.first().equals(m.first()), "Error (" + level + ", " + seed + "): m and t differ at start on their first key (" + m.first() + ", " + t.first() +")");

		mThrowsNoElement = mThrowsIllegal = tThrowsNoElement = tThrowsIllegal = false;

		try {
			m.last();
		}
		catch (NoSuchElementException e) { mThrowsNoElement = true; }
		try {
			t.last();
		}
		catch (NoSuchElementException e) { tThrowsNoElement = true; }

		ensure(mThrowsNoElement == tThrowsNoElement, "Error (" + level + ", " + seed + "): last() divergence at start in NoSuchElementException  (" + mThrowsNoElement + ", " + tThrowsNoElement + ")");


		if (! mThrowsNoElement) ensure(t.last().equals(m.last()), "Error (" + level + ", " + seed + "): m and t differ at start on their last key (" + m.last() + ", " + t.last() +")");


		/* Now we check that m and t are equal. */
		if (!m.equals(t) || ! t.equals(m)) System.err.println("m: " + m + " t: " + t);

		ensure(m.equals(t), "Error (" + level + ", " + seed + "): ! m.equals(t) at start");
		ensure(t.equals(m), "Error (" + level + ", " + seed + "): ! t.equals(m) at start");



		/* Now we check that m actually holds that data. */
		for(Iterator i=t.iterator(); i.hasNext();) {
			ensure(m.contains(i.next()), "Error (" + level + ", " + seed + "): m and t differ on an entry after insertion (iterating on t)");
		}

		/* Now we check that m actually holds that data, but iterating on m. */
		for(Iterator i=m.iterator(); i.hasNext();) {
			ensure(t.contains(i.next()), "Error (" + level + ", " + seed + "): m and t differ on an entry after insertion (iterating on m)");
		}

		/* Now we check that inquiries about random data give the same answer in m and t. For
		   m we use the polymorphic method. */

		for(int i=0; i<n;  i++) {
			KEY_TYPE T = genKey();

			mThrowsNoElement = mThrowsIllegal = tThrowsNoElement = tThrowsIllegal = false;

			try {
				m.contains(T);
			}
			catch (NoSuchElementException e) { mThrowsNoElement = true; }
			catch (IllegalArgumentException e) { mThrowsIllegal = true; }

			try {
				t.contains(KEY2OBJ(T));
			}
			catch (NoSuchElementException e) { tThrowsNoElement = true; }
			catch (IllegalArgumentException e) { tThrowsIllegal = true; }

			ensure(mThrowsNoElement == tThrowsNoElement, "Error (" + level + ", " + seed + "): contains() divergence in NoSuchElementException (" + mThrowsNoElement + ", " + tThrowsNoElement + ")");
			ensure(mThrowsIllegal == tThrowsIllegal, "Error (" + level + ", " + seed + "): contains() divergence in IllegalArgumentException (" + mThrowsIllegal + ", " + tThrowsIllegal + ")");
			if (!mThrowsNoElement && !mThrowsIllegal) ensure(m.contains(KEY2OBJ(T)) == t.contains(KEY2OBJ(T)), "Error (" + level + ", " + seed + "): divergence in keys between t and m (polymorphic method)");
		}

		/* Again, we check that inquiries about random data give the same answer in m and t, but
		   for m we use the standard method. */

		for(int i=0; i<n;  i++) {
			KEY_TYPE T = genKey();

			mThrowsNoElement = mThrowsIllegal = tThrowsNoElement = tThrowsIllegal = false;

			try {
				m.contains(KEY2OBJ(T));
			}
			catch (NoSuchElementException e) { mThrowsNoElement = true; }
			catch (IllegalArgumentException e) { mThrowsIllegal = true; }

			try {
				t.contains(KEY2OBJ(T));
			}
			catch (NoSuchElementException e) { tThrowsNoElement = true; }
			catch (IllegalArgumentException e) { tThrowsIllegal = true; }

			ensure(mThrowsNoElement == tThrowsNoElement, "Error (" + level + ", " + seed + "): contains() divergence in NoSuchElementException for " + T + " (" + mThrowsNoElement + ", " + tThrowsNoElement + ")");
			ensure(mThrowsIllegal == tThrowsIllegal, "Error (" + level + ", " + seed + "): contains() divergence in IllegalArgumentException for " + T + " (" + mThrowsIllegal + ", " + tThrowsIllegal + ")");
			if (!mThrowsNoElement && !mThrowsIllegal) ensure(m.contains(KEY2OBJ(T)) ==  t.contains(KEY2OBJ(T)), "Error (" + level + ", " + seed + "): divergence between t and m (standard method)");
		}

		/* Now we add and remove random data in m and t, checking that the result is the same. */

		for(int i=0; i<20*n;  i++) {
			KEY_TYPE T = genKey();

			mThrowsNoElement = mThrowsIllegal = tThrowsNoElement = tThrowsIllegal = false;

			try {
				rm = m.add(KEY2OBJ(T));
			}
			catch (NoSuchElementException e) { mThrowsNoElement = true; }
			catch (IllegalArgumentException e) { mThrowsIllegal = true; }

			try {
				rt = t.add(KEY2OBJ(T));
			}
			catch (NoSuchElementException e) { tThrowsNoElement = true; }
			catch (IllegalArgumentException e) { tThrowsIllegal = true; }


			ensure(mThrowsNoElement == tThrowsNoElement, "Error (" + level + ", " + seed + "): add() divergence in NoSuchElementException for " + T + " (" + mThrowsNoElement + ", " + tThrowsNoElement + ")");
			ensure(mThrowsIllegal == tThrowsIllegal, "Error (" + level + ", " + seed + "): add() divergence in IllegalArgumentException for " + T + " (" + mThrowsIllegal + ", " + tThrowsIllegal + ")");
			if (!mThrowsNoElement && !mThrowsIllegal) ensure(rm == rt, "Error (" + level + ", " + seed + "): divergence in add() between t and m");

			T = genKey();

			mThrowsNoElement = mThrowsIllegal = tThrowsNoElement = tThrowsIllegal = false;

			try {
				rm = m.remove(KEY2OBJ(T));
			}
			catch (NoSuchElementException e) { mThrowsNoElement = true; }
			catch (IllegalArgumentException e) { mThrowsIllegal = true; }

			try {
				rt = t.remove(KEY2OBJ(T));
			}
			catch (NoSuchElementException e) { tThrowsNoElement = true; }
			catch (IllegalArgumentException e) { tThrowsIllegal = true; }


			ensure(mThrowsNoElement == tThrowsNoElement, "Error (" + level + ", " + seed + "): remove() divergence in NoSuchElementException for " + T + " (" + mThrowsNoElement + ", " + tThrowsNoElement + ")");
			ensure(mThrowsIllegal == tThrowsIllegal, "Error (" + level + ", " + seed + "): remove() divergence in IllegalArgumentException for " + T + " (" + mThrowsIllegal + ", " + tThrowsIllegal + ")");
			if (!mThrowsNoElement && !mThrowsIllegal) ensure(rm == rt, "Error (" + level + ", " + seed + "): divergence in remove() between t and m");
		}

		ensure(m.equals(t), "Error (" + level + ", " + seed + "): ! m.equals(t) after removal");
		ensure(t.equals(m), "Error (" + level + ", " + seed + "): ! t.equals(m) after removal");

		/* Now we check that m actually holds the same data. */

		for(Iterator i=t.iterator(); i.hasNext();) {
			ensure(m.contains(i.next()), "Error (" + level + ", " + seed + "): m and t differ on an entry after removal (iterating on t)");
		}

		/* Now we check that m actually holds that data, but iterating on m. */

		for(Iterator i=m.iterator(); i.hasNext();) {
			ensure(t.contains(i.next()), "Error (" + level + ", " + seed + "): m and t differ on an entry after removal (iterating on m)");
		}

		/* Now we check that both sets agree on first/last keys. */

		mThrowsNoElement = mThrowsIllegal = tThrowsNoElement = tThrowsIllegal = false;

		try {
			m.first();
		}
		catch (NoSuchElementException e) { mThrowsNoElement = true; }
		try {
			t.first();
		}
		catch (NoSuchElementException e) { tThrowsNoElement = true; }

		ensure(mThrowsNoElement == tThrowsNoElement, "Error (" + level + ", " + seed + "): first() divergence in NoSuchElementException  (" + mThrowsNoElement + ", " + tThrowsNoElement + ")");
		if (! mThrowsNoElement) ensure(t.first().equals(m.first()), "Error (" + level + ", " + seed + "): m and t differ on their first key (" + m.first() + ", " + t.first() +")");

		mThrowsNoElement = mThrowsIllegal = tThrowsNoElement = tThrowsIllegal = false;

		try {
			m.last();
		}
		catch (NoSuchElementException e) { mThrowsNoElement = true; }
		try {
			t.last();
		}
		catch (NoSuchElementException e) { tThrowsNoElement = true; }

		ensure(mThrowsNoElement == tThrowsNoElement, "Error (" + level + ", " + seed + "): last() divergence in NoSuchElementException  (" + mThrowsNoElement + ", " + tThrowsNoElement + ")");

		if (! mThrowsNoElement) ensure(t.last().equals(m.last()), "Error (" + level + ", " + seed + "): m and t differ on their last key (" + m.last() + ", " + t.last() +")");

		/* Now we check cloning. */

		if (level == 0) {
			ensure(m.equals(((AVL_TREE_SET)m).clone()), "Error (" + level + ", " + seed + "): m does not equal m.clone()");
			ensure(((AVL_TREE_SET)m).clone().equals(m), "Error (" + level + ", " + seed + "): m.clone() does not equal m");
		}

		int h = m.hashCode();


		/* Now we save and read m. */

		SORTED_SET m2 = null;

		{
			java.io.File ff = new java.io.File("it.unimi.dsi.fastutil.test." + m.getClass().getSimpleName() + "." + n);
			java.io.OutputStream os = new java.io.FileOutputStream(ff);
			java.io.ObjectOutputStream oos = new java.io.ObjectOutputStream(os);

			oos.writeObject(m);
			oos.close();

			java.io.InputStream is = new java.io.FileInputStream(ff);
			java.io.ObjectInputStream ois = new java.io.ObjectInputStream(is);

			m2 = (SORTED_SET)ois.readObject();
			ois.close();
			ff.delete();
		}

		ensure(m2.hashCode() == h, "Error (" + level + ", " + seed + "): hashCode() changed after save/read");

		/* Now we check that m2 actually holds that data. */

		ensure(m2.equals(t), "Error (" + level + ", " + seed + "): ! m2.equals(t) after save/read");
		ensure(t.equals(m2), "Error (" + level + ", " + seed + "): ! t.equals(m2) after save/read");
		/* Now we take out of m everything, and check that it is empty. */

		for(Iterator i=t.iterator(); i.hasNext();) m2.remove(i.next());

		ensure(m2.isEmpty(), "Error (" + level + ", " + seed + "): m2 is not empty (as it should be)");

		/* Now we play with iterators. */

		{
			java.util.ListIterator i, j;
			Object J;
			i = (java.util.ListIterator)m.iterator();
			j = new java.util.LinkedList(t).listIterator();

			for(int k = 0; k < 2*n; k++) {
				ensure(i.hasNext() == j.hasNext(), "Error (" + level + ", " + seed + "): divergence in hasNext()");
				ensure(i.hasPrevious() == j.hasPrevious(), "Error (" + level + ", " + seed + "): divergence in hasPrevious()");

				if (r.nextFloat() < .8 && i.hasNext()) {
					ensure(i.next().equals(J = j.next()), "Error (" + level + ", " + seed + "): divergence in next()");

					if (r.nextFloat() < 0.5) {
						i.remove();
						j.remove();
						t.remove(J);
					}
				}
				else if (r.nextFloat() < .2 && i.hasPrevious()) {
					ensure(i.previous().equals(J = j.previous()), "Error (" + level + ", " + seed + "): divergence in previous()");

					if (r.nextFloat() < 0.5) {
						i.remove();
						j.remove();
						t.remove(J);
					}
				}

				ensure(i.nextIndex() == j.nextIndex(), "Error (" + level + ", " + seed + "): divergence in nextIndex()");
				ensure(i.previousIndex() == j.previousIndex(), "Error (" + level + ", " + seed + "): divergence in previousIndex()");

			}

		}

		{
			boolean badPrevious = false;
			Object previous = null;
			it.unimi.dsi.fastutil.BidirectionalIterator i;
			java.util.ListIterator j;
			Object I, J;
			KEY_TYPE from = genKey();
			j = new java.util.LinkedList(t).listIterator();
			while(j.hasNext()) {
				Object k = j.next();
				if (((Comparable)k).compareTo(KEY2OBJ(from)) > 0) {
					badPrevious = true;
					j.previous();
					break;
				}
				previous = k;
			}

			i = (it.unimi.dsi.fastutil.BidirectionalIterator)m.iterator(from);

			for(int k = 0; k < 2*n; k++) {
				ensure(i.hasNext() == j.hasNext(), "Error (" + level + ", " + seed + "): divergence in hasNext() (iterator with starting point " + from + ")");
				ensure(i.hasPrevious() == j.hasPrevious() || badPrevious && (i.hasPrevious() == (previous != null)), "Error (" + level + ", " + seed + "): divergence in hasPrevious() (iterator with starting point " + from + ")");

				if (r.nextFloat() < .8 && i.hasNext()) {
					ensure((I = i.next()).equals(J = j.next()), "Error (" + level + ", " + seed + "): divergence in next() (" + I + ", " + J + ", iterator with starting point " + from + ")");
					//System.err.println("Done next " + I + " " + J + "  " + badPrevious);

					badPrevious = false;

					if (r.nextFloat() < 0.5) {
						//System.err.println("Removing in next");
						i.remove();
						j.remove();
						t.remove(J);
					}
				}
				else if (!badPrevious && r.nextFloat() < .2 && i.hasPrevious()) {
					ensure((I = i.previous()).equals(J = j.previous()), "Error (" + level + ", " + seed + "): divergence in previous() (" + I + ", " + J + ", iterator with starting point " + from + ")");

					if (r.nextFloat() < 0.5) {
						//System.err.println("Removing in prev");
						i.remove();
						j.remove();
						t.remove(J);
					}
				}
			}

		}

		/* Now we check that m actually holds that data. */

		ensure(m.equals(t), "Error (" + level + ", " + seed + "): ! m.equals(t) after iteration");
		ensure(t.equals(m), "Error (" + level + ", " + seed + "): ! t.equals(m) after iteration");

		/* Now we select a pair of keys and create a subset. */

		if (! m.isEmpty()) {
			java.util.ListIterator i;
			Object start = m.first(), end = m.first();
			for(i = (java.util.ListIterator)m.iterator(); i.hasNext() && r.nextFloat() < .3; start = end = i.next());
			for(; i.hasNext() && r.nextFloat() < .95; end = i.next());

			//System.err.println("Checking subSet from " + start + " to " + end + " (level=" + (level+1) + ")...");
			testSets((SORTED_SET)m.subSet((KEY_CLASS)start, (KEY_CLASS)end), t.subSet(start, end), n, level + 1);

			ensure(m.equals(t), "Error (" + level + ", " + seed + "): ! m.equals(t) after subSet");
			ensure(t.equals(m), "Error (" + level + ", " + seed + "): ! t.equals(m) after subSet");

			//System.err.println("Checking headSet to " + end + " (level=" + (level+1) + ")...");
			testSets((SORTED_SET)m.headSet((KEY_CLASS)end), t.headSet(end), n, level + 1);

			ensure(m.equals(t), "Error (" + level + ", " + seed + "): ! m.equals(t) after headSet");
			ensure(t.equals(m), "Error (" + level + ", " + seed + "): ! t.equals(m) after headSet");

			//System.err.println("Checking tailSet from " + start + " (level=" + (level+1) + ")...");
			testSets((SORTED_SET)m.tailSet((KEY_CLASS)start), t.tailSet(start), n, level + 1);

			ensure(m.equals(t), "Error (" + level + ", " + seed + "): ! m.equals(t) after tailSet");
			ensure(t.equals(m), "Error (" + level + ", " + seed + "): ! t.equals(m) after tailSet");
		}


	}


	private static void runTest(int n) throws Exception {
		AVL_TREE_SET m = new AVL_TREE_SET();
		SortedSet t = new java.util.TreeSet();
		topSet = m;
		k = new Object[n];
		nk = new Object[n];
		kt = new KEY_TYPE[n];
		nkt = new KEY_TYPE[n];

		for(int i = 0; i < n; i++) {
#if KEY_CLASS_Object
			k[i] = kt[i] = genKey();
			nk[i] = nkt[i] = genKey();
#else
			k[i] = new KEY_CLASS(kt[i] = genKey());
			nk[i] = new KEY_CLASS(nkt[i] = genKey());
#endif
		}

		/* We add pairs to t. */
		for(int i = 0; i < n;  i++) t.add(k[i]);

		/* We add to m the same data */
		m.addAll(t);

		testSets(m, t, n, 0);

		System.out.println("Test OK");
		return;
	}


	public static void main(String args[]) throws Exception {
		int n  = Integer.parseInt(args[1]);
		if (args.length > 2) r = new java.util.Random(seed = Long.parseLong(args[2]));


		try {
			if ("speedTest".equals(args[0]) || "speedComp".equals(args[0])) speedTest(n, "speedComp".equals(args[0]));
			else if ("test".equals(args[0])) runTest(n);
		} catch(Throwable e) {
			e.printStackTrace(System.err);
			System.err.println("seed: " + seed);
			throw e;
		}
	}

#endif


}
