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	/*
	* Copyright (c) 1997, 2014, Oracle and/or its affiliates. All rights reserved.
	* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
	*
	* This code is free software; you can redistribute it and/or modify it
	* under the terms of the GNU General Public License version 2 only, as
	* published by the Free Software Foundation. Oracle designates this
	* particular file as subject to the "Classpath" exception as provided
	* by Oracle in the LICENSE file that accompanied this code.
	*
	* This code is distributed in the hope that it will be useful, but WITHOUT
	* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
	* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
	* version 2 for more details (a copy is included in the LICENSE file that
	* accompanied this code).
	*
	* You should have received a copy of the GNU General Public License version
	* 2 along with this work; if not, write to the Free Software Foundation,
	* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
	*
	* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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	package java.util;

	import java.io.Serializable;
	import java.util.function.Function;
	import java.util.function.ToIntFunction;
	import java.util.function.ToLongFunction;
	import java.util.function.ToDoubleFunction;
	import java.util.Comparators;

	/**
	* A comparison function, which imposes a <i>total ordering</i> on some
	* collection of objects. Comparators can be passed to a sort method (such
	* as {@link Collections#sort(List,Comparator) Collections.sort} or {@link
	* Arrays#sort(Object[],Comparator) Arrays.sort}) to allow precise control
	* over the sort order. Comparators can also be used to control the order of
	* certain data structures (such as {@link SortedSet sorted sets} or {@link
	* SortedMap sorted maps}), or to provide an ordering for collections of
	* objects that don't have a {@link Comparable natural ordering}.<p>
	*
	* The ordering imposed by a comparator <tt>c</tt> on a set of elements
	* <tt>S</tt> is said to be <i>consistent with equals</i> if and only if
	* <tt>c.compare(e1, e2)==0</tt> has the same boolean value as
	* <tt>e1.equals(e2)</tt> for every <tt>e1</tt> and <tt>e2</tt> in
	* <tt>S</tt>.<p>
	*
	* Caution should be exercised when using a comparator capable of imposing an
	* ordering inconsistent with equals to order a sorted set (or sorted map).
	* Suppose a sorted set (or sorted map) with an explicit comparator <tt>c</tt>
	* is used with elements (or keys) drawn from a set <tt>S</tt>. If the
	* ordering imposed by <tt>c</tt> on <tt>S</tt> is inconsistent with equals,
	* the sorted set (or sorted map) will behave "strangely." In particular the
	* sorted set (or sorted map) will violate the general contract for set (or
	* map), which is defined in terms of <tt>equals</tt>.<p>
	*
	* For example, suppose one adds two elements {@code a} and {@code b} such that
	* {@code (a.equals(b) && c.compare(a, b) != 0)}
	* to an empty {@code TreeSet} with comparator {@code c}.
	* The second {@code add} operation will return
	* true (and the size of the tree set will increase) because {@code a} and
	* {@code b} are not equivalent from the tree set's perspective, even though
	* this is contrary to the specification of the
	* {@link Set#add Set.add} method.<p>
	*
	* Note: It is generally a good idea for comparators to also implement
	* <tt>java.io.Serializable</tt>, as they may be used as ordering methods in
	* serializable data structures (like {@link TreeSet}, {@link TreeMap}). In
	* order for the data structure to serialize successfully, the comparator (if
	* provided) must implement <tt>Serializable</tt>.<p>
	*
	* For the mathematically inclined, the <i>relation</i> that defines the
	* <i>imposed ordering</i> that a given comparator <tt>c</tt> imposes on a
	* given set of objects <tt>S</tt> is:<pre>
	* {(x, y) such that c.compare(x, y) <= 0}.
	* </pre> The <i>quotient</i> for this total order is:<pre>
	* {(x, y) such that c.compare(x, y) == 0}.
	* </pre>
	*
	* It follows immediately from the contract for <tt>compare</tt> that the
	* quotient is an <i>equivalence relation</i> on <tt>S</tt>, and that the
	* imposed ordering is a <i>total order</i> on <tt>S</tt>. When we say that
	* the ordering imposed by <tt>c</tt> on <tt>S</tt> is <i>consistent with
	* equals</i>, we mean that the quotient for the ordering is the equivalence
	* relation defined by the objects' {@link Object#equals(Object)
	* equals(Object)} method(s):<pre>
	* {(x, y) such that x.equals(y)}. </pre>
	*
	* <p>Unlike {@code Comparable}, a comparator may optionally permit
	* comparison of null arguments, while maintaining the requirements for
	* an equivalence relation.
	*
	* <p>This interface is a member of the
	* <a href="{@docRoot}/../technotes/guides/collections/index.html">
	* Java Collections Framework</a>.
	*
	* @param <T> the type of objects that may be compared by this comparator
	*
	* @author Josh Bloch
	* @author Neal Gafter
	* @see Comparable
	* @see java.io.Serializable
	* @since 1.2
	*/
	@FunctionalInterface
	public interface Comparator<T> {
	/**
	* Compares its two arguments for order. Returns a negative integer,
	* zero, or a positive integer as the first argument is less than, equal
	* to, or greater than the second.<p>
	*
	* In the foregoing description, the notation
	* <tt>sgn(</tt><i>expression</i><tt>)</tt> designates the mathematical
	* <i>signum</i> function, which is defined to return one of <tt>-1</tt>,
	* <tt>0</tt>, or <tt>1</tt> according to whether the value of
	* <i>expression</i> is negative, zero or positive.<p>
	*
	* The implementor must ensure that <tt>sgn(compare(x, y)) ==
	* -sgn(compare(y, x))</tt> for all <tt>x</tt> and <tt>y</tt>. (This
	* implies that <tt>compare(x, y)</tt> must throw an exception if and only
	* if <tt>compare(y, x)</tt> throws an exception.)<p>
	*
	* The implementor must also ensure that the relation is transitive:
	* <tt>((compare(x, y)>0) && (compare(y, z)>0))</tt> implies
	* <tt>compare(x, z)>0</tt>.<p>
	*
	* Finally, the implementor must ensure that <tt>compare(x, y)==0</tt>
	* implies that <tt>sgn(compare(x, z))==sgn(compare(y, z))</tt> for all
	* <tt>z</tt>.<p>
	*
	* It is generally the case, but <i>not</i> strictly required that
	* <tt>(compare(x, y)==0) == (x.equals(y))</tt>. Generally speaking,
	* any comparator that violates this condition should clearly indicate
	* this fact. The recommended language is "Note: this comparator
	* imposes orderings that are inconsistent with equals."
	*
	* @param o1 the first object to be compared.
	* @param o2 the second object to be compared.
	* @return a negative integer, zero, or a positive integer as the
	* first argument is less than, equal to, or greater than the
	* second.
	* @throws NullPointerException if an argument is null and this
	* comparator does not permit null arguments
	* @throws ClassCastException if the arguments' types prevent them from
	* being compared by this comparator.
	*/
	int compare(T o1, T o2);

	/**
	* Indicates whether some other object is "equal to" this
	* comparator. This method must obey the general contract of
	* {@link Object#equals(Object)}. Additionally, this method can return
	* <tt>true</tt> <i>only</i> if the specified object is also a comparator
	* and it imposes the same ordering as this comparator. Thus,
	* <code>comp1.equals(comp2)</code> implies that <tt>sgn(comp1.compare(o1,
	* o2))==sgn(comp2.compare(o1, o2))</tt> for every object reference
	* <tt>o1</tt> and <tt>o2</tt>.<p>
	*
	* Note that it is <i>always</i> safe <i>not</i> to override
	* <tt>Object.equals(Object)</tt>. However, overriding this method may,
	* in some cases, improve performance by allowing programs to determine
	* that two distinct comparators impose the same order.
	*
	* @param obj the reference object with which to compare.
	* @return <code>true</code> only if the specified object is also
	* a comparator and it imposes the same ordering as this
	* comparator.
	* @see Object#equals(Object)
	* @see Object#hashCode()
	*/
	boolean equals(Object obj);

	/**
	* Returns a comparator that imposes the reverse ordering of this
	* comparator.
	*
	* @return a comparator that imposes the reverse ordering of this
	* comparator.
	* @since 1.8
	*/
	default Comparator<T> reversed() {
	return Collections.reverseOrder(this);
	}

	/**
	* Returns a lexicographic-order comparator with another comparator.
	* If this {@code Comparator} considers two elements equal, i.e.
	* {@code compare(a, b) == 0}, {@code other} is used to determine the order.
	*
	* <p>The returned comparator is serializable if the specified comparator
	* is also serializable.
	*
	* @apiNote
	* For example, to sort a collection of {@code String} based on the length
	* and then case-insensitive natural ordering, the comparator can be
	* composed using following code,
	*
	* <pre>{@code
	* Comparator<String> cmp = Comparator.comparingInt(String::length)
	* .thenComparing(String.CASE_INSENSITIVE_ORDER);
	* }</pre>
	*
	* @param other the other comparator to be used when this comparator
	* compares two objects that are equal.
	* @return a lexicographic-order comparator composed of this and then the
	* other comparator
	* @throws NullPointerException if the argument is null.
	* @since 1.8
	*/
	default Comparator<T> thenComparing(Comparator<? super T> other) {
	Objects.requireNonNull(other);
	return (Comparator<T> & Serializable) (c1, c2) -> {
	int res = compare(c1, c2);
	return (res != 0) ? res : other.compare(c1, c2);
	};
	}

	/**
	* Returns a lexicographic-order comparator with a function that
	* extracts a key to be compared with the given {@code Comparator}.
	*
	* @implSpec This default implementation behaves as if {@code
	* thenComparing(comparing(keyExtractor, cmp))}.
	*
	* @param <U> the type of the sort key
	* @param keyExtractor the function used to extract the sort key
	* @param keyComparator the {@code Comparator} used to compare the sort key
	* @return a lexicographic-order comparator composed of this comparator
	* and then comparing on the key extracted by the keyExtractor function
	* @throws NullPointerException if either argument is null.
	* @see #comparing(Function, Comparator)
	* @see #thenComparing(Comparator)
	* @since 1.8
	*/
	default <U> Comparator<T> thenComparing(
	Function<? super T, ? extends U> keyExtractor,
	Comparator<? super U> keyComparator)
	{
	return thenComparing(comparing(keyExtractor, keyComparator));
	}

	/**
	* Returns a lexicographic-order comparator with a function that
	* extracts a {@code Comparable} sort key.
	*
	* @implSpec This default implementation behaves as if {@code
	* thenComparing(comparing(keyExtractor))}.
	*
	* @param <U> the type of the {@link Comparable} sort key
	* @param keyExtractor the function used to extract the {@link
	* Comparable} sort key
	* @return a lexicographic-order comparator composed of this and then the
	* {@link Comparable} sort key.
	* @throws NullPointerException if the argument is null.
	* @see #comparing(Function)
	* @see #thenComparing(Comparator)
	* @since 1.8
	*/
	default <U extends Comparable<? super U>> Comparator<T> thenComparing(
	Function<? super T, ? extends U> keyExtractor)
	{
	return thenComparing(comparing(keyExtractor));
	}

	/**
	* Returns a lexicographic-order comparator with a function that
	* extracts a {@code int} sort key.
	*
	* @implSpec This default implementation behaves as if {@code
	* thenComparing(comparingInt(keyExtractor))}.
	*
	* @param keyExtractor the function used to extract the integer sort key
	* @return a lexicographic-order comparator composed of this and then the
	* {@code int} sort key
	* @throws NullPointerException if the argument is null.
	* @see #comparingInt(ToIntFunction)
	* @see #thenComparing(Comparator)
	* @since 1.8
	*/
	default Comparator<T> thenComparingInt(ToIntFunction<? super T> keyExtractor) {
	return thenComparing(comparingInt(keyExtractor));
	}

	/**
	* Returns a lexicographic-order comparator with a function that
	* extracts a {@code long} sort key.
	*
	* @implSpec This default implementation behaves as if {@code
	* thenComparing(comparingLong(keyExtractor))}.
	*
	* @param keyExtractor the function used to extract the long sort key
	* @return a lexicographic-order comparator composed of this and then the
	* {@code long} sort key
	* @throws NullPointerException if the argument is null.
	* @see #comparingLong(ToLongFunction)
	* @see #thenComparing(Comparator)
	* @since 1.8
	*/
	default Comparator<T> thenComparingLong(ToLongFunction<? super T> keyExtractor) {
	return thenComparing(comparingLong(keyExtractor));
	}

	/**
	* Returns a lexicographic-order comparator with a function that
	* extracts a {@code double} sort key.
	*
	* @implSpec This default implementation behaves as if {@code
	* thenComparing(comparingDouble(keyExtractor))}.
	*
	* @param keyExtractor the function used to extract the double sort key
	* @return a lexicographic-order comparator composed of this and then the
	* {@code double} sort key
	* @throws NullPointerException if the argument is null.
	* @see #comparingDouble(ToDoubleFunction)
	* @see #thenComparing(Comparator)
	* @since 1.8
	*/
	default Comparator<T> thenComparingDouble(ToDoubleFunction<? super T> keyExtractor) {
	return thenComparing(comparingDouble(keyExtractor));
	}

	/**
	* Returns a comparator that imposes the reverse of the <em>natural
	* ordering</em>.
	*
	* <p>The returned comparator is serializable and throws {@link
	* NullPointerException} when comparing {@code null}.
	*
	* @param <T> the {@link Comparable} type of element to be compared
	* @return a comparator that imposes the reverse of the <i>natural
	* ordering</i> on {@code Comparable} objects.
	* @see Comparable
	* @since 1.8
	*/
	public static <T extends Comparable<? super T>> Comparator<T> reverseOrder() {
	return Collections.reverseOrder();
	}

	/**
	* Returns a comparator that compares {@link Comparable} objects in natural
	* order.
	*
	* <p>The returned comparator is serializable and throws {@link
	* NullPointerException} when comparing {@code null}.
	*
	* @param <T> the {@link Comparable} type of element to be compared
	* @return a comparator that imposes the <i>natural ordering</i> on {@code
	* Comparable} objects.
	* @see Comparable
	* @since 1.8
	*/
	@SuppressWarnings("unchecked")
	public static <T extends Comparable<? super T>> Comparator<T> naturalOrder() {
	return (Comparator<T>) Comparators.NaturalOrderComparator.INSTANCE;
	}

	/**
	* Returns a null-friendly comparator that considers {@code null} to be
	* less than non-null. When both are {@code null}, they are considered
	* equal. If both are non-null, the specified {@code Comparator} is used
	* to determine the order. If the specified comparator is {@code null},
	* then the returned comparator considers all non-null values to be equal.
	*
	* <p>The returned comparator is serializable if the specified comparator
	* is serializable.
	*
	* @param <T> the type of the elements to be compared
	* @param comparator a {@code Comparator} for comparing non-null values
	* @return a comparator that considers {@code null} to be less than
	* non-null, and compares non-null objects with the supplied
	* {@code Comparator}.
	* @since 1.8
	*/
	public static <T> Comparator<T> nullsFirst(Comparator<? super T> comparator) {
	return new Comparators.NullComparator<>(true, comparator);
	}

	/**
	* Returns a null-friendly comparator that considers {@code null} to be
	* greater than non-null. When both are {@code null}, they are considered
	* equal. If both are non-null, the specified {@code Comparator} is used
	* to determine the order. If the specified comparator is {@code null},
	* then the returned comparator considers all non-null values to be equal.
	*
	* <p>The returned comparator is serializable if the specified comparator
	* is serializable.
	*
	* @param <T> the type of the elements to be compared
	* @param comparator a {@code Comparator} for comparing non-null values
	* @return a comparator that considers {@code null} to be greater than
	* non-null, and compares non-null objects with the supplied
	* {@code Comparator}.
	* @since 1.8
	*/
	public static <T> Comparator<T> nullsLast(Comparator<? super T> comparator) {
	return new Comparators.NullComparator<>(false, comparator);
	}

	/**
	* Accepts a function that extracts a sort key from a type {@code T}, and
	* returns a {@code Comparator<T>} that compares by that sort key using
	* the specified {@link Comparator}.
	*
	* <p>The returned comparator is serializable if the specified function
	* and comparator are both serializable.
	*
	* @apiNote
	* For example, to obtain a {@code Comparator} that compares {@code
	* Person} objects by their last name ignoring case differences,
	*
	* <pre>{@code
	* Comparator<Person> cmp = Comparator.comparing(
	* Person::getLastName,
	* String.CASE_INSENSITIVE_ORDER);
	* }</pre>
	*
	* @param <T> the type of element to be compared
	* @param <U> the type of the sort key
	* @param keyExtractor the function used to extract the sort key
	* @param keyComparator the {@code Comparator} used to compare the sort key
	* @return a comparator that compares by an extracted key using the
	* specified {@code Comparator}
	* @throws NullPointerException if either argument is null
	* @since 1.8
	*/
	public static <T, U> Comparator<T> comparing(
	Function<? super T, ? extends U> keyExtractor,
	Comparator<? super U> keyComparator)
	{
	Objects.requireNonNull(keyExtractor);
	Objects.requireNonNull(keyComparator);
	return (Comparator<T> & Serializable)
	(c1, c2) -> keyComparator.compare(keyExtractor.apply(c1),
	keyExtractor.apply(c2));
	}

	/**
	* Accepts a function that extracts a {@link java.lang.Comparable
	* Comparable} sort key from a type {@code T}, and returns a {@code
	* Comparator<T>} that compares by that sort key.
	*
	* <p>The returned comparator is serializable if the specified function
	* is also serializable.
	*
	* @apiNote
	* For example, to obtain a {@code Comparator} that compares {@code
	* Person} objects by their last name,
	*
	* <pre>{@code
	* Comparator<Person> byLastName = Comparator.comparing(Person::getLastName);
	* }</pre>
	*
	* @param <T> the type of element to be compared
	* @param <U> the type of the {@code Comparable} sort key
	* @param keyExtractor the function used to extract the {@link
	* Comparable} sort key
	* @return a comparator that compares by an extracted key
	* @throws NullPointerException if the argument is null
	* @since 1.8
	*/
	public static <T, U extends Comparable<? super U>> Comparator<T> comparing(
	Function<? super T, ? extends U> keyExtractor)
	{
	Objects.requireNonNull(keyExtractor);
	return (Comparator<T> & Serializable)
	(c1, c2) -> keyExtractor.apply(c1).compareTo(keyExtractor.apply(c2));
	}

	/**
	* Accepts a function that extracts an {@code int} sort key from a type
	* {@code T}, and returns a {@code Comparator<T>} that compares by that
	* sort key.
	*
	* <p>The returned comparator is serializable if the specified function
	* is also serializable.
	*
	* @param <T> the type of element to be compared
	* @param keyExtractor the function used to extract the integer sort key
	* @return a comparator that compares by an extracted key
	* @see #comparing(Function)
	* @throws NullPointerException if the argument is null
	* @since 1.8
	*/
	public static <T> Comparator<T> comparingInt(ToIntFunction<? super T> keyExtractor) {
	Objects.requireNonNull(keyExtractor);
	return (Comparator<T> & Serializable)
	(c1, c2) -> Integer.compare(keyExtractor.applyAsInt(c1), keyExtractor.applyAsInt(c2));
	}

	/**
	* Accepts a function that extracts a {@code long} sort key from a type
	* {@code T}, and returns a {@code Comparator<T>} that compares by that
	* sort key.
	*
	* <p>The returned comparator is serializable if the specified function is
	* also serializable.
	*
	* @param <T> the type of element to be compared
	* @param keyExtractor the function used to extract the long sort key
	* @return a comparator that compares by an extracted key
	* @see #comparing(Function)
	* @throws NullPointerException if the argument is null
	* @since 1.8
	*/
	public static <T> Comparator<T> comparingLong(ToLongFunction<? super T> keyExtractor) {
	Objects.requireNonNull(keyExtractor);
	return (Comparator<T> & Serializable)
	(c1, c2) -> Long.compare(keyExtractor.applyAsLong(c1), keyExtractor.applyAsLong(c2));
	}

	/**
	* Accepts a function that extracts a {@code double} sort key from a type
	* {@code T}, and returns a {@code Comparator<T>} that compares by that
	* sort key.
	*
	* <p>The returned comparator is serializable if the specified function
	* is also serializable.
	*
	* @param <T> the type of element to be compared
	* @param keyExtractor the function used to extract the double sort key
	* @return a comparator that compares by an extracted key
	* @see #comparing(Function)
	* @throws NullPointerException if the argument is null
	* @since 1.8
	*/
	public static<T> Comparator<T> comparingDouble(ToDoubleFunction<? super T> keyExtractor) {
	Objects.requireNonNull(keyExtractor);
	return (Comparator<T> & Serializable)
	(c1, c2) -> Double.compare(keyExtractor.applyAsDouble(c1), keyExtractor.applyAsDouble(c2));
	}
	}

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