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	/*
	* Copyright (c) 2012, 2015, 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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	* questions.
	*/

	/*
	* This file is available under and governed by the GNU General Public
	* License version 2 only, as published by the Free Software Foundation.
	* However, the following notice accompanied the original version of this
	* file:
	*
	* Copyright (c) 2008-2012, Stephen Colebourne & Michael Nascimento Santos
	*
	* All rights reserved.
	*
	* Redistribution and use in source and binary forms, with or without
	* modification, are permitted provided that the following conditions are met:
	*
	* * Redistributions of source code must retain the above copyright notice,
	* this list of conditions and the following disclaimer.
	*
	* * Redistributions in binary form must reproduce the above copyright notice,
	* this list of conditions and the following disclaimer in the documentation
	* and/or other materials provided with the distribution.
	*
	* * Neither the name of JSR-310 nor the names of its contributors
	* may be used to endorse or promote products derived from this software
	* without specific prior written permission.
	*
	* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
	* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
	* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
	* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
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	* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
	* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
	* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
	* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
	* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
	*/
	package java.time;

	import static java.time.temporal.ChronoUnit.DAYS;
	import static java.time.temporal.ChronoUnit.MONTHS;
	import static java.time.temporal.ChronoUnit.YEARS;

	import java.io.DataInput;
	import java.io.DataOutput;
	import java.io.IOException;
	import java.io.InvalidObjectException;
	import java.io.ObjectInputStream;
	import java.io.Serializable;
	import java.time.chrono.ChronoLocalDate;
	import java.time.chrono.ChronoPeriod;
	import java.time.chrono.Chronology;
	import java.time.chrono.IsoChronology;
	import java.time.format.DateTimeParseException;
	import java.time.temporal.ChronoUnit;
	import java.time.temporal.Temporal;
	import java.time.temporal.TemporalAccessor;
	import java.time.temporal.TemporalAmount;
	import java.time.temporal.TemporalQueries;
	import java.time.temporal.TemporalUnit;
	import java.time.temporal.UnsupportedTemporalTypeException;
	import java.util.Arrays;
	import java.util.Collections;
	import java.util.List;
	import java.util.Objects;
	import java.util.regex.Matcher;
	import java.util.regex.Pattern;

	/**
	* A date-based amount of time in the ISO-8601 calendar system,
	* such as '2 years, 3 months and 4 days'.
	* <p>
	* This class models a quantity or amount of time in terms of years, months and days.
	* See {@link Duration} for the time-based equivalent to this class.
	* <p>
	* Durations and periods differ in their treatment of daylight savings time
	* when added to {@link ZonedDateTime}. A {@code Duration} will add an exact
	* number of seconds, thus a duration of one day is always exactly 24 hours.
	* By contrast, a {@code Period} will add a conceptual day, trying to maintain
	* the local time.
	* <p>
	* For example, consider adding a period of one day and a duration of one day to
	* 18:00 on the evening before a daylight savings gap. The {@code Period} will add
	* the conceptual day and result in a {@code ZonedDateTime} at 18:00 the following day.
	* By contrast, the {@code Duration} will add exactly 24 hours, resulting in a
	* {@code ZonedDateTime} at 19:00 the following day (assuming a one hour DST gap).
	* <p>
	* The supported units of a period are {@link ChronoUnit#YEARS YEARS},
	* {@link ChronoUnit#MONTHS MONTHS} and {@link ChronoUnit#DAYS DAYS}.
	* All three fields are always present, but may be set to zero.
	* <p>
	* The ISO-8601 calendar system is the modern civil calendar system used today
	* in most of the world. It is equivalent to the proleptic Gregorian calendar
	* system, in which today's rules for leap years are applied for all time.
	* <p>
	* The period is modeled as a directed amount of time, meaning that individual parts of the
	* period may be negative.
	*
	* <p>
	* This is a <a href="{@docRoot}/java/lang/doc-files/ValueBased.html">value-based</a>
	* class; use of identity-sensitive operations (including reference equality
	* ({@code ==}), identity hash code, or synchronization) on instances of
	* {@code Period} may have unpredictable results and should be avoided.
	* The {@code equals} method should be used for comparisons.
	*
	* @implSpec
	* This class is immutable and thread-safe.
	*
	* @since 1.8
	*/
	public final class Period
	implements ChronoPeriod, Serializable {

	/**
	* A constant for a period of zero.
	*/
	public static final Period ZERO = new Period(0, 0, 0);
	/**
	* Serialization version.
	*/
	private static final long serialVersionUID = -3587258372562876L;
	/**
	* The pattern for parsing.
	*/
	private static final Pattern PATTERN =
	Pattern.compile("([-+]?)P(?:([-+]?[0-9]+)Y)?(?:([-+]?[0-9]+)M)?(?:([-+]?[0-9]+)W)?(?:([-+]?[0-9]+)D)?", Pattern.CASE_INSENSITIVE);

	/**
	* The set of supported units.
	*/
	private static final List<TemporalUnit> SUPPORTED_UNITS =
	Collections.unmodifiableList(Arrays.<TemporalUnit>asList(YEARS, MONTHS, DAYS));

	/**
	* The number of years.
	*/
	private final int years;
	/**
	* The number of months.
	*/
	private final int months;
	/**
	* The number of days.
	*/
	private final int days;

	//-----------------------------------------------------------------------
	/**
	* Obtains a {@code Period} representing a number of years.
	* <p>
	* The resulting period will have the specified years.
	* The months and days units will be zero.
	*
	* @param years the number of years, positive or negative
	* @return the period of years, not null
	*/
	public static Period ofYears(int years) {
	return create(years, 0, 0);
	}

	/**
	* Obtains a {@code Period} representing a number of months.
	* <p>
	* The resulting period will have the specified months.
	* The years and days units will be zero.
	*
	* @param months the number of months, positive or negative
	* @return the period of months, not null
	*/
	public static Period ofMonths(int months) {
	return create(0, months, 0);
	}

	/**
	* Obtains a {@code Period} representing a number of weeks.
	* <p>
	* The resulting period will be day-based, with the amount of days
	* equal to the number of weeks multiplied by 7.
	* The years and months units will be zero.
	*
	* @param weeks the number of weeks, positive or negative
	* @return the period, with the input weeks converted to days, not null
	*/
	public static Period ofWeeks(int weeks) {
	return create(0, 0, Math.multiplyExact(weeks, 7));
	}

	/**
	* Obtains a {@code Period} representing a number of days.
	* <p>
	* The resulting period will have the specified days.
	* The years and months units will be zero.
	*
	* @param days the number of days, positive or negative
	* @return the period of days, not null
	*/
	public static Period ofDays(int days) {
	return create(0, 0, days);
	}

	//-----------------------------------------------------------------------
	/**
	* Obtains a {@code Period} representing a number of years, months and days.
	* <p>
	* This creates an instance based on years, months and days.
	*
	* @param years the amount of years, may be negative
	* @param months the amount of months, may be negative
	* @param days the amount of days, may be negative
	* @return the period of years, months and days, not null
	*/
	public static Period of(int years, int months, int days) {
	return create(years, months, days);
	}

	//-----------------------------------------------------------------------
	/**
	* Obtains an instance of {@code Period} from a temporal amount.
	* <p>
	* This obtains a period based on the specified amount.
	* A {@code TemporalAmount} represents an amount of time, which may be
	* date-based or time-based, which this factory extracts to a {@code Period}.
	* <p>
	* The conversion loops around the set of units from the amount and uses
	* the {@link ChronoUnit#YEARS YEARS}, {@link ChronoUnit#MONTHS MONTHS}
	* and {@link ChronoUnit#DAYS DAYS} units to create a period.
	* If any other units are found then an exception is thrown.
	* <p>
	* If the amount is a {@code ChronoPeriod} then it must use the ISO chronology.
	*
	* @param amount the temporal amount to convert, not null
	* @return the equivalent period, not null
	* @throws DateTimeException if unable to convert to a {@code Period}
	* @throws ArithmeticException if the amount of years, months or days exceeds an int
	*/
	public static Period from(TemporalAmount amount) {
	if (amount instanceof Period) {
	return (Period) amount;
	}
	if (amount instanceof ChronoPeriod) {
	if (IsoChronology.INSTANCE.equals(((ChronoPeriod) amount).getChronology()) == false) {
	throw new DateTimeException("Period requires ISO chronology: " + amount);
	}
	}
	Objects.requireNonNull(amount, "amount");
	int years = 0;
	int months = 0;
	int days = 0;
	for (TemporalUnit unit : amount.getUnits()) {
	long unitAmount = amount.get(unit);
	if (unit == ChronoUnit.YEARS) {
	years = Math.toIntExact(unitAmount);
	} else if (unit == ChronoUnit.MONTHS) {
	months = Math.toIntExact(unitAmount);
	} else if (unit == ChronoUnit.DAYS) {
	days = Math.toIntExact(unitAmount);
	} else {
	throw new DateTimeException("Unit must be Years, Months or Days, but was " + unit);
	}
	}
	return create(years, months, days);
	}

	//-----------------------------------------------------------------------
	/**
	* Obtains a {@code Period} from a text string such as {@code PnYnMnD}.
	* <p>
	* This will parse the string produced by {@code toString()} which is
	* based on the ISO-8601 period formats {@code PnYnMnD} and {@code PnW}.
	* <p>
	* The string starts with an optional sign, denoted by the ASCII negative
	* or positive symbol. If negative, the whole period is negated.
	* The ASCII letter "P" is next in upper or lower case.
	* There are then four sections, each consisting of a number and a suffix.
	* At least one of the four sections must be present.
	* The sections have suffixes in ASCII of "Y", "M", "W" and "D" for
	* years, months, weeks and days, accepted in upper or lower case.
	* The suffixes must occur in order.
	* The number part of each section must consist of ASCII digits.
	* The number may be prefixed by the ASCII negative or positive symbol.
	* The number must parse to an {@code int}.
	* <p>
	* The leading plus/minus sign, and negative values for other units are
	* not part of the ISO-8601 standard. In addition, ISO-8601 does not
	* permit mixing between the {@code PnYnMnD} and {@code PnW} formats.
	* Any week-based input is multiplied by 7 and treated as a number of days.
	* <p>
	* For example, the following are valid inputs:
	* <pre>
	* "P2Y" -- Period.ofYears(2)
	* "P3M" -- Period.ofMonths(3)
	* "P4W" -- Period.ofWeeks(4)
	* "P5D" -- Period.ofDays(5)
	* "P1Y2M3D" -- Period.of(1, 2, 3)
	* "P1Y2M3W4D" -- Period.of(1, 2, 25)
	* "P-1Y2M" -- Period.of(-1, 2, 0)
	* "-P1Y2M" -- Period.of(-1, -2, 0)
	* </pre>
	*
	* @param text the text to parse, not null
	* @return the parsed period, not null
	* @throws DateTimeParseException if the text cannot be parsed to a period
	*/
	public static Period parse(CharSequence text) {
	Objects.requireNonNull(text, "text");
	Matcher matcher = PATTERN.matcher(text);
	if (matcher.matches()) {
	int negate = ("-".equals(matcher.group(1)) ? -1 : 1);
	String yearMatch = matcher.group(2);
	String monthMatch = matcher.group(3);
	String weekMatch = matcher.group(4);
	String dayMatch = matcher.group(5);
	if (yearMatch != null \|\| monthMatch != null \|\| dayMatch != null \|\| weekMatch != null) {
	try {
	int years = parseNumber(text, yearMatch, negate);
	int months = parseNumber(text, monthMatch, negate);
	int weeks = parseNumber(text, weekMatch, negate);
	int days = parseNumber(text, dayMatch, negate);
	days = Math.addExact(days, Math.multiplyExact(weeks, 7));
	return create(years, months, days);
	} catch (NumberFormatException ex) {
	throw new DateTimeParseException("Text cannot be parsed to a Period", text, 0, ex);
	}
	}
	}
	throw new DateTimeParseException("Text cannot be parsed to a Period", text, 0);
	}

	private static int parseNumber(CharSequence text, String str, int negate) {
	if (str == null) {
	return 0;
	}
	int val = Integer.parseInt(str);
	try {
	return Math.multiplyExact(val, negate);
	} catch (ArithmeticException ex) {
	throw new DateTimeParseException("Text cannot be parsed to a Period", text, 0, ex);
	}
	}

	//-----------------------------------------------------------------------
	/**
	* Obtains a {@code Period} consisting of the number of years, months,
	* and days between two dates.
	* <p>
	* The start date is included, but the end date is not.
	* The period is calculated by removing complete months, then calculating
	* the remaining number of days, adjusting to ensure that both have the same sign.
	* The number of months is then split into years and months based on a 12 month year.
	* A month is considered if the end day-of-month is greater than or equal to the start day-of-month.
	* For example, from {@code 2010-01-15} to {@code 2011-03-18} is one year, two months and three days.
	* <p>
	* The result of this method can be a negative period if the end is before the start.
	* The negative sign will be the same in each of year, month and day.
	*
	* @param startDateInclusive the start date, inclusive, not null
	* @param endDateExclusive the end date, exclusive, not null
	* @return the period between this date and the end date, not null
	* @see ChronoLocalDate#until(ChronoLocalDate)
	*/
	public static Period between(LocalDate startDateInclusive, LocalDate endDateExclusive) {
	return startDateInclusive.until(endDateExclusive);
	}

	//-----------------------------------------------------------------------
	/**
	* Creates an instance.
	*
	* @param years the amount
	* @param months the amount
	* @param days the amount
	*/
	private static Period create(int years, int months, int days) {
	if ((years \| months \| days) == 0) {
	return ZERO;
	}
	return new Period(years, months, days);
	}

	/**
	* Constructor.
	*
	* @param years the amount
	* @param months the amount
	* @param days the amount
	*/
	private Period(int years, int months, int days) {
	this.years = years;
	this.months = months;
	this.days = days;
	}

	//-----------------------------------------------------------------------
	/**
	* Gets the value of the requested unit.
	* <p>
	* This returns a value for each of the three supported units,
	* {@link ChronoUnit#YEARS YEARS}, {@link ChronoUnit#MONTHS MONTHS} and
	* {@link ChronoUnit#DAYS DAYS}.
	* All other units throw an exception.
	*
	* @param unit the {@code TemporalUnit} for which to return the value
	* @return the long value of the unit
	* @throws DateTimeException if the unit is not supported
	* @throws UnsupportedTemporalTypeException if the unit is not supported
	*/
	@Override
	public long get(TemporalUnit unit) {
	if (unit == ChronoUnit.YEARS) {
	return getYears();
	} else if (unit == ChronoUnit.MONTHS) {
	return getMonths();
	} else if (unit == ChronoUnit.DAYS) {
	return getDays();
	} else {
	throw new UnsupportedTemporalTypeException("Unsupported unit: " + unit);
	}
	}

	/**
	* Gets the set of units supported by this period.
	* <p>
	* The supported units are {@link ChronoUnit#YEARS YEARS},
	* {@link ChronoUnit#MONTHS MONTHS} and {@link ChronoUnit#DAYS DAYS}.
	* They are returned in the order years, months, days.
	* <p>
	* This set can be used in conjunction with {@link #get(TemporalUnit)}
	* to access the entire state of the period.
	*
	* @return a list containing the years, months and days units, not null
	*/
	@Override
	public List<TemporalUnit> getUnits() {
	return SUPPORTED_UNITS;
	}

	/**
	* Gets the chronology of this period, which is the ISO calendar system.
	* <p>
	* The {@code Chronology} represents the calendar system in use.
	* The ISO-8601 calendar system is the modern civil calendar system used today
	* in most of the world. It is equivalent to the proleptic Gregorian calendar
	* system, in which today's rules for leap years are applied for all time.
	*
	* @return the ISO chronology, not null
	*/
	@Override
	public IsoChronology getChronology() {
	return IsoChronology.INSTANCE;
	}

	//-----------------------------------------------------------------------
	/**
	* Checks if all three units of this period are zero.
	* <p>
	* A zero period has the value zero for the years, months and days units.
	*
	* @return true if this period is zero-length
	*/
	public boolean isZero() {
	return (this == ZERO);
	}

	/**
	* Checks if any of the three units of this period are negative.
	* <p>
	* This checks whether the years, months or days units are less than zero.
	*
	* @return true if any unit of this period is negative
	*/
	public boolean isNegative() {
	return years < 0 \|\| months < 0 \|\| days < 0;
	}

	//-----------------------------------------------------------------------
	/**
	* Gets the amount of years of this period.
	* <p>
	* This returns the years unit.
	* <p>
	* The months unit is not automatically normalized with the years unit.
	* This means that a period of "15 months" is different to a period
	* of "1 year and 3 months".
	*
	* @return the amount of years of this period, may be negative
	*/
	public int getYears() {
	return years;
	}

	/**
	* Gets the amount of months of this period.
	* <p>
	* This returns the months unit.
	* <p>
	* The months unit is not automatically normalized with the years unit.
	* This means that a period of "15 months" is different to a period
	* of "1 year and 3 months".
	*
	* @return the amount of months of this period, may be negative
	*/
	public int getMonths() {
	return months;
	}

	/**
	* Gets the amount of days of this period.
	* <p>
	* This returns the days unit.
	*
	* @return the amount of days of this period, may be negative
	*/
	public int getDays() {
	return days;
	}

	//-----------------------------------------------------------------------
	/**
	* Returns a copy of this period with the specified amount of years.
	* <p>
	* This sets the amount of the years unit in a copy of this period.
	* The months and days units are unaffected.
	* <p>
	* The months unit is not automatically normalized with the years unit.
	* This means that a period of "15 months" is different to a period
	* of "1 year and 3 months".
	* <p>
	* This instance is immutable and unaffected by this method call.
	*
	* @param years the years to represent, may be negative
	* @return a {@code Period} based on this period with the requested years, not null
	*/
	public Period withYears(int years) {
	if (years == this.years) {
	return this;
	}
	return create(years, months, days);
	}

	/**
	* Returns a copy of this period with the specified amount of months.
	* <p>
	* This sets the amount of the months unit in a copy of this period.
	* The years and days units are unaffected.
	* <p>
	* The months unit is not automatically normalized with the years unit.
	* This means that a period of "15 months" is different to a period
	* of "1 year and 3 months".
	* <p>
	* This instance is immutable and unaffected by this method call.
	*
	* @param months the months to represent, may be negative
	* @return a {@code Period} based on this period with the requested months, not null
	*/
	public Period withMonths(int months) {
	if (months == this.months) {
	return this;
	}
	return create(years, months, days);
	}

	/**
	* Returns a copy of this period with the specified amount of days.
	* <p>
	* This sets the amount of the days unit in a copy of this period.
	* The years and months units are unaffected.
	* <p>
	* This instance is immutable and unaffected by this method call.
	*
	* @param days the days to represent, may be negative
	* @return a {@code Period} based on this period with the requested days, not null
	*/
	public Period withDays(int days) {
	if (days == this.days) {
	return this;
	}
	return create(years, months, days);
	}

	//-----------------------------------------------------------------------
	/**
	* Returns a copy of this period with the specified period added.
	* <p>
	* This operates separately on the years, months and days.
	* No normalization is performed.
	* <p>
	* For example, "1 year, 6 months and 3 days" plus "2 years, 2 months and 2 days"
	* returns "3 years, 8 months and 5 days".
	* <p>
	* The specified amount is typically an instance of {@code Period}.
	* Other types are interpreted using {@link Period#from(TemporalAmount)}.
	* <p>
	* This instance is immutable and unaffected by this method call.
	*
	* @param amountToAdd the amount to add, not null
	* @return a {@code Period} based on this period with the requested period added, not null
	* @throws DateTimeException if the specified amount has a non-ISO chronology or
	* contains an invalid unit
	* @throws ArithmeticException if numeric overflow occurs
	*/
	public Period plus(TemporalAmount amountToAdd) {
	Period isoAmount = Period.from(amountToAdd);
	return create(
	Math.addExact(years, isoAmount.years),
	Math.addExact(months, isoAmount.months),
	Math.addExact(days, isoAmount.days));
	}

	/**
	* Returns a copy of this period with the specified years added.
	* <p>
	* This adds the amount to the years unit in a copy of this period.
	* The months and days units are unaffected.
	* For example, "1 year, 6 months and 3 days" plus 2 years returns "3 years, 6 months and 3 days".
	* <p>
	* This instance is immutable and unaffected by this method call.
	*
	* @param yearsToAdd the years to add, positive or negative
	* @return a {@code Period} based on this period with the specified years added, not null
	* @throws ArithmeticException if numeric overflow occurs
	*/
	public Period plusYears(long yearsToAdd) {
	if (yearsToAdd == 0) {
	return this;
	}
	return create(Math.toIntExact(Math.addExact(years, yearsToAdd)), months, days);
	}

	/**
	* Returns a copy of this period with the specified months added.
	* <p>
	* This adds the amount to the months unit in a copy of this period.
	* The years and days units are unaffected.
	* For example, "1 year, 6 months and 3 days" plus 2 months returns "1 year, 8 months and 3 days".
	* <p>
	* This instance is immutable and unaffected by this method call.
	*
	* @param monthsToAdd the months to add, positive or negative
	* @return a {@code Period} based on this period with the specified months added, not null
	* @throws ArithmeticException if numeric overflow occurs
	*/
	public Period plusMonths(long monthsToAdd) {
	if (monthsToAdd == 0) {
	return this;
	}
	return create(years, Math.toIntExact(Math.addExact(months, monthsToAdd)), days);
	}

	/**
	* Returns a copy of this period with the specified days added.
	* <p>
	* This adds the amount to the days unit in a copy of this period.
	* The years and months units are unaffected.
	* For example, "1 year, 6 months and 3 days" plus 2 days returns "1 year, 6 months and 5 days".
	* <p>
	* This instance is immutable and unaffected by this method call.
	*
	* @param daysToAdd the days to add, positive or negative
	* @return a {@code Period} based on this period with the specified days added, not null
	* @throws ArithmeticException if numeric overflow occurs
	*/
	public Period plusDays(long daysToAdd) {
	if (daysToAdd == 0) {
	return this;
	}
	return create(years, months, Math.toIntExact(Math.addExact(days, daysToAdd)));
	}

	//-----------------------------------------------------------------------
	/**
	* Returns a copy of this period with the specified period subtracted.
	* <p>
	* This operates separately on the years, months and days.
	* No normalization is performed.
	* <p>
	* For example, "1 year, 6 months and 3 days" minus "2 years, 2 months and 2 days"
	* returns "-1 years, 4 months and 1 day".
	* <p>
	* The specified amount is typically an instance of {@code Period}.
	* Other types are interpreted using {@link Period#from(TemporalAmount)}.
	* <p>
	* This instance is immutable and unaffected by this method call.
	*
	* @param amountToSubtract the amount to subtract, not null
	* @return a {@code Period} based on this period with the requested period subtracted, not null
	* @throws DateTimeException if the specified amount has a non-ISO chronology or
	* contains an invalid unit
	* @throws ArithmeticException if numeric overflow occurs
	*/
	public Period minus(TemporalAmount amountToSubtract) {
	Period isoAmount = Period.from(amountToSubtract);
	return create(
	Math.subtractExact(years, isoAmount.years),
	Math.subtractExact(months, isoAmount.months),
	Math.subtractExact(days, isoAmount.days));
	}

	/**
	* Returns a copy of this period with the specified years subtracted.
	* <p>
	* This subtracts the amount from the years unit in a copy of this period.
	* The months and days units are unaffected.
	* For example, "1 year, 6 months and 3 days" minus 2 years returns "-1 years, 6 months and 3 days".
	* <p>
	* This instance is immutable and unaffected by this method call.
	*
	* @param yearsToSubtract the years to subtract, positive or negative
	* @return a {@code Period} based on this period with the specified years subtracted, not null
	* @throws ArithmeticException if numeric overflow occurs
	*/
	public Period minusYears(long yearsToSubtract) {
	return (yearsToSubtract == Long.MIN_VALUE ? plusYears(Long.MAX_VALUE).plusYears(1) : plusYears(-yearsToSubtract));
	}

	/**
	* Returns a copy of this period with the specified months subtracted.
	* <p>
	* This subtracts the amount from the months unit in a copy of this period.
	* The years and days units are unaffected.
	* For example, "1 year, 6 months and 3 days" minus 2 months returns "1 year, 4 months and 3 days".
	* <p>
	* This instance is immutable and unaffected by this method call.
	*
	* @param monthsToSubtract the years to subtract, positive or negative
	* @return a {@code Period} based on this period with the specified months subtracted, not null
	* @throws ArithmeticException if numeric overflow occurs
	*/
	public Period minusMonths(long monthsToSubtract) {
	return (monthsToSubtract == Long.MIN_VALUE ? plusMonths(Long.MAX_VALUE).plusMonths(1) : plusMonths(-monthsToSubtract));
	}

	/**
	* Returns a copy of this period with the specified days subtracted.
	* <p>
	* This subtracts the amount from the days unit in a copy of this period.
	* The years and months units are unaffected.
	* For example, "1 year, 6 months and 3 days" minus 2 days returns "1 year, 6 months and 1 day".
	* <p>
	* This instance is immutable and unaffected by this method call.
	*
	* @param daysToSubtract the months to subtract, positive or negative
	* @return a {@code Period} based on this period with the specified days subtracted, not null
	* @throws ArithmeticException if numeric overflow occurs
	*/
	public Period minusDays(long daysToSubtract) {
	return (daysToSubtract == Long.MIN_VALUE ? plusDays(Long.MAX_VALUE).plusDays(1) : plusDays(-daysToSubtract));
	}

	//-----------------------------------------------------------------------
	/**
	* Returns a new instance with each element in this period multiplied
	* by the specified scalar.
	* <p>
	* This returns a period with each of the years, months and days units
	* individually multiplied.
	* For example, a period of "2 years, -3 months and 4 days" multiplied by
	* 3 will return "6 years, -9 months and 12 days".
	* No normalization is performed.
	*
	* @param scalar the scalar to multiply by, not null
	* @return a {@code Period} based on this period with the amounts multiplied by the scalar, not null
	* @throws ArithmeticException if numeric overflow occurs
	*/
	public Period multipliedBy(int scalar) {
	if (this == ZERO \|\| scalar == 1) {
	return this;
	}
	return create(
	Math.multiplyExact(years, scalar),
	Math.multiplyExact(months, scalar),
	Math.multiplyExact(days, scalar));
	}

	/**
	* Returns a new instance with each amount in this period negated.
	* <p>
	* This returns a period with each of the years, months and days units
	* individually negated.
	* For example, a period of "2 years, -3 months and 4 days" will be
	* negated to "-2 years, 3 months and -4 days".
	* No normalization is performed.
	*
	* @return a {@code Period} based on this period with the amounts negated, not null
	* @throws ArithmeticException if numeric overflow occurs, which only happens if
	* one of the units has the value {@code Long.MIN_VALUE}
	*/
	public Period negated() {
	return multipliedBy(-1);
	}

	//-----------------------------------------------------------------------
	/**
	* Returns a copy of this period with the years and months normalized.
	* <p>
	* This normalizes the years and months units, leaving the days unit unchanged.
	* The months unit is adjusted to have an absolute value less than 11,
	* with the years unit being adjusted to compensate. For example, a period of
	* "1 Year and 15 months" will be normalized to "2 years and 3 months".
	* <p>
	* The sign of the years and months units will be the same after normalization.
	* For example, a period of "1 year and -25 months" will be normalized to
	* "-1 year and -1 month".
	* <p>
	* This instance is immutable and unaffected by this method call.
	*
	* @return a {@code Period} based on this period with excess months normalized to years, not null
	* @throws ArithmeticException if numeric overflow occurs
	*/
	public Period normalized() {
	long totalMonths = toTotalMonths();
	long splitYears = totalMonths / 12;
	int splitMonths = (int) (totalMonths % 12); // no overflow
	if (splitYears == years && splitMonths == months) {
	return this;
	}
	return create(Math.toIntExact(splitYears), splitMonths, days);
	}

	/**
	* Gets the total number of months in this period.
	* <p>
	* This returns the total number of months in the period by multiplying the
	* number of years by 12 and adding the number of months.
	* <p>
	* This instance is immutable and unaffected by this method call.
	*
	* @return the total number of months in the period, may be negative
	*/
	public long toTotalMonths() {
	return years * 12L + months; // no overflow
	}

	//-------------------------------------------------------------------------
	/**
	* Adds this period to the specified temporal object.
	* <p>
	* This returns a temporal object of the same observable type as the input
	* with this period added.
	* If the temporal has a chronology, it must be the ISO chronology.
	* <p>
	* In most cases, it is clearer to reverse the calling pattern by using
	* {@link Temporal#plus(TemporalAmount)}.
	* <pre>
	* // these two lines are equivalent, but the second approach is recommended
	* dateTime = thisPeriod.addTo(dateTime);
	* dateTime = dateTime.plus(thisPeriod);
	* </pre>
	* <p>
	* The calculation operates as follows.
	* First, the chronology of the temporal is checked to ensure it is ISO chronology or null.
	* Second, if the months are zero, the years are added if non-zero, otherwise
	* the combination of years and months is added if non-zero.
	* Finally, any days are added.
	* <p>
	* This approach ensures that a partial period can be added to a partial date.
	* For example, a period of years and/or months can be added to a {@code YearMonth},
	* but a period including days cannot.
	* The approach also adds years and months together when necessary, which ensures
	* correct behaviour at the end of the month.
	* <p>
	* This instance is immutable and unaffected by this method call.
	*
	* @param temporal the temporal object to adjust, not null
	* @return an object of the same type with the adjustment made, not null
	* @throws DateTimeException if unable to add
	* @throws ArithmeticException if numeric overflow occurs
	*/
	@Override
	public Temporal addTo(Temporal temporal) {
	validateChrono(temporal);
	if (months == 0) {
	if (years != 0) {
	temporal = temporal.plus(years, YEARS);
	}
	} else {
	long totalMonths = toTotalMonths();
	if (totalMonths != 0) {
	temporal = temporal.plus(totalMonths, MONTHS);
	}
	}
	if (days != 0) {
	temporal = temporal.plus(days, DAYS);
	}
	return temporal;
	}

	/**
	* Subtracts this period from the specified temporal object.
	* <p>
	* This returns a temporal object of the same observable type as the input
	* with this period subtracted.
	* If the temporal has a chronology, it must be the ISO chronology.
	* <p>
	* In most cases, it is clearer to reverse the calling pattern by using
	* {@link Temporal#minus(TemporalAmount)}.
	* <pre>
	* // these two lines are equivalent, but the second approach is recommended
	* dateTime = thisPeriod.subtractFrom(dateTime);
	* dateTime = dateTime.minus(thisPeriod);
	* </pre>
	* <p>
	* The calculation operates as follows.
	* First, the chronology of the temporal is checked to ensure it is ISO chronology or null.
	* Second, if the months are zero, the years are subtracted if non-zero, otherwise
	* the combination of years and months is subtracted if non-zero.
	* Finally, any days are subtracted.
	* <p>
	* This approach ensures that a partial period can be subtracted from a partial date.
	* For example, a period of years and/or months can be subtracted from a {@code YearMonth},
	* but a period including days cannot.
	* The approach also subtracts years and months together when necessary, which ensures
	* correct behaviour at the end of the month.
	* <p>
	* This instance is immutable and unaffected by this method call.
	*
	* @param temporal the temporal object to adjust, not null
	* @return an object of the same type with the adjustment made, not null
	* @throws DateTimeException if unable to subtract
	* @throws ArithmeticException if numeric overflow occurs
	*/
	@Override
	public Temporal subtractFrom(Temporal temporal) {
	validateChrono(temporal);
	if (months == 0) {
	if (years != 0) {
	temporal = temporal.minus(years, YEARS);
	}
	} else {
	long totalMonths = toTotalMonths();
	if (totalMonths != 0) {
	temporal = temporal.minus(totalMonths, MONTHS);
	}
	}
	if (days != 0) {
	temporal = temporal.minus(days, DAYS);
	}
	return temporal;
	}

	/**
	* Validates that the temporal has the correct chronology.
	*/
	private void validateChrono(TemporalAccessor temporal) {
	Objects.requireNonNull(temporal, "temporal");
	Chronology temporalChrono = temporal.query(TemporalQueries.chronology());
	if (temporalChrono != null && IsoChronology.INSTANCE.equals(temporalChrono) == false) {
	throw new DateTimeException("Chronology mismatch, expected: ISO, actual: " + temporalChrono.getId());
	}
	}

	//-----------------------------------------------------------------------
	/**
	* Checks if this period is equal to another period.
	* <p>
	* The comparison is based on the type {@code Period} and each of the three amounts.
	* To be equal, the years, months and days units must be individually equal.
	* Note that this means that a period of "15 Months" is not equal to a period
	* of "1 Year and 3 Months".
	*
	* @param obj the object to check, null returns false
	* @return true if this is equal to the other period
	*/
	@Override
	public boolean equals(Object obj) {
	if (this == obj) {
	return true;
	}
	if (obj instanceof Period) {
	Period other = (Period) obj;
	return years == other.years &&
	months == other.months &&
	days == other.days;
	}
	return false;
	}

	/**
	* A hash code for this period.
	*
	* @return a suitable hash code
	*/
	@Override
	public int hashCode() {
	return years + Integer.rotateLeft(months, 8) + Integer.rotateLeft(days, 16);
	}

	//-----------------------------------------------------------------------
	/**
	* Outputs this period as a {@code String}, such as {@code P6Y3M1D}.
	* <p>
	* The output will be in the ISO-8601 period format.
	* A zero period will be represented as zero days, 'P0D'.
	*
	* @return a string representation of this period, not null
	*/
	@Override
	public String toString() {
	if (this == ZERO) {
	return "P0D";
	} else {
	StringBuilder buf = new StringBuilder();
	buf.append('P');
	if (years != 0) {
	buf.append(years).append('Y');
	}
	if (months != 0) {
	buf.append(months).append('M');
	}
	if (days != 0) {
	buf.append(days).append('D');
	}
	return buf.toString();
	}
	}

	//-----------------------------------------------------------------------
	/**
	* Writes the object using a
	* <a href="../../serialized-form.html#java.time.Ser">dedicated serialized form</a>.
	* @serialData
	* <pre>
	* out.writeByte(14); // identifies a Period
	* out.writeInt(years);
	* out.writeInt(months);
	* out.writeInt(days);
	* </pre>
	*
	* @return the instance of {@code Ser}, not null
	*/
	private Object writeReplace() {
	return new Ser(Ser.PERIOD_TYPE, this);
	}

	/**
	* Defend against malicious streams.
	*
	* @param s the stream to read
	* @throws java.io.InvalidObjectException always
	*/
	private void readObject(ObjectInputStream s) throws InvalidObjectException {
	throw new InvalidObjectException("Deserialization via serialization delegate");
	}

	void writeExternal(DataOutput out) throws IOException {
	out.writeInt(years);
	out.writeInt(months);
	out.writeInt(days);
	}

	static Period readExternal(DataInput in) throws IOException {
	int years = in.readInt();
	int months = in.readInt();
	int days = in.readInt();
	return Period.of(years, months, days);
	}

	}

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