OpenPyXL 3.0.7
  • 教程
  • 简单用法
  • 性能
  • 优化模式
  • 插入和删除行和列,移动单元格范围
  • 操纵 Pandas 和 NumPy
  • 图表
  • 注释
  • 操控样式
  • 额外工作表特性
  • 条件格式化
  • 数据透视表
  • 打印设置
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  • 验证单元格
  • 定义名称
  • 工作表表格
  • 剖析公式
  • 日期和时间
  • 保护
  • 开发
  • openpyxl 包
  • 3.0.7 (2021-03-09)
  • 3.0.6 (2021-01-14)
  • 3.0.5 (2020-08-21)
  • 3.0.4 (2020-06-24)
  • 3.0.3 (2020-01-20)
  • 3.0.2 (2019-11-25)
  • 3.0.1 (2019-11-14)
  • 3.0.0 (2019-09-25)
  • 2.6.4 (2019-09-25)
  • 2.6.3 (2019-08-19)
  • 2.6.2 (2019-03-29)
  • 2.6.1 (2019-03-04)
  • 2.6.0 (2019-02-06)
  • 2.6.-b1 (2019-01-08)
  • 2.6-a1 (2018-11-21)
  • 2.5.14 (2019-01-23)
  • 2.5.13 (brown bag)
  • 2.5.12 (2018-11-29)
  • 2.5.11 (2018-11-21)
  • 2.5.10 (2018-11-13)
  • 2.5.9 (2018-10-19)
  • 2.5.8 (2018-09-25)
  • 2.5.7 (2018-09-13)
  • 2.5.6 (2018-08-30)
  • 2.5.5 (2018-08-04)
  • 2.5.4 (2018-06-07)
  • 2.5.3 (2018-04-18)
  • 2.5.2 (2018-04-06)
  • 2.5.1 (2018-03-12)
  • 2.5.0 (2018-01-24)
  • 2.5.0-b2 (2018-01-19)
  • 2.5.0-b1 (2017-10-19)
  • 2.5.0-a3 (2017-08-14)
  • 2.5.0-a2 (2017-06-25)
  • 2.5.0-a1 (2017-05-30)
  • 2.4.11 (2018-01-24)
  • 2.4.10 (2018-01-19)
  • 2.4.9 (2017-10-19)
  • 2.4.8 (2017-05-30)
  • 2.4.7 (2017-04-24)
  • 2.4.6 (2017-04-14)
  • 2.4.5 (2017-03-07)
  • 2.4.4 (2017-02-23)
  • 2.4.3 (未发行)
  • 2.4.2 (2017-01-31)
  • 2.4.1 (2016-11-23)
  • 2.4.0 (2016-09-15)
  • 2.4.0-b1 (2016-06-08)
  • 2.4.0-a1 (2016-04-11)
  • 2.3.5 (2016-04-11)
  • 2.3.4 (2016-03-16)
  • 2.3.3 (2016-01-18)
  • 2.3.2 (2015-12-07)
  • 2.3.1 (2015-11-20)
  • 2.3.0 (2015-10-20)
  • 2.3.0-b2 (2015-09-04)
  • 2.3.0-b1 (2015-06-29)
  • 2.2.6 (未发行)
  • 2.2.5 (2015-06-29)
  • 2.2.4 (2015-06-17)
  • 2.2.3 (2015-05-26)
  • 2.2.2 (2015-04-28)
  • 2.2.1 (2015-03-31)
  • 2.2.0 (2015-03-11)
  • 2.2.0-b1 (2015-02-18)
  • 2.1.5 (2015-02-18)
  • 2.1.4 (2014-12-16)
  • 2.1.3 (2014-12-09)
  • 2.1.2 (2014-10-23)
  • 2.1.1 (2014-10-08)
  • 2.1.0 (2014-09-21)
  • 2.0.5 (2014-08-08)
  • 2.0.4 (2014-06-25)
  • 2.0.3 (2014-05-22)
  • 2.0.2 (2014-05-13)
  • 2.0.1 (2014-05-13) brown bag
  • 2.0.0 (2014-05-13) brown bag
  • 1.8.6 (2014-05-05)
  • 1.8.5 (2014-03-25)
  • 1.8.4 (2014-02-25)
  • 1.8.3 (2014-02-09)
  • 1.8.2 (2014-01-17)
  • 1.8.1 (2014-01-14)
  • 1.8.0 (2014-01-08)
  • 1.7.0 (2013-10-31)
  • Source code for datetime

    """Concrete date/time and related types.
    See http://www.iana.org/time-zones/repository/tz-link.html for
    time zone and DST data sources.
    """
    import time as _time
    import math as _math
    import sys
    def _cmp(x, y):
        return 0 if x == y else 1 if x > y else -1
    MINYEAR = 1
    MAXYEAR = 9999
    _MAXORDINAL = 3652059  # date.max.toordinal()
    # Utility functions, adapted from Python's Demo/classes/Dates.py, which
    # also assumes the current Gregorian calendar indefinitely extended in
    # both directions.  Difference:  Dates.py calls January 1 of year 0 day
    # number 1.  The code here calls January 1 of year 1 day number 1.  This is
    # to match the definition of the "proleptic Gregorian" calendar in Dershowitz
    # and Reingold's "Calendrical Calculations", where it's the base calendar
    # for all computations.  See the book for algorithms for converting between
    # proleptic Gregorian ordinals and many other calendar systems.
    # -1 is a placeholder for indexing purposes.
    _DAYS_IN_MONTH = [-1, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
    _DAYS_BEFORE_MONTH = [-1]  # -1 is a placeholder for indexing purposes.
    dbm = 0
    for dim in _DAYS_IN_MONTH[1:]:
        _DAYS_BEFORE_MONTH.append(dbm)
        dbm += dim
    del dbm, dim
    def _is_leap(year):
        "year -> 1 if leap year, else 0."
        return year % 4 == 0 and (year % 100 != 0 or year % 400 == 0)
    def _days_before_year(year):
        "year -> number of days before January 1st of year."
        y = year - 1
        return y*365 + y//4 - y//100 + y//400
    def _days_in_month(year, month):
        "year, month -> number of days in that month in that year."
        assert 1 <= month <= 12, month
        if month == 2 and _is_leap(year):
            return 29
        return _DAYS_IN_MONTH[month]
    def _days_before_month(year, month):
        "year, month -> number of days in year preceding first day of month."
        assert 1 <= month <= 12, 'month must be in 1..12'
        return _DAYS_BEFORE_MONTH[month] + (month > 2 and _is_leap(year))
    def _ymd2ord(year, month, day):
        "year, month, day -> ordinal, considering 01-Jan-0001 as day 1."
        assert 1 <= month <= 12, 'month must be in 1..12'
        dim = _days_in_month(year, month)
        assert 1 <= day <= dim, ('day must be in 1..%d' % dim)
        return (_days_before_year(year) +
                _days_before_month(year, month) +
                day)
    _DI400Y = _days_before_year(401)    # number of days in 400 years
    _DI100Y = _days_before_year(101)    #    "    "   "   " 100   "
    _DI4Y   = _days_before_year(5)      #    "    "   "   "   4   "
    # A 4-year cycle has an extra leap day over what we'd get from pasting
    # together 4 single years.
    assert _DI4Y == 4 * 365 + 1
    # Similarly, a 400-year cycle has an extra leap day over what we'd get from
    # pasting together 4 100-year cycles.
    assert _DI400Y == 4 * _DI100Y + 1
    # OTOH, a 100-year cycle has one fewer leap day than we'd get from
    # pasting together 25 4-year cycles.
    assert _DI100Y == 25 * _DI4Y - 1
    def _ord2ymd(n):
        "ordinal -> (year, month, day), considering 01-Jan-0001 as day 1."
        # n is a 1-based index, starting at 1-Jan-1.  The pattern of leap years
        # repeats exactly every 400 years.  The basic strategy is to find the
        # closest 400-year boundary at or before n, then work with the offset
        # from that boundary to n.  Life is much clearer if we subtract 1 from
        # n first -- then the values of n at 400-year boundaries are exactly
        # those divisible by _DI400Y:
        #
        #     D  M   Y            n              n-1
        #     -- --- ----        ----------     ----------------
        #     31 Dec -400        -_DI400Y       -_DI400Y -1
        #      1 Jan -399         -_DI400Y +1   -_DI400Y      400-year boundary
        #     ...
        #     30 Dec  000        -1             -2
        #     31 Dec  000         0             -1
        #      1 Jan  001         1              0            400-year boundary
        #      2 Jan  001         2              1
        #      3 Jan  001         3              2
        #     ...
        #     31 Dec  400         _DI400Y        _DI400Y -1
        #      1 Jan  401         _DI400Y +1     _DI400Y      400-year boundary
        n -= 1
        n400, n = divmod(n, _DI400Y)
        year = n400 * 400 + 1   # ..., -399, 1, 401, ...
        # Now n is the (non-negative) offset, in days, from January 1 of year, to
        # the desired date.  Now compute how many 100-year cycles precede n.
        # Note that it's possible for n100 to equal 4!  In that case 4 full
        # 100-year cycles precede the desired day, which implies the desired
        # day is December 31 at the end of a 400-year cycle.
        n100, n = divmod(n, _DI100Y)
        # Now compute how many 4-year cycles precede it.
        n4, n = divmod(n, _DI4Y)
        # And now how many single years.  Again n1 can be 4, and again meaning
        # that the desired day is December 31 at the end of the 4-year cycle.
        n1, n = divmod(n, 365)
        year += n100 * 100 + n4 * 4 + n1
        if n1 == 4 or n100 == 4:
            assert n == 0
            return year-1, 12, 31
        # Now the year is correct, and n is the offset from January 1.  We find
        # the month via an estimate that's either exact or one too large.
        leapyear = n1 == 3 and (n4 != 24 or n100 == 3)
        assert leapyear == _is_leap(year)
        month = (n + 50) >> 5
        preceding = _DAYS_BEFORE_MONTH[month] + (month > 2 and leapyear)
        if preceding > n:  # estimate is too large
            month -= 1
            preceding -= _DAYS_IN_MONTH[month] + (month == 2 and leapyear)
        n -= preceding
        assert 0 <= n < _days_in_month(year, month)
        # Now the year and month are correct, and n is the offset from the
        # start of that month:  we're done!
        return year, month, n+1
    # Month and day names.  For localized versions, see the calendar module.
    _MONTHNAMES = [None, "Jan", "Feb", "Mar", "Apr", "May", "Jun",
                         "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"]
    _DAYNAMES = [None, "Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun"]
    def _build_struct_time(y, m, d, hh, mm, ss, dstflag):
        wday = (_ymd2ord(y, m, d) + 6) % 7
        dnum = _days_before_month(y, m) + d
        return _time.struct_time((y, m, d, hh, mm, ss, wday, dnum, dstflag))
    def _format_time(hh, mm, ss, us, timespec='auto'):
        specs = {
            'hours': '{:02d}',
            'minutes': '{:02d}:{:02d}',
            'seconds': '{:02d}:{:02d}:{:02d}',
            'milliseconds': '{:02d}:{:02d}:{:02d}.{:03d}',
            'microseconds': '{:02d}:{:02d}:{:02d}.{:06d}'
        }
        if timespec == 'auto':
            # Skip trailing microseconds when us==0.
            timespec = 'microseconds' if us else 'seconds'
        elif timespec == 'milliseconds':
            us //= 1000
        try:
            fmt = specs[timespec]
        except KeyError:
            raise ValueError('Unknown timespec value')
        else:
            return fmt.format(hh, mm, ss, us)
    def _format_offset(off):
        s = ''
        if off is not None:
            if off.days < 0:
                sign = "-"
                off = -off
            else:
                sign = "+"
            hh, mm = divmod(off, timedelta(hours=1))
            mm, ss = divmod(mm, timedelta(minutes=1))
            s += "%s%02d:%02d" % (sign, hh, mm)
            if ss or ss.microseconds:
                s += ":%02d" % ss.seconds
                if ss.microseconds:
                    s += '.%06d' % ss.microseconds
        return s
    # Correctly substitute for %z and %Z escapes in strftime formats.
    def _wrap_strftime(object, format, timetuple):
        # Don't call utcoffset() or tzname() unless actually needed.
        freplace = None  # the string to use for %f
        zreplace = None  # the string to use for %z
        Zreplace = None  # the string to use for %Z
        # Scan format for %z and %Z escapes, replacing as needed.
        newformat = []
        push = newformat.append
        i, n = 0, len(format)
        while i < n:
            ch = format[i]
            i += 1
            if ch == '%':
                if i < n:
                    ch = format[i]
                    i += 1
                    if ch == 'f':
                        if freplace is None:
                            freplace = '%06d' % getattr(object,
                                                        'microsecond', 0)
                        newformat.append(freplace)
                    elif ch == 'z':
                        if zreplace is None:
                            zreplace = ""
                            if hasattr(object, "utcoffset"):
                                offset = object.utcoffset()
                                if offset is not None:
                                    sign = '+'
                                    if offset.days < 0:
                                        offset = -offset
                                        sign = '-'
                                    h, rest = divmod(offset, timedelta(hours=1))
                                    m, rest = divmod(rest, timedelta(minutes=1))
                                    s = rest.seconds
                                    u = offset.microseconds
                                    if u:
                                        zreplace = '%c%02d%02d%02d.%06d' % (sign, h, m, s, u)
                                    elif s:
                                        zreplace = '%c%02d%02d%02d' % (sign, h, m, s)
                                    else:
                                        zreplace = '%c%02d%02d' % (sign, h, m)
                        assert '%' not in zreplace
                        newformat.append(zreplace)
                    elif ch == 'Z':
                        if Zreplace is None:
                            Zreplace = ""
                            if hasattr(object, "tzname"):
                                s = object.tzname()
                                if s is not None:
                                    # strftime is going to have at this: escape %
                                    Zreplace = s.replace('%', '%%')
                        newformat.append(Zreplace)
                    else:
                        push('%')
                        push(ch)
                else:
                    push('%')
            else:
                push(ch)
        newformat = "".join(newformat)
        return _time.strftime(newformat, timetuple)
    # Helpers for parsing the result of isoformat()
    def _parse_isoformat_date(dtstr):
        # It is assumed that this function will only be called with a
        # string of length exactly 10, and (though this is not used) ASCII-only
        year = int(dtstr[0:4])
        if dtstr[4] != '-':
            raise ValueError('Invalid date separator: %s' % dtstr[4])
        month = int(dtstr[5:7])
        if dtstr[7] != '-':
            raise ValueError('Invalid date separator')
        day = int(dtstr[8:10])
        return [year, month, day]
    def _parse_hh_mm_ss_ff(tstr):
        # Parses things of the form HH[:MM[:SS[.fff[fff]]]]
        len_str = len(tstr)
        time_comps = [0, 0, 0, 0]
        pos = 0
        for comp in range(0, 3):
            if (len_str - pos) < 2:
                raise ValueError('Incomplete time component')
            time_comps[comp] = int(tstr[pos:pos+2])
            pos += 2
            next_char = tstr[pos:pos+1]
            if not next_char or comp >= 2:
                break
            if next_char != ':':
                raise ValueError('Invalid time separator: %c' % next_char)
            pos += 1
        if pos < len_str:
            if tstr[pos] != '.':
                raise ValueError('Invalid microsecond component')
            else:
                pos += 1
                len_remainder = len_str - pos
                if len_remainder not in (3, 6):
                    raise ValueError('Invalid microsecond component')
                time_comps[3] = int(tstr[pos:])
                if len_remainder == 3:
                    time_comps[3] *= 1000
        return time_comps
    def _parse_isoformat_time(tstr):
        # Format supported is HH[:MM[:SS[.fff[fff]]]][+HH:MM[:SS[.ffffff]]]
        len_str = len(tstr)
        if len_str < 2:
            raise ValueError('Isoformat time too short')
        # This is equivalent to re.search('[+-]', tstr), but faster
        tz_pos = (tstr.find('-') + 1 or tstr.find('+') + 1)
        timestr = tstr[:tz_pos-1] if tz_pos > 0 else tstr
        time_comps = _parse_hh_mm_ss_ff(timestr)
        tzi = None
        if tz_pos > 0:
            tzstr = tstr[tz_pos:]
            # Valid time zone strings are:
            # HH:MM               len: 5
            # HH:MM:SS            len: 8
            # HH:MM:SS.ffffff     len: 15
            if len(tzstr) not in (5, 8, 15):
                raise ValueError('Malformed time zone string')
            tz_comps = _parse_hh_mm_ss_ff(tzstr)
            if all(x == 0 for x in tz_comps):
                tzi = timezone.utc
            else:
                tzsign = -1 if tstr[tz_pos - 1] == '-' else 1
                td = timedelta(hours=tz_comps[0], minutes=tz_comps[1],
                               seconds=tz_comps[2], microseconds=tz_comps[3])
                tzi = timezone(tzsign * td)
        time_comps.append(tzi)
        return time_comps
    # Just raise TypeError if the arg isn't None or a string.
    def _check_tzname(name):
        if name is not None and not isinstance(name, str):
            raise TypeError("tzinfo.tzname() must return None or string, "
                            "not '%s'" % type(name))
    # name is the offset-producing method, "utcoffset" or "dst".
    # offset is what it returned.
    # If offset isn't None or timedelta, raises TypeError.
    # If offset is None, returns None.
    # Else offset is checked for being in range.
    # If it is, its integer value is returned.  Else ValueError is raised.
    def _check_utc_offset(name, offset):
        assert name in ("utcoffset", "dst")
        if offset is None:
            return
        if not isinstance(offset, timedelta):
            raise TypeError("tzinfo.%s() must return None "
                            "or timedelta, not '%s'" % (name, type(offset)))
        if not -timedelta(1) < offset < timedelta(1):
            raise ValueError("%s()=%s, must be strictly between "
                             "-timedelta(hours=24) and timedelta(hours=24)" %
                             (name, offset))
    def _check_int_field(value):
        if isinstance(value, int):
            return value
        if not isinstance(value, float):
            try:
                value = value.__int__()
            except AttributeError:
                pass
            else:
                if isinstance(value, int):
                    return value
                raise TypeError('__int__ returned non-int (type %s)' %
                                type(value).__name__)
            raise TypeError('an integer is required (got type %s)' %
                            type(value).__name__)
        raise TypeError('integer argument expected, got float')
    def _check_date_fields(year, month, day):
        year = _check_int_field(year)
        month = _check_int_field(month)
        day = _check_int_field(day)
        if not MINYEAR <= year <= MAXYEAR:
            raise ValueError('year must be in %d..%d' % (MINYEAR, MAXYEAR), year)
        if not 1 <= month <= 12:
            raise ValueError('month must be in 1..12', month)
        dim = _days_in_month(year, month)
        if not 1 <= day <= dim:
            raise ValueError('day must be in 1..%d' % dim, day)
        return year, month, day
    def _check_time_fields(hour, minute, second, microsecond, fold):
        hour = _check_int_field(hour)
        minute = _check_int_field(minute)
        second = _check_int_field(second)
        microsecond = _check_int_field(microsecond)
        if not 0 <= hour <= 23:
            raise ValueError('hour must be in 0..23', hour)
        if not 0 <= minute <= 59:
            raise ValueError('minute must be in 0..59', minute)
        if not 0 <= second <= 59:
            raise ValueError('second must be in 0..59', second)
        if not 0 <= microsecond <= 999999:
            raise ValueError('microsecond must be in 0..999999', microsecond)
        if fold not in (0, 1):
            raise ValueError('fold must be either 0 or 1', fold)
        return hour, minute, second, microsecond, fold
    def _check_tzinfo_arg(tz):
        if tz is not None and not isinstance(tz, tzinfo):
            raise TypeError("tzinfo argument must be None or of a tzinfo subclass")
    def _cmperror(x, y):
        raise TypeError("can't compare '%s' to '%s'" % (
                        type(x).__name__, type(y).__name__))
    def _divide_and_round(a, b):
        """divide a by b and round result to the nearest integer
        When the ratio is exactly half-way between two integers,
        the even integer is returned.
        """
        # Based on the reference implementation for divmod_near
        # in Objects/longobject.c.
        q, r = divmod(a, b)
        # round up if either r / b > 0.5, or r / b == 0.5 and q is odd.
        # The expression r / b > 0.5 is equivalent to 2 * r > b if b is
        # positive, 2 * r < b if b negative.
        r *= 2
        greater_than_half = r > b if b > 0 else r < b
        if greater_than_half or r == b and q % 2 == 1:
            q += 1
        return q
    class timedelta:
        """Represent the difference between two datetime objects.
        Supported operators:
        - add, subtract timedelta
        - unary plus, minus, abs
        - compare to timedelta
        - multiply, divide by int
        In addition, datetime supports subtraction of two datetime objects
        returning a timedelta, and addition or subtraction of a datetime
        and a timedelta giving a datetime.
        Representation: (days, seconds, microseconds).  Why?  Because I
        felt like it.
        """
        __slots__ = '_days', '_seconds', '_microseconds', '_hashcode'
        def __new__(cls, days=0, seconds=0, microseconds=0,
                    milliseconds=0, minutes=0, hours=0, weeks=0):
            # Doing this efficiently and accurately in C is going to be difficult
            # and error-prone, due to ubiquitous overflow possibilities, and that
            # C double doesn't have enough bits of precision to represent
            # microseconds over 10K years faithfully.  The code here tries to make
            # explicit where go-fast assumptions can be relied on, in order to
            # guide the C implementation; it's way more convoluted than speed-
            # ignoring auto-overflow-to-long idiomatic Python could be.
            # XXX Check that all inputs are ints or floats.
            # Final values, all integer.
            # s and us fit in 32-bit signed ints; d isn't bounded.
            d = s = us = 0
            # Normalize everything to days, seconds, microseconds.
            days += weeks*7
            seconds += minutes*60 + hours*3600
            microseconds += milliseconds*1000
            # Get rid of all fractions, and normalize s and us.
            # Take a deep breath <wink>.
            if isinstance(days, float):
                dayfrac, days = _math.modf(days)
                daysecondsfrac, daysecondswhole = _math.modf(dayfrac * (24.*3600.))
                assert daysecondswhole == int(daysecondswhole)  # can't overflow
                s = int(daysecondswhole)
                assert days == int(days)
                d = int(days)
            else:
                daysecondsfrac = 0.0
                d = days
            assert isinstance(daysecondsfrac, float)
            assert abs(daysecondsfrac) <= 1.0
            assert isinstance(d, int)
            assert abs(s) <= 24 * 3600
            # days isn't referenced again before redefinition
            if isinstance(seconds, float):
                secondsfrac, seconds = _math.modf(seconds)
                assert seconds == int(seconds)
                seconds = int(seconds)
                secondsfrac += daysecondsfrac
                assert abs(secondsfrac) <= 2.0
            else:
                secondsfrac = daysecondsfrac
            # daysecondsfrac isn't referenced again
            assert isinstance(secondsfrac, float)
            assert abs(secondsfrac) <= 2.0
            assert isinstance(seconds, int)
            days, seconds = divmod(seconds, 24*3600)
            d += days
            s += int(seconds)    # can't overflow
            assert isinstance(s, int)
            assert abs(s) <= 2 * 24 * 3600
            # seconds isn't referenced again before redefinition
            usdouble = secondsfrac * 1e6
            assert abs(usdouble) < 2.1e6    # exact value not critical
            # secondsfrac isn't referenced again
            if isinstance(microseconds, float):
                microseconds = round(microseconds + usdouble)
                seconds, microseconds = divmod(microseconds, 1000000)
                days, seconds = divmod(seconds, 24*3600)
                d += days
                s += seconds
            else:
                microseconds = int(microseconds)
                seconds, microseconds = divmod(microseconds, 1000000)
                days, seconds = divmod(seconds, 24*3600)
                d += days
                s += seconds
                microseconds = round(microseconds + usdouble)
            assert isinstance(s, int)
            assert isinstance(microseconds, int)
            assert abs(s) <= 3 * 24 * 3600
            assert abs(microseconds) < 3.1e6
            # Just a little bit of carrying possible for microseconds and seconds.
            seconds, us = divmod(microseconds, 1000000)
            s += seconds
            days, s = divmod(s, 24*3600)
            d += days
            assert isinstance(d, int)
            assert isinstance(s, int) and 0 <= s < 24*3600
            assert isinstance(us, int) and 0 <= us < 1000000
            if abs(d) > 999999999:
                raise OverflowError("timedelta # of days is too large: %d" % d)
            self = object.__new__(cls)
            self._days = d
            self._seconds = s
            self._microseconds = us
            self._hashcode = -1
            return self
        def __repr__(self):
            args = []
            if self._days:
                args.append("days=%d" % self._days)
            if self._seconds:
                args.append("seconds=%d" % self._seconds)
            if self._microseconds:
                args.append("microseconds=%d" % self._microseconds)
            if not args:
                args.append('0')
            return "%s.%s(%s)" % (self.__class__.__module__,
                                  self.__class__.__qualname__,
                                  ', '.join(args))
        def __str__(self):
            mm, ss = divmod(self._seconds, 60)
            hh, mm = divmod(mm, 60)
            s = "%d:%02d:%02d" % (hh, mm, ss)
            if self._days:
                def plural(n):
                    return n, abs(n) != 1 and "s" or ""
                s = ("%d day%s, " % plural(self._days)) + s
            if self._microseconds:
                s = s + ".%06d" % self._microseconds
            return s
        def total_seconds(self):
            """Total seconds in the duration."""
            return ((self.days * 86400 + self.seconds) * 10**6 +
                    self.microseconds) / 10**6
        # Read-only field accessors
        @property
        def days(self):
            """days"""
            return self._days
        @property
        def seconds(self):
            """seconds"""
            return self._seconds
        @property
        def microseconds(self):
            """microseconds"""
            return self._microseconds
        def __add__(self, other):
            if isinstance(other, timedelta):
                # for CPython compatibility, we cannot use
                # our __class__ here, but need a real timedelta
                return timedelta(self._days + other._days,
                                 self._seconds + other._seconds,
                                 self._microseconds + other._microseconds)
            return NotImplemented
        __radd__ = __add__
        def __sub__(self, other):
            if isinstance(other, timedelta):
                # for CPython compatibility, we cannot use
                # our __class__ here, but need a real timedelta
                return timedelta(self._days - other._days,
                                 self._seconds - other._seconds,
                                 self._microseconds - other._microseconds)
            return NotImplemented
        def __rsub__(self, other):
            if isinstance(other, timedelta):
                return -self + other
            return NotImplemented
        def __neg__(self):
            # for CPython compatibility, we cannot use
            # our __class__ here, but need a real timedelta
            return timedelta(-self._days,
                             -self._seconds,
                             -self._microseconds)
        def __pos__(self):
            return self
        def __abs__(self):
            if self._days < 0:
                return -self
            else:
                return self
        def __mul__(self, other):
            if isinstance(other, int):
                # for CPython compatibility, we cannot use
                # our __class__ here, but need a real timedelta
                return timedelta(self._days * other,
                                 self._seconds * other,
                                 self._microseconds * other)
            if isinstance(other, float):
                usec = self._to_microseconds()
                a, b = other.as_integer_ratio()
                return timedelta(0, 0, _divide_and_round(usec * a, b))
            return NotImplemented
        __rmul__ = __mul__
        def _to_microseconds(self):
            return ((self._days * (24*3600) + self._seconds) * 1000000 +
                    self._microseconds)
        def __floordiv__(self, other):
            if not isinstance(other, (int, timedelta)):
                return NotImplemented
            usec = self._to_microseconds()
            if isinstance(other, timedelta):
                return usec // other._to_microseconds()
            if isinstance(other, int):
                return timedelta(0, 0, usec // other)
        def __truediv__(self, other):
            if not isinstance(other, (int, float, timedelta)):
                return NotImplemented
            usec = self._to_microseconds()
            if isinstance(other, timedelta):
                return usec / other._to_microseconds()
            if isinstance(other, int):
                return timedelta(0, 0, _divide_and_round(usec, other))
            if isinstance(other, float):
                a, b = other.as_integer_ratio()
                return timedelta(0, 0, _divide_and_round(b * usec, a))
        def __mod__(self, other):
            if isinstance(other, timedelta):
                r = self._to_microseconds() % other._to_microseconds()
                return timedelta(0, 0, r)
            return NotImplemented
        def __divmod__(self, other):
            if isinstance(other, timedelta):
                q, r = divmod(self._to_microseconds(),
                              other._to_microseconds())
                return q, timedelta(0, 0, r)
            return NotImplemented
        # Comparisons of timedelta objects with other.
        def __eq__(self, other):
            if isinstance(other, timedelta):
                return self._cmp(other) == 0
            else:
                return NotImplemented
        def __le__(self, other):
            if isinstance(other, timedelta):
                return self._cmp(other) <= 0
            else:
                return NotImplemented
        def __lt__(self, other):
            if isinstance(other, timedelta):
                return self._cmp(other) < 0
            else:
                return NotImplemented
        def __ge__(self, other):
            if isinstance(other, timedelta):
                return self._cmp(other) >= 0
            else:
                return NotImplemented
        def __gt__(self, other):
            if isinstance(other, timedelta):
                return self._cmp(other) > 0
            else:
                return NotImplemented
        def _cmp(self, other):
            assert isinstance(other, timedelta)
            return _cmp(self._getstate(), other._getstate())
        def __hash__(self):
            if self._hashcode == -1:
                self._hashcode = hash(self._getstate())
            return self._hashcode
        def __bool__(self):
            return (self._days != 0 or
                    self._seconds != 0 or
                    self._microseconds != 0)
        # Pickle support.
        def _getstate(self):
            return (self._days, self._seconds, self._microseconds)
        def __reduce__(self):
            return (self.__class__, self._getstate())
    timedelta.min = timedelta(-999999999)
    timedelta.max = timedelta(days=999999999, hours=23, minutes=59, seconds=59,
                              microseconds=999999)
    timedelta.resolution = timedelta(microseconds=1)
    class date:
        """Concrete date type.
        Constructors:
        __new__()
        fromtimestamp()
        today()
        fromordinal()
        Operators:
        __repr__, __str__
        __eq__, __le__, __lt__, __ge__, __gt__, __hash__
        __add__, __radd__, __sub__ (add/radd only with timedelta arg)
        Methods:
        timetuple()
        toordinal()
        weekday()
        isoweekday(), isocalendar(), isoformat()
        ctime()
        strftime()
        Properties (readonly):
        year, month, day
        """
        __slots__ = '_year', '_month', '_day', '_hashcode'
        def __new__(cls, year, month=None, day=None):
            """Constructor.
            Arguments:
            year, month, day (required, base 1)
            """
            if (month is None and
                isinstance(year, (bytes, str)) and len(year) == 4 and
                1 <= ord(year[2:3]) <= 12):
                # Pickle support
                if isinstance(year, str):
                    try:
                        year = year.encode('latin1')
                    except UnicodeEncodeError:
                        # More informative error message.
                        raise ValueError(
                            "Failed to encode latin1 string when unpickling "
                            "a date object. "
                            "pickle.load(data, encoding='latin1') is assumed.")
                self = object.__new__(cls)
                self.__setstate(year)
                self._hashcode = -1
                return self
            year, month, day = _check_date_fields(year, month, day)
            self = object.__new__(cls)
            self._year = year
            self._month = month
            self._day = day
            self._hashcode = -1
            return self
        # Additional constructors
        @classmethod
        def fromtimestamp(cls, t):
            "Construct a date from a POSIX timestamp (like time.time())."
            y, m, d, hh, mm, ss, weekday, jday, dst = _time.localtime(t)
            return cls(y, m, d)
        @classmethod
        def today(cls):
            "Construct a date from time.time()."
            t = _time.time()
            return cls.fromtimestamp(t)
        @classmethod
        def fromordinal(cls, n):
            """Construct a date from a proleptic Gregorian ordinal.
            January 1 of year 1 is day 1.  Only the year, month and day are
            non-zero in the result.
            """
            y, m, d = _ord2ymd(n)
            return cls(y, m, d)
        @classmethod
        def fromisoformat(cls, date_string):
            """Construct a date from the output of date.isoformat()."""
            if not isinstance(date_string, str):
                raise TypeError('fromisoformat: argument must be str')
            try:
                assert len(date_string) == 10
                return cls(*_parse_isoformat_date(date_string))
            except Exception:
                raise ValueError(f'Invalid isoformat string: {date_string!r}')
        # Conversions to string
        def __repr__(self):
            """Convert to formal string, for repr().
            >>> dt = datetime(2010, 1, 1)
            >>> repr(dt)
            'datetime.datetime(2010, 1, 1, 0, 0)'
            >>> dt = datetime(2010, 1, 1, tzinfo=timezone.utc)
            >>> repr(dt)
            'datetime.datetime(2010, 1, 1, 0, 0, tzinfo=datetime.timezone.utc)'
            """
            return "%s.%s(%d, %d, %d)" % (self.__class__.__module__,
                                          self.__class__.__qualname__,
                                          self._year,
                                          self._month,
                                          self._day)
        # XXX These shouldn't depend on time.localtime(), because that
        # clips the usable dates to [1970 .. 2038).  At least ctime() is
        # easily done without using strftime() -- that's better too because
        # strftime("%c", ...) is locale specific.
        def ctime(self):
            "Return ctime() style string."
            weekday = self.toordinal() % 7 or 7
            return "%s %s %2d 00:00:00 %04d" % (
                _DAYNAMES[weekday],
                _MONTHNAMES[self._month],
                self._day, self._year)
        def strftime(self, fmt):
            "Format using strftime()."
            return _wrap_strftime(self, fmt, self.timetuple())
        def __format__(self, fmt):
            if not isinstance(fmt, str):
                raise TypeError("must be str, not %s" % type(fmt).__name__)
            if len(fmt) != 0:
                return self.strftime(fmt)
            return str(self)
        def isoformat(self):
            """Return the date formatted according to ISO.
            This is 'YYYY-MM-DD'.
            References:
            - http://www.w3.org/TR/NOTE-datetime
            - http://www.cl.cam.ac.uk/~mgk25/iso-time.html
            """
            return "%04d-%02d-%02d" % (self._year, self._month, self._day)
        __str__ = isoformat
        # Read-only field accessors
        @property
        def year(self):
            """year (1-9999)"""
            return self._year
        @property
        def month(self):
            """month (1-12)"""
            return self._month
        @property
        def day(self):
            """day (1-31)"""
            return self._day
        # Standard conversions, __eq__, __le__, __lt__, __ge__, __gt__,
        # __hash__ (and helpers)
        def timetuple(self):
            "Return local time tuple compatible with time.localtime()."
            return _build_struct_time(self._year, self._month, self._day,
                                      0, 0, 0, -1)
        def toordinal(self):
            """Return proleptic Gregorian ordinal for the year, month and day.
            January 1 of year 1 is day 1.  Only the year, month and day values
            contribute to the result.
            """
            return _ymd2ord(self._year, self._month, self._day)
        def replace(self, year=None, month=None, day=None):
            """Return a new date with new values for the specified fields."""
            if year is None:
                year = self._year
            if month is None:
                month = self._month
            if day is None:
                day = self._day
            return type(self)(year, month, day)
        # Comparisons of date objects with other.
        def __eq__(self, other):
            if isinstance(other, date):
                return self._cmp(other) == 0
            return NotImplemented
        def __le__(self, other):
            if isinstance(other, date):
                return self._cmp(other) <= 0
            return NotImplemented
        def __lt__(self, other):
            if isinstance(other, date):
                return self._cmp(other) < 0
            return NotImplemented
        def __ge__(self, other):
            if isinstance(other, date):
                return self._cmp(other) >= 0
            return NotImplemented
        def __gt__(self, other):
            if isinstance(other, date):
                return self._cmp(other) > 0
            return NotImplemented
        def _cmp(self, other):
            assert isinstance(other, date)
            y, m, d = self._year, self._month, self._day
            y2, m2, d2 = other._year, other._month, other._day
            return _cmp((y, m, d), (y2, m2, d2))
        def __hash__(self):
            "Hash."
            if self._hashcode == -1:
                self._hashcode = hash(self._getstate())
            return self._hashcode
        # Computations
        def __add__(self, other):
            "Add a date to a timedelta."
            if isinstance(other, timedelta):
                o = self.toordinal() + other.days
                if 0 < o <= _MAXORDINAL:
                    return date.fromordinal(o)
                raise OverflowError("result out of range")
            return NotImplemented
        __radd__ = __add__
        def __sub__(self, other):
            """Subtract two dates, or a date and a timedelta."""
            if isinstance(other, timedelta):
                return self + timedelta(-other.days)
            if isinstance(other, date):
                days1 = self.toordinal()
                days2 = other.toordinal()
                return timedelta(days1 - days2)
            return NotImplemented
        def weekday(self):
            "Return day of the week, where Monday == 0 ... Sunday == 6."
            return (self.toordinal() + 6) % 7
        # Day-of-the-week and week-of-the-year, according to ISO
        def isoweekday(self):
            "Return day of the week, where Monday == 1 ... Sunday == 7."
            # 1-Jan-0001 is a Monday
            return self.toordinal() % 7 or 7
        def isocalendar(self):
            """Return a 3-tuple containing ISO year, week number, and weekday.
            The first ISO week of the year is the (Mon-Sun) week
            containing the year's first Thursday; everything else derives
            from that.
            The first week is 1; Monday is 1 ... Sunday is 7.
            ISO calendar algorithm taken from
            http://www.phys.uu.nl/~vgent/calendar/isocalendar.htm
            (used with permission)
            """
            year = self._year
            week1monday = _isoweek1monday(year)
            today = _ymd2ord(self._year, self._month, self._day)
            # Internally, week and day have origin 0
            week, day = divmod(today - week1monday, 7)
            if week < 0:
                year -= 1
                week1monday = _isoweek1monday(year)
                week, day = divmod(today - week1monday, 7)
            elif week >= 52:
                if today >= _isoweek1monday(year+1):
                    year += 1
                    week = 0
            return year, week+1, day+1
        # Pickle support.
        def _getstate(self):
            yhi, ylo = divmod(self._year, 256)
            return bytes([yhi, ylo, self._month, self._day]),
        def __setstate(self, string):
            yhi, ylo, self._month, self._day = string
            self._year = yhi * 256 + ylo
        def __reduce__(self):
            return (self.__class__, self._getstate())
    _date_class = date  # so functions w/ args named "date" can get at the class
    date.min = date(1, 1, 1)
    date.max = date(9999, 12, 31)
    date.resolution = timedelta(days=1)
    class tzinfo:
        """Abstract base class for time zone info classes.
        Subclasses must override the name(), utcoffset() and dst() methods.
        """
        __slots__ = ()
        def tzname(self, dt):
            "datetime -> string name of time zone."
            raise NotImplementedError("tzinfo subclass must override tzname()")
        def utcoffset(self, dt):
            "datetime -> timedelta, positive for east of UTC, negative for west of UTC"
            raise NotImplementedError("tzinfo subclass must override utcoffset()")
        def dst(self, dt):
            """datetime -> DST offset as timedelta, positive for east of UTC.
            Return 0 if DST not in effect.  utcoffset() must include the DST
            offset.
            """
            raise NotImplementedError("tzinfo subclass must override dst()")
        def fromutc(self, dt):
            "datetime in UTC -> datetime in local time."
            if not isinstance(dt, datetime):
                raise TypeError("fromutc() requires a datetime argument")
            if dt.tzinfo is not self:
                raise ValueError("dt.tzinfo is not self")
            dtoff = dt.utcoffset()
            if dtoff is None:
                raise ValueError("fromutc() requires a non-None utcoffset() "
                                 "result")
            # See the long comment block at the end of this file for an
            # explanation of this algorithm.
            dtdst = dt.dst()
            if dtdst is None:
                raise ValueError("fromutc() requires a non-None dst() result")
            delta = dtoff - dtdst
            if delta:
                dt += delta
                dtdst = dt.dst()
                if dtdst is None:
                    raise ValueError("fromutc(): dt.dst gave inconsistent "
                                     "results; cannot convert")
            return dt + dtdst
        # Pickle support.
        def __reduce__(self):
            getinitargs = getattr(self, "__getinitargs__", None)
            if getinitargs:
                args = getinitargs()
            else:
                args = ()
            getstate = getattr(self, "__getstate__", None)
            if getstate:
                state = getstate()
            else:
                state = getattr(self, "__dict__", None) or None
            if state is None:
                return (self.__class__, args)
            else:
                return (self.__class__, args, state)
    _tzinfo_class = tzinfo
    class time:
        """Time with time zone.
        Constructors:
        __new__()
        Operators:
        __repr__, __str__
        __eq__, __le__, __lt__, __ge__, __gt__, __hash__
        Methods:
        strftime()
        isoformat()
        utcoffset()
        tzname()
        dst()
        Properties (readonly):
        hour, minute, second, microsecond, tzinfo, fold
        """
        __slots__ = '_hour', '_minute', '_second', '_microsecond', '_tzinfo', '_hashcode', '_fold'
        def __new__(cls, hour=0, minute=0, second=0, microsecond=0, tzinfo=None, *, fold=0):
            """Constructor.
            Arguments:
            hour, minute (required)
            second, microsecond (default to zero)
            tzinfo (default to None)
            fold (keyword only, default to zero)
            """
            if (isinstance(hour, (bytes, str)) and len(hour) == 6 and
                ord(hour[0:1])&0x7F < 24):
                # Pickle support
                if isinstance(hour, str):
                    try:
                        hour = hour.encode('latin1')
                    except UnicodeEncodeError:
                        # More informative error message.
                        raise ValueError(
                            "Failed to encode latin1 string when unpickling "
                            "a time object. "
                            "pickle.load(data, encoding='latin1') is assumed.")
                self = object.__new__(cls)
                self.__setstate(hour, minute or None)
                self._hashcode = -1
                return self
            hour, minute, second, microsecond, fold = _check_time_fields(
                hour, minute, second, microsecond, fold)
            _check_tzinfo_arg(tzinfo)
            self = object.__new__(cls)
            self._hour = hour
            self._minute = minute
            self._second = second
            self._microsecond = microsecond
            self._tzinfo = tzinfo
            self._hashcode = -1
            self._fold = fold
            return self
        # Read-only field accessors
        @property
        def hour(self):
            """hour (0-23)"""
            return self._hour
        @property
        def minute(self):
            """minute (0-59)"""
            return self._minute
        @property
        def second(self):
            """second (0-59)"""
            return self._second
        @property
        def microsecond(self):
            """microsecond (0-999999)"""
            return self._microsecond
        @property
        def tzinfo(self):
            """timezone info object"""
            return self._tzinfo
        @property
        def fold(self):
            return self._fold
        # Standard conversions, __hash__ (and helpers)
        # Comparisons of time objects with other.
        def __eq__(self, other):
            if isinstance(other, time):
                return self._cmp(other, allow_mixed=True) == 0
            else:
                return NotImplemented
        def __le__(self, other):
            if isinstance(other, time):
                return self._cmp(other) <= 0
            else:
                return NotImplemented
        def __lt__(self, other):
            if isinstance(other, time):
                return self._cmp(other) < 0
            else:
                return NotImplemented
        def __ge__(self, other):
            if isinstance(other, time):
                return self._cmp(other) >= 0
            else:
                return NotImplemented
        def __gt__(self, other):
            if isinstance(other, time):
                return self._cmp(other) > 0
            else:
                return NotImplemented
        def _cmp(self, other, allow_mixed=False):
            assert isinstance(other, time)
            mytz = self._tzinfo
            ottz = other._tzinfo
            myoff = otoff = None
            if mytz is ottz:
                base_compare = True
            else:
                myoff = self.utcoffset()
                otoff = other.utcoffset()
                base_compare = myoff == otoff
            if base_compare:
                return _cmp((self._hour, self._minute, self._second,
                             self._microsecond),
                            (other._hour, other._minute, other._second,
                             other._microsecond))
            if myoff is None or otoff is None:
                if allow_mixed:
                    return 2 # arbitrary non-zero value
                else:
                    raise TypeError("cannot compare naive and aware times")
            myhhmm = self._hour * 60 + self._minute - myoff//timedelta(minutes=1)
            othhmm = other._hour * 60 + other._minute - otoff//timedelta(minutes=1)
            return _cmp((myhhmm, self._second, self._microsecond),
                        (othhmm, other._second, other._microsecond))
        def __hash__(self):
            """Hash."""
            if self._hashcode == -1:
                if self.fold:
                    t = self.replace(fold=0)
                else:
                    t = self
                tzoff = t.utcoffset()
                if not tzoff:  # zero or None
                    self._hashcode = hash(t._getstate()[0])
                else:
                    h, m = divmod(timedelta(hours=self.hour, minutes=self.minute) - tzoff,
                                  timedelta(hours=1))
                    assert not m % timedelta(minutes=1), "whole minute"
                    m //= timedelta(minutes=1)
                    if 0 <= h < 24:
                        self._hashcode = hash(time(h, m, self.second, self.microsecond))
                    else:
                        self._hashcode = hash((h, m, self.second, self.microsecond))
            return self._hashcode
        # Conversion to string
        def _tzstr(self):
            """Return formatted timezone offset (+xx:xx) or an empty string."""
            off = self.utcoffset()
            return _format_offset(off)
        def __repr__(self):
            """Convert to formal string, for repr()."""
            if self._microsecond != 0:
                s = ", %d, %d" % (self._second, self._microsecond)
            elif self._second != 0:
                s = ", %d" % self._second
            else:
                s = ""
            s= "%s.%s(%d, %d%s)" % (self.__class__.__module__,
                                    self.__class__.__qualname__,
                                    self._hour, self._minute, s)
            if self._tzinfo is not None:
                assert s[-1:] == ")"
                s = s[:-1] + ", tzinfo=%r" % self._tzinfo + ")"
            if self._fold:
                assert s[-1:] == ")"
                s = s[:-1] + ", fold=1)"
            return s
        def isoformat(self, timespec='auto'):
            """Return the time formatted according to ISO.
            The full format is 'HH:MM:SS.mmmmmm+zz:zz'. By default, the fractional
            part is omitted if self.microsecond == 0.
            The optional argument timespec specifies the number of additional
            terms of the time to include.
            """
            s = _format_time(self._hour, self._minute, self._second,
                              self._microsecond, timespec)
            tz = self._tzstr()
            if tz:
                s += tz
            return s
        __str__ = isoformat
        @classmethod
        def fromisoformat(cls, time_string):
            """Construct a time from the output of isoformat()."""
            if not isinstance(time_string, str):
                raise TypeError('fromisoformat: argument must be str')
            try:
                return cls(*_parse_isoformat_time(time_string))
            except Exception:
                raise ValueError(f'Invalid isoformat string: {time_string!r}')
        def strftime(self, fmt):
            """Format using strftime().  The date part of the timestamp passed
            to underlying strftime should not be used.
            """
            # The year must be >= 1000 else Python's strftime implementation
            # can raise a bogus exception.
            timetuple = (1900, 1, 1,
                         self._hour, self._minute, self._second,
                         0, 1, -1)
            return _wrap_strftime(self, fmt, timetuple)
        def __format__(self, fmt):
            if not isinstance(fmt, str):
                raise TypeError("must be str, not %s" % type(fmt).__name__)
            if len(fmt) != 0:
                return self.strftime(fmt)
            return str(self)
        # Timezone functions
        def utcoffset(self):
            """Return the timezone offset as timedelta, positive east of UTC
             (negative west of UTC)."""
            if self._tzinfo is None:
                return None
            offset = self._tzinfo.utcoffset(None)
            _check_utc_offset("utcoffset", offset)
            return offset
        def tzname(self):
            """Return the timezone name.
            Note that the name is 100% informational -- there's no requirement that
            it mean anything in particular. For example, "GMT", "UTC", "-500",
            "-5:00", "EDT", "US/Eastern", "America/New York" are all valid replies.
            """
            if self._tzinfo is None:
                return None
            name = self._tzinfo.tzname(None)
            _check_tzname(name)
            return name
        def dst(self):
            """Return 0 if DST is not in effect, or the DST offset (as timedelta
            positive eastward) if DST is in effect.
            This is purely informational; the DST offset has already been added to
            the UTC offset returned by utcoffset() if applicable, so there's no
            need to consult dst() unless you're interested in displaying the DST
            info.
            """
            if self._tzinfo is None:
                return None
            offset = self._tzinfo.dst(None)
            _check_utc_offset("dst", offset)
            return offset
        def replace(self, hour=None, minute=None, second=None, microsecond=None,
                    tzinfo=True, *, fold=None):
            """Return a new time with new values for the specified fields."""
            if hour is None:
                hour = self.hour
            if minute is None:
                minute = self.minute
            if second is None:
                second = self.second
            if microsecond is None:
                microsecond = self.microsecond
            if tzinfo is True:
                tzinfo = self.tzinfo
            if fold is None:
                fold = self._fold
            return type(self)(hour, minute, second, microsecond, tzinfo, fold=fold)
        # Pickle support.
        def _getstate(self, protocol=3):
            us2, us3 = divmod(self._microsecond, 256)
            us1, us2 = divmod(us2, 256)
            h = self._hour
            if self._fold and protocol > 3:
                h += 128
            basestate = bytes([h, self._minute, self._second,
                               us1, us2, us3])
            if self._tzinfo is None:
                return (basestate,)
            else:
                return (basestate, self._tzinfo)
        def __setstate(self, string, tzinfo):
            if tzinfo is not None and not isinstance(tzinfo, _tzinfo_class):
                raise TypeError("bad tzinfo state arg")
            h, self._minute, self._second, us1, us2, us3 = string
            if h > 127:
                self._fold = 1
                self._hour = h - 128
            else:
                self._fold = 0
                self._hour = h
            self._microsecond = (((us1 << 8) | us2) << 8) | us3
            self._tzinfo = tzinfo
        def __reduce_ex__(self, protocol):
            return (time, self._getstate(protocol))
        def __reduce__(self):
            return self.__reduce_ex__(2)
    _time_class = time  # so functions w/ args named "time" can get at the class
    time.min = time(0, 0, 0)
    time.max = time(23, 59, 59, 999999)
    time.resolution = timedelta(microseconds=1)
    class datetime(date):
        """datetime(year, month, day[, hour[, minute[, second[, microsecond[,tzinfo]]]]])
        The year, month and day arguments are required. tzinfo may be None, or an
        instance of a tzinfo subclass. The remaining arguments may be ints.
        """
        __slots__ = date.__slots__ + time.__slots__
        def __new__(cls, year, month=None, day=None, hour=0, minute=0, second=0,
                    microsecond=0, tzinfo=None, *, fold=0):
            if (isinstance(year, (bytes, str)) and len(year) == 10 and
                1 <= ord(year[2:3])&0x7F <= 12):
                # Pickle support
                if isinstance(year, str):
                    try:
                        year = bytes(year, 'latin1')
                    except UnicodeEncodeError:
                        # More informative error message.
                        raise ValueError(
                            "Failed to encode latin1 string when unpickling "
                            "a datetime object. "
                            "pickle.load(data, encoding='latin1') is assumed.")
                self = object.__new__(cls)
                self.__setstate(year, month)
                self._hashcode = -1
                return self
            year, month, day = _check_date_fields(year, month, day)
            hour, minute, second, microsecond, fold = _check_time_fields(
                hour, minute, second, microsecond, fold)
            _check_tzinfo_arg(tzinfo)
            self = object.__new__(cls)
            self._year = year
            self._month = month
            self._day = day
            self._hour = hour
            self._minute = minute
            self._second = second
            self._microsecond = microsecond
            self._tzinfo = tzinfo
            self._hashcode = -1
            self._fold = fold
            return self
        # Read-only field accessors
        @property
        def hour(self):
            """hour (0-23)"""
            return self._hour
        @property
        def minute(self):
            """minute (0-59)"""
            return self._minute
        @property
        def second(self):
            """second (0-59)"""
            return self._second
        @property
        def microsecond(self):
            """microsecond (0-999999)"""
            return self._microsecond
        @property
        def tzinfo(self):
            """timezone info object"""
            return self._tzinfo
        @property
        def fold(self):
            return self._fold
        @classmethod
        def _fromtimestamp(cls, t, utc, tz):
            """Construct a datetime from a POSIX timestamp (like time.time()).
            A timezone info object may be passed in as well.
            """
            frac, t = _math.modf(t)
            us = round(frac * 1e6)
            if us >= 1000000:
                t += 1
                us -= 1000000
            elif us < 0:
                t -= 1
                us += 1000000
            converter = _time.gmtime if utc else _time.localtime
            y, m, d, hh, mm, ss, weekday, jday, dst = converter(t)
            ss = min(ss, 59)    # clamp out leap seconds if the platform has them
            result = cls(y, m, d, hh, mm, ss, us, tz)
            if tz is None:
                # As of version 2015f max fold in IANA database is
                # 23 hours at 1969-09-30 13:00:00 in Kwajalein.
                # Let's probe 24 hours in the past to detect a transition:
                max_fold_seconds = 24 * 3600
                # On Windows localtime_s throws an OSError for negative values,
                # thus we can't perform fold detection for values of time less
                # than the max time fold. See comments in _datetimemodule's
                # version of this method for more details.
                if t < max_fold_seconds and sys.platform.startswith("win"):
                    return result
                y, m, d, hh, mm, ss = converter(t - max_fold_seconds)[:6]
                probe1 = cls(y, m, d, hh, mm, ss, us, tz)
                trans = result - probe1 - timedelta(0, max_fold_seconds)
                if trans.days < 0:
                    y, m, d, hh, mm, ss = converter(t + trans // timedelta(0, 1))[:6]
                    probe2 = cls(y, m, d, hh, mm, ss, us, tz)
                    if probe2 == result:
                        result._fold = 1
            else:
                result = tz.fromutc(result)
            return result
        @classmethod
        def fromtimestamp(cls, t, tz=None):
            """Construct a datetime from a POSIX timestamp (like time.time()).
            A timezone info object may be passed in as well.
            """
            _check_tzinfo_arg(tz)
            return cls._fromtimestamp(t, tz is not None, tz)
        @classmethod
        def utcfromtimestamp(cls, t):
            """Construct a naive UTC datetime from a POSIX timestamp."""
            return cls._fromtimestamp(t, True, None)
        @classmethod
        def now(cls, tz=None):
            "Construct a datetime from time.time() and optional time zone info."
            t = _time.time()
            return cls.fromtimestamp(t, tz)
        @classmethod
        def utcnow(cls):
            "Construct a UTC datetime from time.time()."
            t = _time.time()
            return cls.utcfromtimestamp(t)
        @classmethod
        def combine(cls, date, time, tzinfo=True):
            "Construct a datetime from a given date and a given time."
            if not isinstance(date, _date_class):
                raise TypeError("date argument must be a date instance")
            if not isinstance(time, _time_class):
                raise TypeError("time argument must be a time instance")
            if tzinfo is True:
                tzinfo = time.tzinfo
            return cls(date.year, date.month, date.day,
                       time.hour, time.minute, time.second, time.microsecond,
                       tzinfo, fold=time.fold)
        @classmethod
        def fromisoformat(cls, date_string):
            """Construct a datetime from the output of datetime.isoformat()."""
            if not isinstance(date_string, str):
                raise TypeError('fromisoformat: argument must be str')
            # Split this at the separator
            dstr = date_string[0:10]
            tstr = date_string[11:]
            try:
                date_components = _parse_isoformat_date(dstr)
            except ValueError:
                raise ValueError(f'Invalid isoformat string: {date_string!r}')
            if tstr:
                try:
                    time_components = _parse_isoformat_time(tstr)
                except ValueError:
                    raise ValueError(f'Invalid isoformat string: {date_string!r}')
            else:
                time_components = [0, 0, 0, 0, None]
            return cls(*(date_components + time_components))
        def timetuple(self):
            "Return local time tuple compatible with time.localtime()."
            dst = self.dst()
            if dst is None:
                dst = -1
            elif dst:
                dst = 1
            else:
                dst = 0
            return _build_struct_time(self.year, self.month, self.day,
                                      self.hour, self.minute, self.second,
                                      dst)
        def _mktime(self):
            """Return integer POSIX timestamp."""
            epoch = datetime(1970, 1, 1)
            max_fold_seconds = 24 * 3600
            t = (self - epoch) // timedelta(0, 1)
            def local(u):
                y, m, d, hh, mm, ss = _time.localtime(u)[:6]
                return (datetime(y, m, d, hh, mm, ss) - epoch) // timedelta(0, 1)
            # Our goal is to solve t = local(u) for u.
            a = local(t) - t
            u1 = t - a
            t1 = local(u1)
            if t1 == t:
                # We found one solution, but it may not be the one we need.
                # Look for an earlier solution (if `fold` is 0), or a
                # later one (if `fold` is 1).
                u2 = u1 + (-max_fold_seconds, max_fold_seconds)[self.fold]
                b = local(u2) - u2
                if a == b:
                    return u1
            else:
                b = t1 - u1
                assert a != b
            u2 = t - b
            t2 = local(u2)
            if t2 == t:
                return u2
            if t1 == t:
                return u1
            # We have found both offsets a and b, but neither t - a nor t - b is
            # a solution.  This means t is in the gap.
            return (max, min)[self.fold](u1, u2)
        def timestamp(self):
            "Return POSIX timestamp as float"
            if self._tzinfo is None:
                s = self._mktime()
                return s + self.microsecond / 1e6
            else:
                return (self - _EPOCH).total_seconds()
        def utctimetuple(self):
            "Return UTC time tuple compatible with time.gmtime()."
            offset = self.utcoffset()
            if offset:
                self -= offset
            y, m, d = self.year, self.month, self.day
            hh, mm, ss = self.hour, self.minute, self.second
            return _build_struct_time(y, m, d, hh, mm, ss, 0)
        def date(self):
            "Return the date part."
            return date(self._year, self._month, self._day)
        def time(self):
            "Return the time part, with tzinfo None."
            return time(self.hour, self.minute, self.second, self.microsecond, fold=self.fold)
        def timetz(self):
            "Return the time part, with same tzinfo."
            return time(self.hour, self.minute, self.second, self.microsecond,
                        self._tzinfo, fold=self.fold)
        def replace(self, year=None, month=None, day=None, hour=None,
                    minute=None, second=None, microsecond=None, tzinfo=True,
                    *, fold=None):
            """Return a new datetime with new values for the specified fields."""
            if year is None:
                year = self.year
            if month is None:
                month = self.month
            if day is None:
                day = self.day
            if hour is None:
                hour = self.hour
            if minute is None:
                minute = self.minute
            if second is None:
                second = self.second
            if microsecond is None:
                microsecond = self.microsecond
            if tzinfo is True:
                tzinfo = self.tzinfo
            if fold is None:
                fold = self.fold
            return type(self)(year, month, day, hour, minute, second,
                              microsecond, tzinfo, fold=fold)
        def _local_timezone(self):
            if self.tzinfo is None:
                ts = self._mktime()
            else:
                ts = (self - _EPOCH) // timedelta(seconds=1)
            localtm = _time.localtime(ts)
            local = datetime(*localtm[:6])
            try:
                # Extract TZ data if available
                gmtoff = localtm.tm_gmtoff
                zone = localtm.tm_zone
            except AttributeError:
                delta = local - datetime(*_time.gmtime(ts)[:6])
                zone = _time.strftime('%Z', localtm)
                tz = timezone(delta, zone)
            else:
                tz = timezone(timedelta(seconds=gmtoff), zone)
            return tz
        def astimezone(self, tz=None):
            if tz is None:
                tz = self._local_timezone()
            elif not isinstance(tz, tzinfo):
                raise TypeError("tz argument must be an instance of tzinfo")
            mytz = self.tzinfo
            if mytz is None:
                mytz = self._local_timezone()
                myoffset = mytz.utcoffset(self)
            else:
                myoffset = mytz.utcoffset(self)
                if myoffset is None:
                    mytz = self.replace(tzinfo=None)._local_timezone()
                    myoffset = mytz.utcoffset(self)
            if tz is mytz:
                return self
            # Convert self to UTC, and attach the new time zone object.
            utc = (self - myoffset).replace(tzinfo=tz)
            # Convert from UTC to tz's local time.
            return tz.fromutc(utc)
        # Ways to produce a string.
        def ctime(self):
            "Return ctime() style string."
            weekday = self.toordinal() % 7 or 7
            return "%s %s %2d %02d:%02d:%02d %04d" % (
                _DAYNAMES[weekday],
                _MONTHNAMES[self._month],
                self._day,
                self._hour, self._minute, self._second,
                self._year)
        def isoformat(self, sep='T', timespec='auto'):
            """Return the time formatted according to ISO.
            The full format looks like 'YYYY-MM-DD HH:MM:SS.mmmmmm'.
            By default, the fractional part is omitted if self.microsecond == 0.
            If self.tzinfo is not None, the UTC offset is also attached, giving
            giving a full format of 'YYYY-MM-DD HH:MM:SS.mmmmmm+HH:MM'.
            Optional argument sep specifies the separator between date and
            time, default 'T'.
            The optional argument timespec specifies the number of additional
            terms of the time to include.
            """
            s = ("%04d-%02d-%02d%c" % (self._year, self._month, self._day, sep) +
                 _format_time(self._hour, self._minute, self._second,
                              self._microsecond, timespec))
            off = self.utcoffset()
            tz = _format_offset(off)
            if tz:
                s += tz
            return s
        def __repr__(self):
            """Convert to formal string, for repr()."""
            L = [self._year, self._month, self._day,  # These are never zero
                 self._hour, self._minute, self._second, self._microsecond]
            if L[-1] == 0:
                del L[-1]
            if L[-1] == 0:
                del L[-1]
            s = "%s.%s(%s)" % (self.__class__.__module__,
                               self.__class__.__qualname__,
                               ", ".join(map(str, L)))
            if self._tzinfo is not None:
                assert s[-1:] == ")"
                s = s[:-1] + ", tzinfo=%r" % self._tzinfo + ")"
            if self._fold:
                assert s[-1:] == ")"
                s = s[:-1] + ", fold=1)"
            return s
        def __str__(self):
            "Convert to string, for str()."
            return self.isoformat(sep=' ')
        @classmethod
        def strptime(cls, date_string, format):
            'string, format -> new datetime parsed from a string (like time.strptime()).'
            import _strptime
            return _strptime._strptime_datetime(cls, date_string, format)
        def utcoffset(self):
            """Return the timezone offset as timedelta positive east of UTC (negative west of
            UTC)."""
            if self._tzinfo is None:
                return None
            offset = self._tzinfo.utcoffset(self)
            _check_utc_offset("utcoffset", offset)
            return offset
        def tzname(self):
            """Return the timezone name.
            Note that the name is 100% informational -- there's no requirement that
            it mean anything in particular. For example, "GMT", "UTC", "-500",
            "-5:00", "EDT", "US/Eastern", "America/New York" are all valid replies.
            """
            if self._tzinfo is None:
                return None
            name = self._tzinfo.tzname(self)
            _check_tzname(name)
            return name
        def dst(self):
            """Return 0 if DST is not in effect, or the DST offset (as timedelta
            positive eastward) if DST is in effect.
            This is purely informational; the DST offset has already been added to
            the UTC offset returned by utcoffset() if applicable, so there's no
            need to consult dst() unless you're interested in displaying the DST
            info.
            """
            if self._tzinfo is None:
                return None
            offset = self._tzinfo.dst(self)
            _check_utc_offset("dst", offset)
            return offset
        # Comparisons of datetime objects with other.
        def __eq__(self, other):
            if isinstance(other, datetime):
                return self._cmp(other, allow_mixed=True) == 0
            elif not isinstance(other, date):
                return NotImplemented
            else:
                return False
        def __le__(self, other):
            if isinstance(other, datetime):
                return self._cmp(other) <= 0
            elif not isinstance(other, date):
                return NotImplemented
            else:
                _cmperror(self, other)
        def __lt__(self, other):
            if isinstance(other, datetime):
                return self._cmp(other) < 0
            elif not isinstance(other, date):
                return NotImplemented
            else:
                _cmperror(self, other)
        def __ge__(self, other):
            if isinstance(other, datetime):
                return self._cmp(other) >= 0
            elif not isinstance(other, date):
                return NotImplemented
            else:
                _cmperror(self, other)
        def __gt__(self, other):
            if isinstance(other, datetime):
                return self._cmp(other) > 0
            elif not isinstance(other, date):
                return NotImplemented
            else:
                _cmperror(self, other)
        def _cmp(self, other, allow_mixed=False):
            assert isinstance(other, datetime)
            mytz = self._tzinfo
            ottz = other._tzinfo
            myoff = otoff = None
            if mytz is ottz:
                base_compare = True
            else:
                myoff = self.utcoffset()
                otoff = other.utcoffset()
                # Assume that allow_mixed means that we are called from __eq__
                if allow_mixed:
                    if myoff != self.replace(fold=not self.fold).utcoffset():
                        return 2
                    if otoff != other.replace(fold=not other.fold).utcoffset():
                        return 2
                base_compare = myoff == otoff
            if base_compare:
                return _cmp((self._year, self._month, self._day,
                             self._hour, self._minute, self._second,
                             self._microsecond),
                            (other._year, other._month, other._day,
                             other._hour, other._minute, other._second,
                             other._microsecond))
            if myoff is None or otoff is None:
                if allow_mixed:
                    return 2 # arbitrary non-zero value
                else:
                    raise TypeError("cannot compare naive and aware datetimes")
            # XXX What follows could be done more efficiently...
            diff = self - other     # this will take offsets into account
            if diff.days < 0:
                return -1
            return diff and 1 or 0
        def __add__(self, other):
            "Add a datetime and a timedelta."
            if not isinstance(other, timedelta):
                return NotImplemented
            delta = timedelta(self.toordinal(),
                              hours=self._hour,
                              minutes=self._minute,
                              seconds=self._second,
                              microseconds=self._microsecond)
            delta += other
            hour, rem = divmod(delta.seconds, 3600)
            minute, second = divmod(rem, 60)
            if 0 < delta.days <= _MAXORDINAL:
                return datetime.combine(date.fromordinal(delta.days),
                                        time(hour, minute, second,
                                             delta.microseconds,
                                             tzinfo=self._tzinfo))
            raise OverflowError("result out of range")
        __radd__ = __add__
        def __sub__(self, other):
            "Subtract two datetimes, or a datetime and a timedelta."
            if not isinstance(other, datetime):
                if isinstance(other, timedelta):
                    return self + -other
                return NotImplemented
            days1 = self.toordinal()
            days2 = other.toordinal()
            secs1 = self._second + self._minute * 60 + self._hour * 3600
            secs2 = other._second + other._minute * 60 + other._hour * 3600
            base = timedelta(days1 - days2,
                             secs1 - secs2,
                             self._microsecond - other._microsecond)
            if self._tzinfo is other._tzinfo:
                return base
            myoff = self.utcoffset()
            otoff = other.utcoffset()
            if myoff == otoff:
                return base
            if myoff is None or otoff is None:
                raise TypeError("cannot mix naive and timezone-aware time")
            return base + otoff - myoff
        def __hash__(self):
            if self._hashcode == -1:
                if self.fold:
                    t = self.replace(fold=0)
                else:
                    t = self
                tzoff = t.utcoffset()
                if tzoff is None:
                    self._hashcode = hash(t._getstate()[0])
                else:
                    days = _ymd2ord(self.year, self.month, self.day)
                    seconds = self.hour * 3600 + self.minute * 60 + self.second
                    self._hashcode = hash(timedelta(days, seconds, self.microsecond) - tzoff)
            return self._hashcode
        # Pickle support.
        def _getstate(self, protocol=3):
            yhi, ylo = divmod(self._year, 256)
            us2, us3 = divmod(self._microsecond, 256)
            us1, us2 = divmod(us2, 256)
            m = self._month
            if self._fold and protocol > 3:
                m += 128
            basestate = bytes([yhi, ylo, m, self._day,
                               self._hour, self._minute, self._second,
                               us1, us2, us3])
            if self._tzinfo is None:
                return (basestate,)
            else:
                return (basestate, self._tzinfo)
        def __setstate(self, string, tzinfo):
            if tzinfo is not None and not isinstance(tzinfo, _tzinfo_class):
                raise TypeError("bad tzinfo state arg")
            (yhi, ylo, m, self._day, self._hour,
             self._minute, self._second, us1, us2, us3) = string
            if m > 127:
                self._fold = 1
                self._month = m - 128
            else:
                self._fold = 0
                self._month = m
            self._year = yhi * 256 + ylo
            self._microsecond = (((us1 << 8) | us2) << 8) | us3
            self._tzinfo = tzinfo
        def __reduce_ex__(self, protocol):
            return (self.__class__, self._getstate(protocol))
        def __reduce__(self):
            return self.__reduce_ex__(2)
    datetime.min = datetime(1, 1, 1)
    datetime.max = datetime(9999, 12, 31, 23, 59, 59, 999999)
    datetime.resolution = timedelta(microseconds=1)
    def _isoweek1monday(year):
        # Helper to calculate the day number of the Monday starting week 1
        # XXX This could be done more efficiently
        THURSDAY = 3
        firstday = _ymd2ord(year, 1, 1)
        firstweekday = (firstday + 6) % 7  # See weekday() above
        week1monday = firstday - firstweekday
        if firstweekday > THURSDAY:
            week1monday += 7
        return week1monday
    class timezone(tzinfo):
        __slots__ = '_offset', '_name'
        # Sentinel value to disallow None
        _Omitted = object()
        def __new__(cls, offset, name=_Omitted):
            if not isinstance(offset, timedelta):
                raise TypeError("offset must be a timedelta")
            if name is cls._Omitted:
                if not offset:
                    return cls.utc
                name = None
            elif not isinstance(name, str):
                raise TypeError("name must be a string")
            if not cls._minoffset <= offset <= cls._maxoffset:
                raise ValueError("offset must be a timedelta "
                                 "strictly between -timedelta(hours=24) and "
                                 "timedelta(hours=24).")
            return cls._create(offset, name)
        @classmethod
        def _create(cls, offset, name=None):
            self = tzinfo.__new__(cls)
            self._offset = offset
            self._name = name
            return self
        def __getinitargs__(self):
            """pickle support"""
            if self._name is None:
                return (self._offset,)
            return (self._offset, self._name)
        def __eq__(self, other):
            if isinstance(other, timezone):
                return self._offset == other._offset
            return NotImplemented
        def __hash__(self):
            return hash(self._offset)
        def __repr__(self):
            """Convert to formal string, for repr().
            >>> tz = timezone.utc
            >>> repr(tz)
            'datetime.timezone.utc'
            >>> tz = timezone(timedelta(hours=-5), 'EST')
            >>> repr(tz)
            "datetime.timezone(datetime.timedelta(-1, 68400), 'EST')"
            """
            if self is self.utc:
                return 'datetime.timezone.utc'
            if self._name is None:
                return "%s.%s(%r)" % (self.__class__.__module__,
                                      self.__class__.__qualname__,
                                      self._offset)
            return "%s.%s(%r, %r)" % (self.__class__.__module__,
                                      self.__class__.__qualname__,
                                      self._offset, self._name)
        def __str__(self):
            return self.tzname(None)
        def utcoffset(self, dt):
            if isinstance(dt, datetime) or dt is None:
                return self._offset
            raise TypeError("utcoffset() argument must be a datetime instance"
                            " or None")
        def tzname(self, dt):
            if isinstance(dt, datetime) or dt is None:
                if self._name is None:
                    return self._name_from_offset(self._offset)
                return self._name
            raise TypeError("tzname() argument must be a datetime instance"
                            " or None")
        def dst(self, dt):
            if isinstance(dt, datetime) or dt is None:
                return None
            raise TypeError("dst() argument must be a datetime instance"
                            " or None")
        def fromutc(self, dt):
            if isinstance(dt, datetime):
                if dt.tzinfo is not self:
                    raise ValueError("fromutc: dt.tzinfo "
                                     "is not self")
                return dt + self._offset
            raise TypeError("fromutc() argument must be a datetime instance"
                            " or None")
        _maxoffset = timedelta(hours=24, microseconds=-1)
        _minoffset = -_maxoffset
        @staticmethod
        def _name_from_offset(delta):
            if not delta:
                return 'UTC'
            if delta < timedelta(0):
                sign = '-'
                delta = -delta
            else:
                sign = '+'
            hours, rest = divmod(delta, timedelta(hours=1))
            minutes, rest = divmod(rest, timedelta(minutes=1))
            seconds = rest.seconds
            microseconds = rest.microseconds
            if microseconds:
                return (f'UTC{sign}{hours:02d}:{minutes:02d}:{seconds:02d}'
                        f'.{microseconds:06d}')
            if seconds:
                return f'UTC{sign}{hours:02d}:{minutes:02d}:{seconds:02d}'
            return f'UTC{sign}{hours:02d}:{minutes:02d}'
    timezone.utc = timezone._create(timedelta(0))
    # bpo-37642: These attributes are rounded to the nearest minute for backwards
    # compatibility, even though the constructor will accept a wider range of
    # values. This may change in the future.
    timezone.min = timezone._create(-timedelta(hours=23, minutes=59))
    timezone.max = timezone._create(timedelta(hours=23, minutes=59))
    _EPOCH = datetime(1970, 1, 1, tzinfo=timezone.utc)
    # Some time zone algebra.  For a datetime x, let
    #     x.n = x stripped of its timezone -- its naive time.
    #     x.o = x.utcoffset(), and assuming that doesn't raise an exception or
    #           return None
    #     x.d = x.dst(), and assuming that doesn't raise an exception or
    #           return None
    #     x.s = x's standard offset, x.o - x.d
    #
    # Now some derived rules, where k is a duration (timedelta).
    #
    # 1. x.o = x.s + x.d
    #    This follows from the definition of x.s.
    #
    # 2. If x and y have the same tzinfo member, x.s = y.s.
    #    This is actually a requirement, an assumption we need to make about
    #    sane tzinfo classes.
    #
    # 3. The naive UTC time corresponding to x is x.n - x.o.
    #    This is again a requirement for a sane tzinfo class.
    #
    # 4. (x+k).s = x.s
    #    This follows from #2, and that datimetimetz+timedelta preserves tzinfo.
    #
    # 5. (x+k).n = x.n + k
    #    Again follows from how arithmetic is defined.
    #
    # Now we can explain tz.fromutc(x).  Let's assume it's an interesting case
    # (meaning that the various tzinfo methods exist, and don't blow up or return
    # None when called).
    #
    # The function wants to return a datetime y with timezone tz, equivalent to x.
    # x is already in UTC.
    #
    # By #3, we want
    #
    #     y.n - y.o = x.n                             [1]
    #
    # The algorithm starts by attaching tz to x.n, and calling that y.  So
    # x.n = y.n at the start.  Then it wants to add a duration k to y, so that [1]
    # becomes true; in effect, we want to solve [2] for k:
    #
    #    (y+k).n - (y+k).o = x.n                      [2]
    #
    # By #1, this is the same as
    #
    #    (y+k).n - ((y+k).s + (y+k).d) = x.n          [3]
    #
    # By #5, (y+k).n = y.n + k, which equals x.n + k because x.n=y.n at the start.
    # Substituting that into [3],
    #
    #    x.n + k - (y+k).s - (y+k).d = x.n; the x.n terms cancel, leaving
    #    k - (y+k).s - (y+k).d = 0; rearranging,
    #    k = (y+k).s - (y+k).d; by #4, (y+k).s == y.s, so
    #    k = y.s - (y+k).d
    #
    # On the RHS, (y+k).d can't be computed directly, but y.s can be, and we
    # approximate k by ignoring the (y+k).d term at first.  Note that k can't be
    # very large, since all offset-returning methods return a duration of magnitude
    # less than 24 hours.  For that reason, if y is firmly in std time, (y+k).d must
    # be 0, so ignoring it has no consequence then.
    #
    # In any case, the new value is
    #
    #     z = y + y.s                                 [4]
    #
    # It's helpful to step back at look at [4] from a higher level:  it's simply
    # mapping from UTC to tz's standard time.
    #
    # At this point, if
    #
    #     z.n - z.o = x.n                             [5]
    #
    # we have an equivalent time, and are almost done.  The insecurity here is
    # at the start of daylight time.  Picture US Eastern for concreteness.  The wall
    # time jumps from 1:59 to 3:00, and wall hours of the form 2:MM don't make good
    # sense then.  The docs ask that an Eastern tzinfo class consider such a time to
    # be EDT (because it's "after 2"), which is a redundant spelling of 1:MM EST
    # on the day DST starts.  We want to return the 1:MM EST spelling because that's
    # the only spelling that makes sense on the local wall clock.
    #
    # In fact, if [5] holds at this point, we do have the standard-time spelling,
    # but that takes a bit of proof.  We first prove a stronger result.  What's the
    # difference between the LHS and RHS of [5]?  Let
    #
    #     diff = x.n - (z.n - z.o)                    [6]
    #
    # Now
    #     z.n =                       by [4]
    #     (y + y.s).n =               by #5
    #     y.n + y.s =                 since y.n = x.n
    #     x.n + y.s =                 since z and y are have the same tzinfo member,
    #                                     y.s = z.s by #2
    #     x.n + z.s
    #
    # Plugging that back into [6] gives
    #
    #     diff =
    #     x.n - ((x.n + z.s) - z.o) =     expanding
    #     x.n - x.n - z.s + z.o =         cancelling
    #     - z.s + z.o =                   by #2
    #     z.d
    #
    # So diff = z.d.
    #
    # If [5] is true now, diff = 0, so z.d = 0 too, and we have the standard-time
    # spelling we wanted in the endcase described above.  We're done.  Contrarily,
    # if z.d = 0, then we have a UTC equivalent, and are also done.
    #
    # If [5] is not true now, diff = z.d != 0, and z.d is the offset we need to
    # add to z (in effect, z is in tz's standard time, and we need to shift the
    # local clock into tz's daylight time).
    #
    # Let
    #
    #     z' = z + z.d = z + diff                     [7]
    #
    # and we can again ask whether
    #
    #     z'.n - z'.o = x.n                           [8]
    #
    # If so, we're done.  If not, the tzinfo class is insane, according to the
    # assumptions we've made.  This also requires a bit of proof.  As before, let's
    # compute the difference between the LHS and RHS of [8] (and skipping some of
    # the justifications for the kinds of substitutions we've done several times
    # already):
    #
    #     diff' = x.n - (z'.n - z'.o) =           replacing z'.n via [7]
    #             x.n  - (z.n + diff - z'.o) =    replacing diff via [6]
    #             x.n - (z.n + x.n - (z.n - z.o) - z'.o) =
    #             x.n - z.n - x.n + z.n - z.o + z'.o =    cancel x.n
    #             - z.n + z.n - z.o + z'.o =              cancel z.n
    #             - z.o + z'.o =                      #1 twice
    #             -z.s - z.d + z'.s + z'.d =          z and z' have same tzinfo
    #             z'.d - z.d
    #
    # So z' is UTC-equivalent to x iff z'.d = z.d at this point.  If they are equal,
    # we've found the UTC-equivalent so are done.  In fact, we stop with [7] and
    # return z', not bothering to compute z'.d.
    #
    # How could z.d and z'd differ?  z' = z + z.d [7], so merely moving z' by
    # a dst() offset, and starting *from* a time already in DST (we know z.d != 0),
    # would have to change the result dst() returns:  we start in DST, and moving
    # a little further into it takes us out of DST.
    #
    # There isn't a sane case where this can happen.  The closest it gets is at
    # the end of DST, where there's an hour in UTC with no spelling in a hybrid
    # tzinfo class.  In US Eastern, that's 5:MM UTC = 0:MM EST = 1:MM EDT.  During
    # that hour, on an Eastern clock 1:MM is taken as being in standard time (6:MM
    # UTC) because the docs insist on that, but 0:MM is taken as being in daylight
    # time (4:MM UTC).  There is no local time mapping to 5:MM UTC.  The local
    # clock jumps from 1:59 back to 1:00 again, and repeats the 1:MM hour in
    # standard time.  Since that's what the local clock *does*, we want to map both
    # UTC hours 5:MM and 6:MM to 1:MM Eastern.  The result is ambiguous
    # in local time, but so it goes -- it's the way the local clock works.
    #
    # When x = 5:MM UTC is the input to this algorithm, x.o=0, y.o=-5 and y.d=0,
    # so z=0:MM.  z.d=60 (minutes) then, so [5] doesn't hold and we keep going.
    # z' = z + z.d = 1:MM then, and z'.d=0, and z'.d - z.d = -60 != 0 so [8]
    # (correctly) concludes that z' is not UTC-equivalent to x.
    #
    # Because we know z.d said z was in daylight time (else [5] would have held and
    # we would have stopped then), and we know z.d != z'.d (else [8] would have held
    # and we have stopped then), and there are only 2 possible values dst() can
    # return in Eastern, it follows that z'.d must be 0 (which it is in the example,
    # but the reasoning doesn't depend on the example -- it depends on there being
    # two possible dst() outcomes, one zero and the other non-zero).  Therefore
    # z' must be in standard time, and is the spelling we want in this case.
    #
    # Note again that z' is not UTC-equivalent as far as the hybrid tzinfo class is
    # concerned (because it takes z' as being in standard time rather than the
    # daylight time we intend here), but returning it gives the real-life "local
    # clock repeats an hour" behavior when mapping the "unspellable" UTC hour into
    # tz.
    #
    # When the input is 6:MM, z=1:MM and z.d=0, and we stop at once, again with
    # the 1:MM standard time spelling we want.
    #
    # So how can this break?  One of the assumptions must be violated.  Two
    # possibilities:
    #
    # 1) [2] effectively says that y.s is invariant across all y belong to a given
    #    time zone.  This isn't true if, for political reasons or continental drift,
    #    a region decides to change its base offset from UTC.
    #
    # 2) There may be versions of "double daylight" time where the tail end of
    #    the analysis gives up a step too early.  I haven't thought about that
    #    enough to say.
    #
    # In any case, it's clear that the default fromutc() is strong enough to handle
    # "almost all" time zones:  so long as the standard offset is invariant, it
    # doesn't matter if daylight time transition points change from year to year, or
    # if daylight time is skipped in some years; it doesn't matter how large or
    # small dst() may get within its bounds; and it doesn't even matter if some
    # perverse time zone returns a negative dst()).  So a breaking case must be
    # pretty bizarre, and a tzinfo subclass can override fromutc() if it is.
    try:
        from _datetime import *
    except ImportError:
        pass
    else:
        # Clean up unused names
        del (_DAYNAMES, _DAYS_BEFORE_MONTH, _DAYS_IN_MONTH, _DI100Y, _DI400Y,
             _DI4Y, _EPOCH, _MAXORDINAL, _MONTHNAMES, _build_struct_time,
             _check_date_fields, _check_int_field, _check_time_fields,
             _check_tzinfo_arg, _check_tzname, _check_utc_offset, _cmp, _cmperror,
             _date_class, _days_before_month, _days_before_year, _days_in_month,
             _format_time, _format_offset, _is_leap, _isoweek1monday, _math,
             _ord2ymd, _time, _time_class, _tzinfo_class, _wrap_strftime, _ymd2ord,
             _divide_and_round, _parse_isoformat_date, _parse_isoformat_time,
             _parse_hh_mm_ss_ff)
        # XXX Since import * above excludes names that start with _,
        # docstring does not get overwritten. In the future, it may be
        # appropriate to maintain a single module level docstring and
        # remove the following line.
        from _datetime import __doc__