# Implements a proleptic Gregorian calendar date as a Julian day number.

class Date :
 # Creates an object instance for the specified Gregorian date.
 def __init__( self, month, day, year ):
 self._julianDay = 0
 assert self._isValidGregorian( month, day, year ), \
 "Invalid Gregorian date."

 # The first line of the equation, T = (M - 14) / 12, has to be changed
 # since Python's implementation of integer division is not the same
 # as the mathematical definition.
 tmp = 0
 if month < 3 :
 tmp = -1
 self._julianDay = day - 32075 + \
 (1461 * (year + 4800 + tmp) // 4) + \
 (367 * (month - 2 - tmp * 12) // 12) - \
 (3 * ((year + 4900 + tmp) // 100) // 4)

 # Extracts the appropriate Gregorian date component.
 def month( self ):
 return (self._toGregorian())[0] # returning M from (M, d, y)

 def day( self ):
 return (self._toGregorian())[1] # returning D from (m, D, y)

 def year( self ):
 return (self._toGregorian())[2] # returning Y from (m, d, Y)

 # Returns day of the week as an int between 0 (Mon) and 6 (Sun).
 def dayOfWeek( self ):
 month, day, year = self._toGregorian()
 if month < 3 :
 month = month + 12
 year = year - 1
 return ((13 * month + 3) // 5 + day + \
 year + year // 4 - year // 100 + year // 400) % 7

 # Returns the date as a string in Gregorian format.
 def __str__( self ):
 month, day, year = self._toGregorian()
 return "%02d/%02d/%04d" % (month, day, year)

 # Logically compares the two dates.
 def __eq__( self, otherDate ):
 return self._julianDay == otherDate._julianDay

 def __lt__( self, otherDate ):
 return self._julianDay < otherDate._julianDay

 def __le__( self, otherDate ):
 return self._julianDay <= otherDate._julianDay

 # The remaining methods are to be included at this point.
 # ......

 # Returns the Gregorian date as a tuple: (month, day, year).
 def _toGregorian( self ):
 A = self._julianDay + 68569
 B = 4 * A // 146097
 A = A - (146097 * B + 3) // 4
 year = 4000 * (A + 1) // 1461001
 A = A - (1461 * year // 4) + 31
 month = 80 * A // 2447
 day = A - (2447 * month // 80)
 A = month // 11
 month = month + 2 - (12 * A)
 year = 100 * (B - 49) + year + A
 return month, day, year