





'''simple docstring'''







lowerCAmelCase_					:    int      	=			{}






def  _lowerCamelCase				( lowercase						:      int    ,							lowercase						:      int    ,							lowercase						:      int						)	->	int:





				if late == 3 or absent == 2:
								return 0

				# if we have no days left, and have not failed any other rules,
				# we have a prize string
				if days == 0:
								return 1

				# No easy solution, so now we need to do the recursive calculation

				# First, check if the combination is already in the cache, and
				# if yes, return the stored value from there since we already
				# know the number of possible prize strings from this point on
				_a								= (days, absent, late)
				if key in cache:
								return cache[key]

				# now we calculate the three possible ways that can unfold from
				# this point on, depending on our attendance today

				# 1) if we are late (but not absent), the "absent" counter stays as
				# it is, but the "late" counter increases by one
				_a								= _calculate(days - 1    ,							lowercase    ,							late + 1						)

				# 2) if we are absent, the "absent" counter increases by 1, and the
				# "late" counter resets to 0
				_a								= _calculate(days - 1    ,							absent + 1    ,							0						)

				# 3) if we are on time, this resets the "late" counter and keeps the
				# absent counter
				_a								= _calculate(days - 1    ,							lowercase    ,							0						)

				_a								= state_late + state_absent + state_ontime

				_a								= prizestrings
				return prizestrings






def  _lowerCamelCase				( lowercase						:      int = 30						)	->	int:
				return _calculate(lowercase    ,							absent=0    ,							late=0						)


if __name__ == "__main__":
					print(solution())




"""simple docstring"""



def   __lowerCAmelCase						(						lowercase  :  int )	->						bool:


    """simple docstring"""





    if p < 2:
        raise ValueError("p should not be less than 2!" )
    elif p == 2:
        return True

    snake_case    :      Dict      					=    4
    snake_case    :      str      					=    (1 << p) - 1
    for _ in range(p - 2 ):
        snake_case    :      Any      					=    ((s * s) - 2) % m
    return s == 0


if __name__ == "__main__":
  print(lucas_lehmer_test(7))
  print(lucas_lehmer_test(11))





