

from itertools import product



def    _lowercase			(	a__						:			Optional[Any]							,  a__						:			Tuple					)							->					Any:





	"""simple docstring"""


	_UpperCamelCase			=   sides_number
	_UpperCamelCase			=   max_face_number * dice_number
	_UpperCamelCase			=   [0] * (max_total + 1)

	_UpperCamelCase			=   1
	_UpperCamelCase			=   range(_UpperCamelCase							,  max_face_number + 1					)
	for dice_numbers in product(_UpperCamelCase							,  repeat=_UpperCamelCase					):
		_UpperCamelCase			=   sum(_UpperCamelCase					)
		totals_frequencies[total] += 1

	return totals_frequencies



def    _lowercase			(	)							->					Optional[Any]:





	"""simple docstring"""


	_UpperCamelCase			=   total_frequency_distribution(
	    sides_number=4							,  dice_number=9					)
	_UpperCamelCase			=   total_frequency_distribution(
	    sides_number=6							,  dice_number=6					)

	_UpperCamelCase			=   0
	_UpperCamelCase			=   9
	_UpperCamelCase			=   4 * 9
	_UpperCamelCase			=   6
	for peter_total in range(_UpperCamelCase							,  max_peter_total + 1					):
		peter_wins_count += peter_totals_frequencies[peter_total] * sum(
		    colin_totals_frequencies[min_colin_total:peter_total]					)

	_UpperCamelCase			=   (4**9) * (6**6)
	_UpperCamelCase			=   peter_wins_count / total_games_number

	_UpperCamelCase			=   round(_UpperCamelCase							,  ndigits=7					)

	return rounded_peter_win_probability


if __name__ == "__main__":
	print(F'''{solution() = }''')








from maths.prime_factors import prime_factors


def 		lowercase_	(  _UpperCamelCase	):


			'''simple docstring'''







			if not isinstance(_UpperCamelCase							,      _UpperCamelCase	):
						__lowercase			       = F'Input value of [number={number}] must be an integer'
						raise TypeError(_UpperCamelCase	)
			if number < 1:
						raise ValueError('''Input must be a positive integer'''	)
			return -1 if len(prime_factors(_UpperCamelCase	)	) % 2 else 1


if __name__ == "__main__":
	import doctest

	doctest.testmod()


