





import math

__lowercase       :Optional[int]       =  10
__lowercase       :Optional[Any]       =  7
__lowercase       :Union[str, Any]       =  BALLS_PER_COLOUR * NUM_COLOURS







def       UpperCAmelCase							(     _lowerCamelCase      :  int = 20     ):





						'''simple docstring'''


						SCREAMING_SNAKE_CASE__     :				Optional[int]   =					math.comb(_lowerCamelCase			,   _lowerCamelCase     )
						SCREAMING_SNAKE_CASE__     :				int   =					math.comb(NUM_BALLS - BALLS_PER_COLOUR			,   _lowerCamelCase     )

						SCREAMING_SNAKE_CASE__     :				Dict   =					NUM_COLOURS * (1 - missing_colour / total)

						return f"""{result:.9f}"""


if __name__ == "__main__":
				print(solution(20))






from __future__ import annotations

from fractions import Fraction







def       UpperCAmelCase							(     _lowerCamelCase      :  int			,   _lowerCamelCase      :  int     ):





						'''simple docstring'''


						return (
						    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
						)







def       UpperCAmelCase							(     _lowerCamelCase      :  int     ):





						'''simple docstring'''


						SCREAMING_SNAKE_CASE__     :				int   =					[]
						SCREAMING_SNAKE_CASE__     :				str   =					11
						SCREAMING_SNAKE_CASE__     :				Any   =					int("1" + "0" * digit_len     )
						for num in range(_lowerCamelCase			,   _lowerCamelCase     ):
												while den <= 99:
																		if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
																								if is_digit_cancelling(_lowerCamelCase			,   _lowerCamelCase     ):
																														solutions.append(f"""{num}/{den}"""     )
																		den += 1
												num += 1
												SCREAMING_SNAKE_CASE__     :				str   =					10
						return solutions







def       UpperCAmelCase							(     _lowerCamelCase      :  int = 2     ):





						'''simple docstring'''


						SCREAMING_SNAKE_CASE__     :				Optional[int]   =					1.0
						for fraction in fraction_list(_lowerCamelCase     ):
												SCREAMING_SNAKE_CASE__     :				Any   =					Fraction(_lowerCamelCase     )
												result *= frac.denominator / frac.numerator
						return int(_lowerCamelCase     )


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