






'''simple docstring'''
from itertools import product

def 							a	(   _UpperCAmelCase = 1_5 )				->				int:






					"""simple docstring"""







					a_									=   0.0
					a_									=   42
					a_									=   42
					a_									=   42
					a_									=   42
					a_									=   42
					a_									=   42

					for series in product(range(2 )					,  repeat=_UpperCAmelCase ):
										a_									=   series.count(1 )
										a_									=   num_turns - num_blue
										if num_red >= num_blue:
															continue
										a_									=   1.0
										for ind, col in enumerate(_UpperCAmelCase					,  2 ):
															if col == 0:
																				prob *= (ind - 1) / ind
															else:
																				prob *= 1 / ind

										total_prob += prob

					return int(1 / total_prob )


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









'''simple docstring'''
def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = 2 )				->				float:






					"""simple docstring"""







					return round((float(_UpperCAmelCase ) * 9 / 5) + 3_2					,  _UpperCAmelCase )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = 2 )				->				float:






					"""simple docstring"""







					return round(float(_UpperCAmelCase ) + 2_7_3.1_5					,  _UpperCAmelCase )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = 2 )				->				float:






					"""simple docstring"""







					return round((float(_UpperCAmelCase ) * 9 / 5) + 4_9_1.6_7					,  _UpperCAmelCase )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = 2 )				->				float:






					"""simple docstring"""







					return round((float(_UpperCAmelCase ) - 3_2) * 5 / 9					,  _UpperCAmelCase )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = 2 )				->				float:






					"""simple docstring"""







					return round(((float(_UpperCAmelCase ) - 3_2) * 5 / 9) + 2_7_3.1_5					,  _UpperCAmelCase )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = 2 )				->				float:






					"""simple docstring"""







					return round(float(_UpperCAmelCase ) + 4_5_9.6_7					,  _UpperCAmelCase )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = 2 )				->				float:






					"""simple docstring"""







					return round(float(_UpperCAmelCase ) - 2_7_3.1_5					,  _UpperCAmelCase )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = 2 )				->				float:






					"""simple docstring"""







					return round(((float(_UpperCAmelCase ) - 2_7_3.1_5) * 9 / 5) + 3_2					,  _UpperCAmelCase )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = 2 )				->				float:






					"""simple docstring"""







					return round((float(_UpperCAmelCase ) * 9 / 5)					,  _UpperCAmelCase )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = 2 )				->				float:






					"""simple docstring"""







					return round((float(_UpperCAmelCase ) - 4_9_1.6_7) * 5 / 9					,  _UpperCAmelCase )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = 2 )				->				float:






					"""simple docstring"""







					return round(float(_UpperCAmelCase ) - 4_5_9.6_7					,  _UpperCAmelCase )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = 2 )				->				float:






					"""simple docstring"""







					return round((float(_UpperCAmelCase ) * 5 / 9)					,  _UpperCAmelCase )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = 2 )				->				float:






					"""simple docstring"""







					return round((float(_UpperCAmelCase ) * 1.2_5 + 2_7_3.1_5)					,  _UpperCAmelCase )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = 2 )				->				float:






					"""simple docstring"""







					return round((float(_UpperCAmelCase ) * 2.2_5 + 3_2)					,  _UpperCAmelCase )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = 2 )				->				float:






					"""simple docstring"""







					return round((float(_UpperCAmelCase ) * 1.2_5)					,  _UpperCAmelCase )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = 2 )				->				float:






					"""simple docstring"""







					return round((float(_UpperCAmelCase ) * 2.2_5 + 3_2 + 4_5_9.6_7)					,  _UpperCAmelCase )


if __name__ == "__main__":
						import doctest

						doctest.testmod()

