def 					_snake_case	(  __snake_case = 10**12						):
					_UpperCamelCase			     =     1
					_UpperCamelCase			     =     0

					_UpperCamelCase			     =     1
					_UpperCamelCase			     =     1

					while numerator <= 2 * min_total - 1:
										prev_numerator += 2 * numerator
										numerator += 2 * prev_numerator

										prev_denominator += 2 * denominator
										denominator += 2 * prev_denominator

					return (denominator + 1) // 2


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





from collections.abc import Callable

import numpy as np






def  lowerCamelCase_	(      lowerCAmelCase__	:	Callable			,	lowerCAmelCase__	:	float			,	lowerCAmelCase__	:	float			,	lowerCAmelCase__	:	float			,	lowerCAmelCase__	:	float				)       ->							np.array:

							'''simple docstring'''






							A      						=    int(np.ceil((x_end - xa) / step_size				)				)
							A      						=    np.zeros((n + 1,)				)
							A      						=    ya
							A      						=    xa

							for k in range(lowerCAmelCase__				):
														A      						=    y[k] + step_size * ode_func(lowerCAmelCase__			,	y[k]				)
														A      						=    y[k] + (
														    (step_size / 2) * (ode_func(lowerCAmelCase__			,	y[k]				) + ode_func(x + step_size			,	lowerCAmelCase__				))
														)
														x += step_size

							return y


if __name__ == "__main__":
				import doctest

				doctest.testmod()