



'''simple docstring'''




import math
import random



def       __lowerCamelCase  (					_lowercase	,				_lowercase = False		)      ->			float:
							if deriv:
														return value * (1 - value)
							return 1 / (1 + math.exp(-value		))


# Initial Value
a   :			Union[str, Any]					  =    0.0_2



def       __lowerCamelCase  (					_lowercase	,				_lowercase		)      ->			float:
							UpperCAmelCase     :		Any							     =		float(2 * (random.randint(1	,				1_0_0		)) - 1		)

							for _ in range(_lowercase		):
														# Forward propagation
														UpperCAmelCase     :		str							     =		sigmoid_function(INITIAL_VALUE * weight		)
														# How much did we miss?
														UpperCAmelCase     :		List[str]							     =		(expected / 1_0_0) - layer_a
														# Error delta
														UpperCAmelCase     :		Dict							     =		layer_1_error * sigmoid_function(_lowercase	,				_lowercase		)
														# Update weight
														weight += INITIAL_VALUE * layer_1_delta

							return layer_a * 1_0_0


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							a   :			List[str]					  =    int(input("""Expected value: """))
							a   :			List[str]					  =    int(input("""Number of propagations: """))
							print(forward_propagation(expected, number_propagations))






'''simple docstring'''




from itertools import count



def       __lowerCamelCase  (					_lowercase = 5_0		)      ->			int:
							UpperCAmelCase     :		Any							     =		[1] * min_block_length

							for n in count(_lowercase		):
														fill_count_functions.append(1		)

														for block_length in range(_lowercase	,				n + 1		):
																					for block_start in range(n - block_length		):
																												fill_count_functions[n] += fill_count_functions[
																												    n - block_start - block_length - 1
																												]

																					fill_count_functions[n] += 1

														if fill_count_functions[n] > 1_0_0_0_0_0_0:
																					break

							return n


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

