
def        A__					(						lowerCamelCase						)  ->	list:
				UpperCamelCase_:							Union[str, Any]	=						int(lowerCamelCase						)
				if n_element < 1:
								UpperCamelCase_:							Dict	=						ValueError("""a should be a positive number"""						)
								raise my_error

				UpperCamelCase_:							int	=						[1]
				UpperCamelCase_,   UpperCamelCase_,   UpperCamelCase_:							Union[str, Any]	=						(0, 0, 0)
				UpperCamelCase_:							Tuple	=						1
				while index < n_element:
								while hamming_list[i] * 2 <= hamming_list[-1]:
												i += 1
								while hamming_list[j] * 3 <= hamming_list[-1]:
												j += 1
								while hamming_list[k] * 5 <= hamming_list[-1]:
												k += 1
								hamming_list.append(
								    min(hamming_list[i] * 2     ,    hamming_list[j] * 3     ,    hamming_list[k] * 5						)						)
								index += 1
				return hamming_list


if __name__ == "__main__":
							lowerCamelCase_						: Optional[Any]         =  input("""Enter the last number (nth term) of the Hamming Number Series: """)
							print("""Formula of Hamming Number Series => 2^i * 3^j * 5^k""")
							lowerCamelCase_						: Union[str, Any]         =  hamming(int(n))
							print("""-----------------------------------------------------""")
							print(F"""The list with nth numbers is: {hamming_numbers}""")
							print("""-----------------------------------------------------""")








from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403







def        A__					(						lowerCamelCase     ,    lowerCamelCase     ,    lowerCamelCase = "x"     ,    lowerCamelCase = 10**-10     ,    lowerCamelCase = 1     ,    )  ->	complex:
				UpperCamelCase_:							Optional[Any]	=						symbols(lowerCamelCase						)
				UpperCamelCase_:							int	=						lambdify(lowerCamelCase     ,    lowerCamelCase						)
				UpperCamelCase_:							Optional[Any]	=						lambdify(lowerCamelCase     ,    diff(lowerCamelCase     ,    lowerCamelCase						)						)

				UpperCamelCase_:							Tuple	=						starting_point

				while True:
								if diff_function(lowerCamelCase						) != 0:
												UpperCamelCase_:							List[Any]	=						prev_guess - multiplicity * func(lowerCamelCase						) / diff_function(
												    lowerCamelCase						)
								else:
												raise ZeroDivisionError("""Could not find root"""						) from None

								# Precision is checked by comparing the difference of consecutive guesses
								if abs(next_guess - prev_guess						) < precision:
												return next_guess

								UpperCamelCase_:							Any	=						next_guess


# Let's Execute
if __name__ == "__main__":
							# Find root of trigonometric function
							# Find value of pi
							print(F"""The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}""")

							# Find root of polynomial
							# Find fourth Root of 5
							print(F"""The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5J)}""")

							# Find value of e
							print(
							    """The root of log(y) - 1 = 0 is """,
							    F"""{newton_raphson('log(y) - 1', 2, variable='y')}""",
							)

							# Exponential Roots
							print(
							    """The root of exp(x) - 1 = 0 is""",
							    F"""{newton_raphson('exp(x) - 1', 10, precision=0.005)}""",
							)

							# Find root of cos(x)
							print(F"""The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}""")






