
import itertools
import string
from collections.abc import Generator, Iterable







def        A__					(						lowerCamelCase     ,    lowerCamelCase						)  ->	Generator[tuple[str, ...], None, None]:
				UpperCamelCase_:							Tuple	=						iter(lowerCamelCase						)
				while True:
								UpperCamelCase_:							Optional[int]	=						tuple(itertools.islice(lowerCamelCase     ,    lowerCamelCase						)						)
								if not chunk:
												return
								yield chunk







def        A__					(						lowerCamelCase						)  ->	str:
				UpperCamelCase_:							int	=						"""""".join([c.upper() for c in dirty if c in string.ascii_letters]						)
				UpperCamelCase_:							Tuple	=						""""""

				if len(lowerCamelCase						) < 2:
								return dirty

				for i in range(len(lowerCamelCase						) - 1						):
								clean += dirty[i]

								if dirty[i] == dirty[i + 1]:
												clean += "X"

				clean += dirty[-1]

				if len(lowerCamelCase						) & 1:
								clean += "X"

				return clean







def        A__					(						lowerCamelCase						)  ->	list[str]:
				# I and J are used interchangeably to allow
				# us to use a 5x5 table (25 letters)
				UpperCamelCase_:							Tuple	=						"""ABCDEFGHIKLMNOPQRSTUVWXYZ"""
				# we're using a list instead of a '2d' array because it makes the math
				# for setting up the table and doing the actual encoding/decoding simpler
				UpperCamelCase_:							str	=						[]

				# copy key chars into the table if they are in `alphabet` ignoring duplicates
				for char in key.upper():
								if char not in table and char in alphabet:
												table.append(lowerCamelCase						)

    # fill the rest of the table in with the remaining alphabet chars
				for char in alphabet:
								if char not in table:
												table.append(lowerCamelCase						)

				return table







def        A__					(						lowerCamelCase     ,    lowerCamelCase						)  ->	str:
				UpperCamelCase_:							int	=						generate_table(lowerCamelCase						)
				UpperCamelCase_:							Optional[Any]	=						prepare_input(lowerCamelCase						)
				UpperCamelCase_:							int	=						""""""

				# https://en.wikipedia.org/wiki/Playfair_cipher#Description
				for chara, chara in chunker(lowerCamelCase     ,    2						):
								UpperCamelCase_,   UpperCamelCase_:							List[Any]	=						divmod(table.index(lowerCamelCase						)     ,    5						)
								UpperCamelCase_,   UpperCamelCase_:							Any	=						divmod(table.index(lowerCamelCase						)     ,    5						)

								if rowa == rowa:
												ciphertext += table[rowa * 5 + (cola + 1) % 5]
												ciphertext += table[rowa * 5 + (cola + 1) % 5]
								elif cola == cola:
												ciphertext += table[((rowa + 1) % 5) * 5 + cola]
												ciphertext += table[((rowa + 1) % 5) * 5 + cola]
								else:  # rectangle
												ciphertext += table[rowa * 5 + cola]
												ciphertext += table[rowa * 5 + cola]

				return ciphertext







def        A__					(						lowerCamelCase     ,    lowerCamelCase						)  ->	str:
				UpperCamelCase_:							Union[str, Any]	=						generate_table(lowerCamelCase						)
				UpperCamelCase_:							Dict	=						""""""

				# https://en.wikipedia.org/wiki/Playfair_cipher#Description
				for chara, chara in chunker(lowerCamelCase     ,    2						):
								UpperCamelCase_,   UpperCamelCase_:							str	=						divmod(table.index(lowerCamelCase						)     ,    5						)
								UpperCamelCase_,   UpperCamelCase_:							Optional[Any]	=						divmod(table.index(lowerCamelCase						)     ,    5						)

								if rowa == rowa:
												plaintext += table[rowa * 5 + (cola - 1) % 5]
												plaintext += table[rowa * 5 + (cola - 1) % 5]
								elif cola == cola:
												plaintext += table[((rowa - 1) % 5) * 5 + cola]
												plaintext += table[((rowa - 1) % 5) * 5 + cola]
								else:  # rectangle
												plaintext += table[rowa * 5 + cola]
												plaintext += table[rowa * 5 + cola]

				return plaintext








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)}""")






