





"""simple docstring"""


def     UpperCamelCase       (SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    ):
						UpperCamelCase							:		List[Any]							      = list(SCREAMING_SNAKE_CASE    )
						UpperCamelCase							:		Dict							      = list(SCREAMING_SNAKE_CASE    )
						UpperCamelCase							:		Tuple							      = len(SCREAMING_SNAKE_CASE    )
						UpperCamelCase							:		List[Any]							      = len(SCREAMING_SNAKE_CASE    )

						UpperCamelCase							:		List[Any]							      = [
						    [0 for _ in range(len_destination_seq + 1    )] for _ in range(len_source_seq + 1    )
						]
						UpperCamelCase							:		Tuple							      = [
						    ["""0""" for _ in range(len_destination_seq + 1    )] for _ in range(len_source_seq + 1    )
						]

						for i in range(1       ,    len_source_seq + 1    ):
												UpperCamelCase							:		List[str]							      = i * delete_cost
												UpperCamelCase							:		List[str]							      = f"""D{source_seq[i - 1]:c}"""

						for i in range(1       ,    len_destination_seq + 1    ):
												UpperCamelCase							:		List[str]							      = i * insert_cost
												UpperCamelCase							:		str							      = f"""I{destination_seq[i - 1]:c}"""

						for i in range(1       ,    len_source_seq + 1    ):
												for j in range(1       ,    len_destination_seq + 1    ):
																		if source_seq[i - 1] == destination_seq[j - 1]:
																								UpperCamelCase							:		int							      = costs[i - 1][j - 1] + copy_cost
																								UpperCamelCase							:		int							      = f"""C{source_seq[i - 1]:c}"""
																		else:
																								UpperCamelCase							:		str							      = costs[i - 1][j - 1] + replace_cost
																								UpperCamelCase							:		Union[str, Any]							      = f"""R{source_seq[i - 1]:c}""" + str(destination_seq[j - 1]    )

																		if costs[i - 1][j] + delete_cost < costs[i][j]:
																								UpperCamelCase							:		str							      = costs[i - 1][j] + delete_cost
																								UpperCamelCase							:		List[str]							      = f"""D{source_seq[i - 1]:c}"""

																		if costs[i][j - 1] + insert_cost < costs[i][j]:
																								UpperCamelCase							:		Union[str, Any]							      = costs[i][j - 1] + insert_cost
																								UpperCamelCase							:		str							      = f"""I{destination_seq[j - 1]:c}"""

						return costs, ops

def     UpperCamelCase       (SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE    ):
						if i == 0 and j == 0:
												return []
						else:
												if ops[i][j][0] == "C" or ops[i][j][0] == "R":
																		UpperCamelCase							:		Optional[Any]							      = assemble_transformation(SCREAMING_SNAKE_CASE       ,    i - 1       ,    j - 1    )
																		seq.append(ops[i][j]    )
																		return seq
												elif ops[i][j][0] == "D":
																		UpperCamelCase							:		Dict							      = assemble_transformation(SCREAMING_SNAKE_CASE       ,    i - 1       ,    SCREAMING_SNAKE_CASE    )
																		seq.append(ops[i][j]    )
																		return seq
												else:
																		UpperCamelCase							:		Tuple							      = assemble_transformation(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    j - 1    )
																		seq.append(ops[i][j]    )
																		return seq


if __name__ == "__main__":
		__magic_name__	,       __magic_name__					:				Tuple	= compute_transform_tables("""Python""", """Algorithms""", -1, 1, 2, 2)

		__magic_name__					:				Union[str, Any]	= len(operations)
		__magic_name__					:				List[str]	= len(operations[0])
		__magic_name__					:				Any	= assemble_transformation(operations, m - 1, n - 1)

		__magic_name__					:				Optional[int]	= list("""Python""")
		__magic_name__					:				Tuple	= 0
		__magic_name__					:				Dict	= 0

		with open("""min_cost.txt""", """w""") as file:
				for op in sequence:
						print("""""".join(string))

						if op[0] == "C":
								file.write("""%-16s""" % """Copy %c""" % op[1])
								file.write("""\t\t\t""" + """""".join(string))
								file.write("""\r\n""")

								cost -= 1
						elif op[0] == "R":
								__magic_name__					:				int	= op[2]

								file.write("""%-16s""" % ("""Replace %c""" % op[1] + """ with """ + str(op[2])))
								file.write("""\t\t""" + """""".join(string))
								file.write("""\r\n""")

								cost += 1
						elif op[0] == "D":
								string.pop(i)

								file.write("""%-16s""" % """Delete %c""" % op[1])
								file.write("""\t\t\t""" + """""".join(string))
								file.write("""\r\n""")

								cost += 2
						else:
								string.insert(i, op[1])

								file.write("""%-16s""" % """Insert %c""" % op[1])
								file.write("""\t\t\t""" + """""".join(string))
								file.write("""\r\n""")

								cost += 2

						i += 1

				print("""""".join(string))
				print("""Cost: """, cost)

				file.write("""\r\nMinimum cost: """ + str(cost))










"""simple docstring"""


from __future__ import annotations

def     UpperCamelCase       (SCREAMING_SNAKE_CASE    ):
						UpperCamelCase							:		Tuple							      = [0] * max_one

						for i in range(0       ,    SCREAMING_SNAKE_CASE    ):
												UpperCamelCase							:		Union[str, Any]							      = i

						for i in range(2       ,    SCREAMING_SNAKE_CASE    ):
												if totients[i] == i:
																		for j in range(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE    ):
																								totients[j] -= totients[j] // i

						return totients

def     UpperCamelCase       (SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE    ):
						return sorted(str(SCREAMING_SNAKE_CASE    )    ) == sorted(str(SCREAMING_SNAKE_CASE    )    )

def     UpperCamelCase       (SCREAMING_SNAKE_CASE = 1000_0000    ):
						UpperCamelCase							:		List[str]							      = 1  # i
						UpperCamelCase							:		Optional[int]							      = 0  # φ(i)
						UpperCamelCase							:		List[str]							      = get_totients(max_n + 1    )

						for i in range(2       ,    max_n + 1    ):
												UpperCamelCase							:		Tuple							      = totients[i]

												if i * min_denominator < min_numerator * t and has_same_digits(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE    ):
																		UpperCamelCase							:		str							      = i
																		UpperCamelCase							:		Tuple							      = t

						return min_numerator


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



