




'''simple docstring'''





from __future__ import annotations

from collections.abc import Sequence
from typing import Literal


def 					UpperCamelCase_(     snake_case							:	str							,    snake_case							:	str					):

							'''simple docstring'''






							snake_case_      =				list(lowerCamelCase__					)
							snake_case_      =				list(lowerCamelCase__					)
							snake_case_      =				0
							for i in range(len(lowerCamelCase__					)					):
														if lista[i] != lista[i]:
																					count += 1
																					snake_case_      =				"_"
							if count > 1:
														return False
							else:
														return "".join(lowerCamelCase__					)


def 					UpperCamelCase_(     snake_case							:	list[str]					):

							'''simple docstring'''






							snake_case_      =				[]
							while True:
														snake_case_      =				["$"] * len(lowerCamelCase__					)
														snake_case_      =				[]
														for i in range(len(lowerCamelCase__					)					):
																					for j in range(i + 1							,    len(lowerCamelCase__					)					):
																												snake_case_      =				compare_string(binary[i]							,    binary[j]					)
																												if k is False:
																																			snake_case_      =				"*"
																																			snake_case_      =				"*"
																																			temp.append("X"					)
														for i in range(len(lowerCamelCase__					)					):
																					if checka[i] == "$":
																												pi.append(binary[i]					)
														if len(lowerCamelCase__					) == 0:
																					return pi
														snake_case_      =				list(set(lowerCamelCase__					)					)


def 					UpperCamelCase_(     snake_case							:	int							,    snake_case							:	Sequence[float]					):

							'''simple docstring'''






							snake_case_      =				[]
							for minterm in minterms:
														snake_case_      =				""
														for _ in range(lowerCamelCase__					):
																					snake_case_      =				str(minterm % 2					) + string
																					minterm //= 2
														temp.append(lowerCamelCase__					)
							return temp


def 					UpperCamelCase_(     snake_case							:	str							,    snake_case							:	str							,    snake_case							:	int					):

							'''simple docstring'''






							snake_case_      =				list(lowerCamelCase__					)
							snake_case_      =				list(lowerCamelCase__					)
							snake_case_      =				0
							for i in range(len(lowerCamelCase__					)					):
														if lista[i] != lista[i]:
																					count_n += 1
							return count_n == count


def 					UpperCamelCase_(     snake_case							:	list[list[int]]							,    snake_case							:	list[str]					):

							'''simple docstring'''






							snake_case_      =				[]
							snake_case_      =				[0] * len(lowerCamelCase__					)
							for i in range(len(chart[0]					)					):
														snake_case_      =				0
														snake_case_      =				-1
														for j in range(len(lowerCamelCase__					)					):
																					if chart[j][i] == 1:
																												count += 1
																												snake_case_      =				j
														if count == 1:
																					snake_case_      =				1
							for i in range(len(lowerCamelCase__					)					):
														if select[i] == 1:
																					for j in range(len(chart[0]					)					):
																												if chart[i][j] == 1:
																																			for k in range(len(lowerCamelCase__					)					):
																																										snake_case_      =				0
																					temp.append(prime_implicants[i]					)
							while True:
														snake_case_      =				0
														snake_case_      =				-1
														snake_case_      =				0
														for i in range(len(lowerCamelCase__					)					):
																					snake_case_      =				chart[i].count(1					)
																					if count_n > max_n:
																												snake_case_      =				count_n
																												snake_case_      =				i

														if max_n == 0:
																					return temp

														temp.append(prime_implicants[rem]					)

														for i in range(len(chart[0]					)					):
																					if chart[rem][i] == 1:
																												for j in range(len(lowerCamelCase__					)					):
																																			snake_case_      =				0


def 					UpperCamelCase_(     snake_case							:	list[str]							,    snake_case							:	list[str]					):

							'''simple docstring'''






							snake_case_      =				[[0 for x in range(len(lowerCamelCase__					)					)] for x in range(len(lowerCamelCase__					)					)]
							for i in range(len(lowerCamelCase__					)					):
														snake_case_      =				prime_implicants[i].count("_"					)
														for j in range(len(lowerCamelCase__					)					):
																					if is_for_table(prime_implicants[i]							,    binary[j]							,    lowerCamelCase__					):
																												snake_case_      =				1

							return chart


def 					UpperCamelCase_(     ):

							'''simple docstring'''






							snake_case_      =				int(input("Enter the no. of variables\n"					)					)
							snake_case_      =				[
							    float(lowerCamelCase__					)
							    for x in input(
							        "Enter the decimal representation of Minterms 'Spaces Separated'\n"					).split()
							]
							snake_case_      =				decimal_to_binary(lowerCamelCase__							,    lowerCamelCase__					)

							snake_case_      =				check(lowerCamelCase__					)
							print("Prime Implicants are:"					)
							print(lowerCamelCase__					)
							snake_case_      =				prime_implicant_chart(lowerCamelCase__							,    lowerCamelCase__					)

							snake_case_      =				selection(lowerCamelCase__							,    lowerCamelCase__					)
							print("Essential Prime Implicants are:"					)
							print(lowerCamelCase__					)


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		main()










'''simple docstring'''





def 					UpperCamelCase_(     snake_case							:	int = 1_0_0_0_0_0_0					):

							'''simple docstring'''






							snake_case_      =				set(range(3							,    snake_case							,    2					)					)
							primes.add(2					)
							for p in range(3							,    snake_case							,    2					):
														if p not in primes:
																					continue
														primes.difference_update(set(range(p * p							,    snake_case							,    snake_case					)					)					)

							snake_case_      =				[float(snake_case					) for n in range(limit + 1					)]

							for p in primes:
														for n in range(snake_case							,    limit + 1							,    snake_case					):
																					phi[n] *= 1 - 1 / p

							return int(sum(phi[2:]					)					)


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




