

from __future__ import annotations

from collections.abc import Sequence
from typing import Literal

def 						UpperCamelCase					(lowercase_: str    ,      lowercase_: str					)     ->      str | Literal[False]:
	A__							:    int        =		list(lowercase_					)
	A__							:    int        =		list(lowercase_					)
	A__							:    Any        =		0
	for i in range(len(lowercase_					)					):
		if lista[i] != lista[i]:
			count += 1
			A__							:    Dict        =		"""_"""
	if count > 1:
		return False
	else:
		return "".join(lowercase_					)

def 						UpperCamelCase					(lowercase_: list[str]					)     ->      list[str]:
	A__							:    str        =		[]
	while True:
		A__							:    Any        =		["""$"""] * len(lowercase_					)
		A__							:    Tuple        =		[]
		for i in range(len(lowercase_					)					):
			for j in range(i + 1    ,      len(lowercase_					)					):
				A__							:    Any        =		compare_string(binary[i]    ,      binary[j]					)
				if k is False:
					A__							:    Optional[int]        =		"""*"""
					A__							:    Optional[int]        =		"""*"""
					temp.append("""X"""					)
		for i in range(len(lowercase_					)					):
			if checka[i] == "$":
				pi.append(binary[i]					)
		if len(lowercase_					) == 0:
			return pi
		A__							:    Optional[Any]        =		list(set(lowercase_					)					)

def 						UpperCamelCase					(lowercase_: int    ,      lowercase_: Sequence[float]					)     ->      list[str]:
	A__							:    Optional[Any]        =		[]
	for minterm in minterms:
		A__							:    List[Any]        =		""""""
		for _ in range(lowercase_					):
			A__							:    Tuple        =		str(minterm % 2					) + string
			minterm //= 2
		temp.append(lowercase_					)
	return temp

def 						UpperCamelCase					(lowercase_: str    ,      lowercase_: str    ,      lowercase_: int					)     ->      bool:
	A__							:    Dict        =		list(lowercase_					)
	A__							:    Dict        =		list(lowercase_					)
	A__							:    List[str]        =		0
	for i in range(len(lowercase_					)					):
		if lista[i] != lista[i]:
			count_n += 1
	return count_n == count

def 						UpperCamelCase					(lowercase_: list[list[int]]    ,      lowercase_: list[str]					)     ->      list[str]:
	A__							:    Tuple        =		[]
	A__							:    List[Any]        =		[0] * len(lowercase_					)
	for i in range(len(chart[0]					)					):
		A__							:    str        =		0
		A__							:    Dict        =		-1
		for j in range(len(lowercase_					)					):
			if chart[j][i] == 1:
				count += 1
				A__							:    Union[str, Any]        =		j
		if count == 1:
			A__							:    List[Any]        =		1
	for i in range(len(lowercase_					)					):
		if select[i] == 1:
			for j in range(len(chart[0]					)					):
				if chart[i][j] == 1:
					for k in range(len(lowercase_					)					):
						A__							:    Union[str, Any]        =		0
			temp.append(prime_implicants[i]					)
	while True:
		A__							:    List[str]        =		0
		A__							:    Union[str, Any]        =		-1
		A__							:    Union[str, Any]        =		0
		for i in range(len(lowercase_					)					):
			A__							:    Any        =		chart[i].count(1					)
			if count_n > max_n:
				A__							:    Optional[int]        =		count_n
				A__							:    Tuple        =		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(lowercase_					)					):
					A__							:    int        =		0

def 						UpperCamelCase					(lowercase_: list[str]    ,      lowercase_: list[str]					)     ->      list[list[int]]:
	A__							:    Dict        =		[[0 for x in range(len(lowercase_					)					)] for x in range(len(lowercase_					)					)]
	for i in range(len(lowercase_					)					):
		A__							:    Optional[int]        =		prime_implicants[i].count("""_"""					)
		for j in range(len(lowercase_					)					):
			if is_for_table(prime_implicants[i]    ,      binary[j]    ,      lowercase_					):
				A__							:    Any        =		1

	return chart

def 						UpperCamelCase					()     ->      None:
	A__							:    List[Any]        =		int(input("""Enter the no. of variables\n"""					)					)
	A__							:    Optional[int]        =		[
	    float(lowercase_					)
	    for x in input(
	        """Enter the decimal representation of Minterms 'Spaces Separated'\n"""					).split()
	]
	A__							:    Optional[int]        =		decimal_to_binary(lowercase_    ,      lowercase_					)

	A__							:    List[str]        =		check(lowercase_					)
	print("""Prime Implicants are:"""					)
	print(lowercase_					)
	A__							:    Optional[Any]        =		prime_implicant_chart(lowercase_    ,      lowercase_					)

	A__							:    Tuple        =		selection(lowercase_    ,      lowercase_					)
	print("""Essential Prime Implicants are:"""					)
	print(lowercase_					)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()






from math import factorial

def 						UpperCamelCase					(lowercase_: int = 20					)     ->      int:
	A__							:    Union[str, Any]        =		2 * n  # middle entry of odd rows starting at row 3 is the solution for n = 1,
	# 2, 3,...
	A__							:    Tuple        =		n // 2

	return int(factorial(lowercase_					) / (factorial(lowercase_					) * factorial(n - k					))					)


if __name__ == "__main__":
	import sys

	if len(sys.argv) == 1:
		print(solution(20))
	else:
		try:
			A_       : List[str]         =			int(sys.argv[1])
			print(solution(n))
		except ValueError:
			print('Invalid entry - please enter a number.')



