"""simple docstring"""




from __future__ import annotations

from collections.abc import Sequence
from typing import Literal







def 				_UpperCAmelCase		(							lowerCamelCase__      ,	lowerCamelCase__  ):





		"""simple docstring"""




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







def 				_UpperCAmelCase		(							lowerCamelCase__  ):





		"""simple docstring"""




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







def 				_UpperCAmelCase		(							lowerCamelCase__      ,	lowerCamelCase__  ):





		"""simple docstring"""




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







def 				_UpperCAmelCase		(							lowerCamelCase__      ,	lowerCamelCase__      ,	lowerCamelCase__  ):





		"""simple docstring"""




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







def 				_UpperCAmelCase		(							lowerCamelCase__      ,	lowerCamelCase__  ):





		"""simple docstring"""




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







def 				_UpperCAmelCase		(							lowerCamelCase__      ,	lowerCamelCase__  ):





		"""simple docstring"""




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

		return chart







def 				_UpperCAmelCase		(							):





		"""simple docstring"""




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

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

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


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			main()





"""simple docstring"""




from __future__ import annotations

from typing import Any

class    a_   :




					def __init__(						self    :  Union[str, Any]	,    snake_case__    :  int = 6  ):
							lowerCAmelCase__   = None
							lowerCAmelCase__   = None
							self.create_linked_list(snake_case__  )




					def     _SCREAMING_SNAKE_CASE    (						self    :  Tuple	,    snake_case__    :  int  ):
							lowerCAmelCase__   = Node()
							lowerCAmelCase__   = current_node
							lowerCAmelCase__   = current_node
							lowerCAmelCase__   = current_node
							for _ in range(1	,    snake_case__  ):
									lowerCAmelCase__   = Node()
									lowerCAmelCase__   = current_node
									lowerCAmelCase__   = previous_node
									lowerCAmelCase__   = current_node
							lowerCAmelCase__   = self.front
							lowerCAmelCase__   = previous_node




					def     _SCREAMING_SNAKE_CASE    (						self    :  Any  ):
							return (
							    self.front == self.rear
							    and self.front is not None
							    and self.front.data is None
							)




					def     _SCREAMING_SNAKE_CASE    (						self    :  Any  ):
							self.check_can_perform_operation()
							return self.front.data if self.front else None




					def     _SCREAMING_SNAKE_CASE    (						self    :  Dict	,    snake_case__    :  Any  ):
							if self.rear is None:
									return

							self.check_is_full()
							if not self.is_empty():
									lowerCAmelCase__   = self.rear.next
							if self.rear:
									lowerCAmelCase__   = data




					def     _SCREAMING_SNAKE_CASE    (						self    :  Any  ):
							self.check_can_perform_operation()
							if self.rear is None or self.front is None:
									return None
							if self.front == self.rear:
									lowerCAmelCase__   = self.front.data
									lowerCAmelCase__   = None
									return data

							lowerCAmelCase__   = self.front
							lowerCAmelCase__   = old_front.next
							lowerCAmelCase__   = old_front.data
							lowerCAmelCase__   = None
							return data




					def     _SCREAMING_SNAKE_CASE    (						self    :  Union[str, Any]  ):
							if self.is_empty():
									raise Exception("""Empty Queue"""  )




					def     _SCREAMING_SNAKE_CASE    (						self    :  Optional[Any]  ):
							if self.rear and self.rear.next == self.front:
									raise Exception("""Full Queue"""  )

class    a_   :




					def __init__(						self    :  Union[str, Any]  ):
							lowerCAmelCase__   = None
							lowerCAmelCase__   = None
							lowerCAmelCase__   = None


if __name__ == "__main__":
			import doctest

			doctest.testmod()




