





'''simple docstring'''







from __future__ import annotations

from collections.abc import Sequence
from typing import Literal





def        lowerCamelCase_      (  SCREAMING_SNAKE_CASE__      :			str,			SCREAMING_SNAKE_CASE__      :			str   ) ->	str | Literal[False]:
						UpperCAmelCase_			:      Union[str, Any]     						=  list(SCREAMING_SNAKE_CASE__   )
						UpperCAmelCase_			:      Any     						=  list(SCREAMING_SNAKE_CASE__   )
						UpperCAmelCase_			:      Dict     						=  0
						for i in range(len(SCREAMING_SNAKE_CASE__   )   ):
												if lista[i] != lista[i]:
																		count += 1
																		UpperCAmelCase_			:      Tuple     						=  '''_'''
						if count > 1:
												return False
						else:
												return "".join(SCREAMING_SNAKE_CASE__   )





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





def        lowerCamelCase_      (  SCREAMING_SNAKE_CASE__      :			int,			SCREAMING_SNAKE_CASE__      :			Sequence[float]   ) ->	list[str]:
						UpperCAmelCase_			:      Any     						=  []
						for minterm in minterms:
												UpperCAmelCase_			:      Optional[int]     						=  ''''''
												for _ in range(SCREAMING_SNAKE_CASE__   ):
																		UpperCAmelCase_			:      Dict     						=  str(minterm % 2   ) + string
																		minterm //= 2
												temp.append(SCREAMING_SNAKE_CASE__   )
						return temp





def        lowerCamelCase_      (  SCREAMING_SNAKE_CASE__      :			str,			SCREAMING_SNAKE_CASE__      :			str,			SCREAMING_SNAKE_CASE__      :			int   ) ->	bool:
						UpperCAmelCase_			:      Dict     						=  list(SCREAMING_SNAKE_CASE__   )
						UpperCAmelCase_			:      List[str]     						=  list(SCREAMING_SNAKE_CASE__   )
						UpperCAmelCase_			:      Union[str, Any]     						=  0
						for i in range(len(SCREAMING_SNAKE_CASE__   )   ):
												if lista[i] != lista[i]:
																		count_n += 1
						return count_n == count





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





def        lowerCamelCase_      (  SCREAMING_SNAKE_CASE__      :			list[str],			SCREAMING_SNAKE_CASE__      :			list[str]   ) ->	list[list[int]]:
						UpperCAmelCase_			:      Dict     						=  [[0 for x in range(len(SCREAMING_SNAKE_CASE__   )   )] for x in range(len(SCREAMING_SNAKE_CASE__   )   )]
						for i in range(len(SCREAMING_SNAKE_CASE__   )   ):
												UpperCAmelCase_			:      Dict     						=  prime_implicants[i].count('''_'''   )
												for j in range(len(SCREAMING_SNAKE_CASE__   )   ):
																		if is_for_table(prime_implicants[i],			binary[j],			SCREAMING_SNAKE_CASE__   ):
																								UpperCAmelCase_			:      Optional[int]     						=  1

						return chart





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

						UpperCAmelCase_			:      Dict     						=  check(SCREAMING_SNAKE_CASE__   )
						print('''Prime Implicants are:'''   )
						print(SCREAMING_SNAKE_CASE__   )
						UpperCAmelCase_			:      int     						=  prime_implicant_chart(SCREAMING_SNAKE_CASE__,			SCREAMING_SNAKE_CASE__   )

						UpperCAmelCase_			:      List[Any]     						=  selection(SCREAMING_SNAKE_CASE__,			SCREAMING_SNAKE_CASE__   )
						print('''Essential Prime Implicants are:'''   )
						print(SCREAMING_SNAKE_CASE__   )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					main()












'''simple docstring'''







class 					__a      :

							def __init__(							self							:     List[Any]       ,     __magic_name__							:     int   )					->       None:







													"""simple docstring"""
													UpperCAmelCase_			:      Optional[Any]     						=  size
													UpperCAmelCase_			:      Tuple     						=  [0] * size
													UpperCAmelCase_			:      Optional[Any]     						=  [0] * size

							@staticmethod
							def     UpperCAmelCase__	(							__magic_name__							:     int   )					->       int:







													"""simple docstring"""
													return index | (index + 1)

							@staticmethod
							def     UpperCAmelCase__	(							__magic_name__							:     int   )					->       int:







													"""simple docstring"""
													return (index & (index + 1)) - 1

							def     UpperCAmelCase__	(							self							:     Optional[int]       ,     __magic_name__							:     int       ,     __magic_name__							:     int   )					->       None:







													"""simple docstring"""
													UpperCAmelCase_			:      int     						=  value
													while index < self.size:
																			UpperCAmelCase_			:      str     						=  self.get_prev(__magic_name__   ) + 1
																			if current_left_border == index:
																									UpperCAmelCase_			:      List[str]     						=  value
																			else:
																									UpperCAmelCase_			:      Optional[int]     						=  max(__magic_name__       ,     __magic_name__       ,     __magic_name__   )
																			UpperCAmelCase_			:      Tuple     						=  self.get_next(__magic_name__   )



							def     UpperCAmelCase__	(							self							:     Any       ,     __magic_name__							:     int       ,     __magic_name__							:     int   )					->       int:







													"""simple docstring"""
													right -= 1  # Because of right is exclusive
													UpperCAmelCase_			:      List[str]     						=  0
													while left <= right:
																			UpperCAmelCase_			:      Optional[Any]     						=  self.get_prev(__magic_name__   )
																			if left <= current_left:
																									UpperCAmelCase_			:      Dict     						=  max(__magic_name__       ,     self.tree[right]   )
																									UpperCAmelCase_			:      Optional[Any]     						=  current_left
																			else:
																									UpperCAmelCase_			:      str     						=  max(__magic_name__       ,     self.arr[right]   )
																									right -= 1
													return result


if __name__ == "__main__":
					import doctest

					doctest.testmod()





