





from __future__ import annotations

from collections.abc import Sequence
from typing import Literal




def _a (  SCREAMING_SNAKE_CASE__      :  str			,				SCREAMING_SNAKE_CASE__      :  str       )	->    str | Literal[False]:

							'''simple docstring'''






							SCREAMING_SNAKE_CASE__       :      Optional[int]     =						list(_lowerCamelCase       )
							SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						list(_lowerCamelCase       )
							SCREAMING_SNAKE_CASE__       :      Tuple     =						0
							for i in range(len(_lowerCamelCase       )       ):
														if lista[i] != lista[i]:
																					count += 1
																					SCREAMING_SNAKE_CASE__       :      Optional[int]     =						"_"
							if count > 1:
														return False
							else:
														return "".join(_lowerCamelCase       )




def _a (  SCREAMING_SNAKE_CASE__      :  list[str]       )	->    list[str]:

							'''simple docstring'''






							SCREAMING_SNAKE_CASE__       :      List[Any]     =						[]
							while True:
														SCREAMING_SNAKE_CASE__       :      Dict     =						["$"] * len(_lowerCamelCase       )
														SCREAMING_SNAKE_CASE__       :      Any     =						[]
														for i in range(len(_lowerCamelCase       )       ):
																					for j in range(i + 1			,				len(_lowerCamelCase       )       ):
																												SCREAMING_SNAKE_CASE__       :      str     =						compare_string(binary[i]			,				binary[j]       )
																												if k is False:
																																			SCREAMING_SNAKE_CASE__       :      str     =						"*"
																																			SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						"*"
																																			temp.append("X"       )
														for i in range(len(_lowerCamelCase       )       ):
																					if checka[i] == "$":
																												pi.append(binary[i]       )
														if len(_lowerCamelCase       ) == 0:
																					return pi
														SCREAMING_SNAKE_CASE__       :      Tuple     =						list(set(_lowerCamelCase       )       )




def _a (  SCREAMING_SNAKE_CASE__      :  int			,				SCREAMING_SNAKE_CASE__      :  Sequence[float]       )	->    list[str]:

							'''simple docstring'''






							SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						[]
							for minterm in minterms:
														SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						""
														for _ in range(_lowerCamelCase       ):
																					SCREAMING_SNAKE_CASE__       :      Tuple     =						str(minterm % 2       ) + string
																					minterm //= 2
														temp.append(_lowerCamelCase       )
							return temp




def _a (  SCREAMING_SNAKE_CASE__      :  str			,				SCREAMING_SNAKE_CASE__      :  str			,				SCREAMING_SNAKE_CASE__      :  int       )	->    bool:

							'''simple docstring'''






							SCREAMING_SNAKE_CASE__       :      Tuple     =						list(_lowerCamelCase       )
							SCREAMING_SNAKE_CASE__       :      Optional[int]     =						list(_lowerCamelCase       )
							SCREAMING_SNAKE_CASE__       :      str     =						0
							for i in range(len(_lowerCamelCase       )       ):
														if lista[i] != lista[i]:
																					count_n += 1
							return count_n == count




def _a (  SCREAMING_SNAKE_CASE__      :  list[list[int]]			,				SCREAMING_SNAKE_CASE__      :  list[str]       )	->    list[str]:

							'''simple docstring'''






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




def _a (  SCREAMING_SNAKE_CASE__      :  list[str]			,				SCREAMING_SNAKE_CASE__      :  list[str]       )	->    list[list[int]]:

							'''simple docstring'''






							SCREAMING_SNAKE_CASE__       :      Dict     =						[[0 for x in range(len(_lowerCamelCase       )       )] for x in range(len(_lowerCamelCase       )       )]
							for i in range(len(_lowerCamelCase       )       ):
														SCREAMING_SNAKE_CASE__       :      List[str]     =						prime_implicants[i].count("_"       )
														for j in range(len(_lowerCamelCase       )       ):
																					if is_for_table(prime_implicants[i]			,				binary[j]			,				_lowerCamelCase       ):
																												SCREAMING_SNAKE_CASE__       :      Dict     =						1

							return chart




def _a (  )	->    None:

							'''simple docstring'''






							SCREAMING_SNAKE_CASE__       :      Any     =						int(input("Enter the no. of variables\n"       )       )
							SCREAMING_SNAKE_CASE__       :      List[str]     =						[
							    float(_lowerCamelCase       )
							    for x in input(
							        "Enter the decimal representation of Minterms 'Spaces Separated'\n"       ).split()
							]
							SCREAMING_SNAKE_CASE__       :      List[str]     =						decimal_to_binary(_lowerCamelCase			,				_lowerCamelCase       )

							SCREAMING_SNAKE_CASE__       :      str     =						check(_lowerCamelCase       )
							print("Prime Implicants are:"       )
							print(_lowerCamelCase       )
							SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						prime_implicant_chart(_lowerCamelCase			,				_lowerCamelCase       )

							SCREAMING_SNAKE_CASE__       :      Any     =						selection(_lowerCamelCase			,				_lowerCamelCase       )
							print("Essential Prime Implicants are:"       )
							print(_lowerCamelCase       )


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		main()













def _a (  SCREAMING_SNAKE_CASE__      :  int = 50_00_00_00       )	->    int:

							'''simple docstring'''






							SCREAMING_SNAKE_CASE__       :      str     =						set()
							SCREAMING_SNAKE_CASE__       :      Dict     =						int((limit - 24) ** (1 / 2)       )

							SCREAMING_SNAKE_CASE__       :      Any     =						set(range(3			,				prime_square_limit + 1			,				2       )       )
							primes.add(2       )
							for p in range(3			,				prime_square_limit + 1			,				2       ):
														if p not in primes:
																					continue
														primes.difference_update(set(range(p * p			,				prime_square_limit + 1			,				SCREAMING_SNAKE_CASE__       )       )       )

							for primea in primes:
														SCREAMING_SNAKE_CASE__       :      Optional[int]     =						primea * primea
														for primea in primes:
																					SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						primea * primea * primea
																					if square + cube >= limit - 16:
																												break
																					for primea in primes:
																												SCREAMING_SNAKE_CASE__       :      List[str]     =						primea * primea * primea * primea
																												SCREAMING_SNAKE_CASE__       :      Optional[int]     =						square + cube + tetr
																												if total >= limit:
																																			break
																												ret.add(SCREAMING_SNAKE_CASE__       )

							return len(SCREAMING_SNAKE_CASE__       )


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






