
"""simple docstring"""




from __future__ import annotations

from collections.abc import Sequence
from typing import Literal

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

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

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

def lowercase_  (   _snake_case   ,_snake_case   ,_snake_case						):
							SCREAMING_SNAKE_CASE__						:       str           =   list(_snake_case						)
							SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   list(_snake_case						)
							SCREAMING_SNAKE_CASE__						:       str           =   0
							for i in range(len(_snake_case						)						):
														if lista[i] != lista[i]:
																					count_n += 1
							return count_n == count

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

def lowercase_  (   _snake_case   ,_snake_case						):
							SCREAMING_SNAKE_CASE__						:       Tuple           =   [[0 for x in range(len(_snake_case						)						)] for x in range(len(_snake_case						)						)]
							for i in range(len(_snake_case						)						):
														SCREAMING_SNAKE_CASE__						:       Optional[int]           =   prime_implicants[i].count("""_"""						)
														for j in range(len(_snake_case						)						):
																					if is_for_table(prime_implicants[i]   ,binary[j]   ,_snake_case						):
																												SCREAMING_SNAKE_CASE__						:       Tuple           =   1

							return chart

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

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

							SCREAMING_SNAKE_CASE__						:       Tuple           =   selection(_snake_case   ,_snake_case						)
							print("""Essential Prime Implicants are:"""						)
							print(_snake_case						)


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					main()











def 		lowerCAmelCase_    (  __UpperCAmelCase:			int = 100_0000      )      ->	int:
    UpperCamelCase__							:				str          =      limit + 1
    UpperCamelCase__							:				List[str]          =      [0] * limit
    for first_term in range(1		,   __UpperCAmelCase      ):
        for n in range(__UpperCAmelCase		,   __UpperCAmelCase		,   __UpperCAmelCase      ):
            UpperCamelCase__							:				str          =      first_term + n / first_term
            if common_difference % 4:  # d must be divisble by 4
                continue
            else:
                common_difference /= 4
                if (
                    first_term > common_difference
                    and first_term < 4 * common_difference
                ):  # since x,y,z are positive integers
                    frequency[n] += 1  # so z>0 and a>d ,also 4d<a

    UpperCamelCase__							:				Any          =      sum(1 for x in frequency[1:limit] if x == 10      )

    return count


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

