

'''simple docstring'''






from __future__ import annotations

from collections.abc import Sequence
from typing import Literal


def 	_A  (					A__  ,       A__   ):






 """simple docstring"""



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


def 	_A  (					A__   ):






 """simple docstring"""



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


def 	_A  (					A__  ,       A__   ):






 """simple docstring"""



 __lowercase													=				[]
 for minterm in minterms:
  __lowercase													=				''''''
  for _ in range(A__   ):
   __lowercase													=				str(minterm % 2   ) + string
   minterm //= 2
  temp.append(A__   )
 return temp


def 	_A  (					A__  ,       A__  ,       A__   ):






 """simple docstring"""



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


def 	_A  (					A__  ,       A__   ):






 """simple docstring"""



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


def 	_A  (					A__  ,       A__   ):






 """simple docstring"""



 __lowercase													=				[[0 for x in range(len(A__   )   )] for x in range(len(A__   )   )]
 for i in range(len(A__   )   ):
  __lowercase													=				prime_implicants[i].count('''_'''   )
  for j in range(len(A__   )   ):
   if is_for_table(prime_implicants[i]  ,       binary[j]  ,       A__   ):
    __lowercase													=				1

 return chart


def 	_A  (					):






 """simple docstring"""



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

 __lowercase													=				check(A__   )
 print('''Prime Implicants are:'''   )
 print(A__   )
 __lowercase													=				prime_implicant_chart(A__  ,       A__   )

 __lowercase													=				selection(A__  ,       A__   )
 print('''Essential Prime Implicants are:'''   )
 print(A__   )


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 main()




'''simple docstring'''






def 	_A  (					):






 """simple docstring"""



 for n in range(1  ,       1000000   ):
  yield n * (n + 1) // 2


def 	_A  (					A__   ):






 """simple docstring"""



 __lowercase													=				1
 __lowercase													=				2
 while i * i <= n:
  __lowercase													=				0
  while n % i == 0:
   n //= i
   multiplicity += 1
  divisors_count *= multiplicity + 1
  i += 1
 if n > 1:
  divisors_count *= 2
 return divisors_count


def 	_A  (					):






 """simple docstring"""



 return next(i for i in triangle_number_generator() if count_divisors(A__   ) > 500   )


if __name__ == "__main__":
 print(solution())

