


from __future__ import annotations

from collections.abc import Sequence
from typing import Literal


def 	UpperCAmelCase__      (      UpperCAmelCase__ :str ,					UpperCAmelCase__ :str					):






 '''simple docstring'''

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


def 	UpperCAmelCase__      (      UpperCAmelCase__ :list[str]					):






 '''simple docstring'''

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


def 	UpperCAmelCase__      (      UpperCAmelCase__ :int ,					UpperCAmelCase__ :Sequence[float]					):






 '''simple docstring'''

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


def 	UpperCAmelCase__      (      UpperCAmelCase__ :str ,					UpperCAmelCase__ :str ,					UpperCAmelCase__ :int					):






 '''simple docstring'''

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


def 	UpperCAmelCase__      (      UpperCAmelCase__ :list[list[int]] ,					UpperCAmelCase__ :list[str]					):






 '''simple docstring'''

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


def 	UpperCAmelCase__      (      UpperCAmelCase__ :list[str] ,					UpperCAmelCase__ :list[str]					):






 '''simple docstring'''

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

 return chart


def 	UpperCAmelCase__      (      ):






 '''simple docstring'''

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

 a						=		check(UpperCAmelCase__					)
 print("Prime Implicants are:"					)
 print(UpperCAmelCase__					)
 a						=		prime_implicant_chart(UpperCAmelCase__ ,					UpperCAmelCase__					)

 a						=		selection(UpperCAmelCase__ ,					UpperCAmelCase__					)
 print("Essential Prime Implicants are:"					)
 print(UpperCAmelCase__					)


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     main()






from __future__ import annotations


def 	UpperCAmelCase__      (      UpperCAmelCase__ :int					):






 '''simple docstring'''

 a						=		str(UpperCAmelCase__					)
 return len(UpperCAmelCase__					) == 9 and set(UpperCAmelCase__					) == set("123456789"					)


def 	UpperCAmelCase__      (      ):






 '''simple docstring'''

 for base_num in range(99_99 ,					49_99 ,					-1					):
  a						=		10_00_02 * base_num
  if is_9_pandigital(UpperCAmelCase__					):
   return candidate

 for base_num in range(3_33 ,					99 ,					-1					):
  a						=		1_00_20_03 * base_num
  if is_9_pandigital(UpperCAmelCase__					):
   return candidate

 return None


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

