

"""simple docstring"""


UpperCAmelCase													=[
    (1_000, "M"),
    (900, "CM"),
    (500, "D"),
    (400, "CD"),
    (100, "C"),
    (90, "XC"),
    (50, "L"),
    (40, "XL"),
    (10, "X"),
    (9, "IX"),
    (5, "V"),
    (4, "IV"),
    (1, "I"),
]



def   _A					(	_a	:						str				):



      """simple docstring"""






      A				  =		{"""I""": 1, """V""": 5, """X""": 1_0, """L""": 5_0, """C""": 1_0_0, """D""": 5_0_0, """M""": 1_0_0_0}
      A				  =		0
      A				  =		0
      while place < len(_a				):
            if (place + 1 < len(_a				)) and (vals[roman[place]] < vals[roman[place + 1]]):
                  total += vals[roman[place + 1]] - vals[roman[place]]
                  place += 2
            else:
                  total += vals[roman[place]]
                  place += 1
      return total



def   _A					(	_a	:						int				):



      """simple docstring"""






      A				  =		[]
      for arabic, roman in ROMAN:
            ((A)  ,			(A))				  =		divmod(_a     ,   _a				)
            result.append(roman * factor				)
            if number == 0:
                  break
      return "".join(_a				)


if __name__ == "__main__":
  import doctest

  doctest.testmod()







"""simple docstring"""


from __future__ import annotations

from collections.abc import Sequence
from typing import Literal



def   _A					(	_a	:						str     ,   _a	:						str				):



      """simple docstring"""






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



def   _A					(	_a	:						list[str]				):



      """simple docstring"""






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



def   _A					(	_a	:						int     ,   _a	:						Sequence[float]				):



      """simple docstring"""






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



def   _A					(	_a	:						str     ,   _a	:						str     ,   _a	:						int				):



      """simple docstring"""






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



def   _A					(	_a	:						list[list[int]]     ,   _a	:						list[str]				):



      """simple docstring"""






      A				  =		[]
      A				  =		[0] * len(_a				)
      for i in range(len(chart[0]				)				):
            A				  =		0
            A				  =		-1
            for j in range(len(_a				)				):
                  if chart[j][i] == 1:
                        count += 1
                        A				  =		j
            if count == 1:
                  A				  =		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				)				):
                                    A				  =		0
                  temp.append(prime_implicants[i]				)
      while True:
            A				  =		0
            A				  =		-1
            A				  =		0
            for i in range(len(_a				)				):
                  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(_a				)				):
                              A				  =		0



def   _A					(	_a	:						list[str]     ,   _a	:						list[str]				):



      """simple docstring"""






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

      return chart



def   _A					(	):



      """simple docstring"""






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

      A				  =		check(_a				)
      print("""Prime Implicants are:"""				)
      print(_a				)
      A				  =		prime_implicant_chart(_a     ,   _a				)

      A				  =		selection(_a     ,   _a				)
      print("""Essential Prime Implicants are:"""				)
      print(_a				)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()




