






from __future__ import annotations

from collections.abc import Sequence
from typing import Literal




def 				A		(					lowercase__  :  str ,		lowercase__  :  str  )		-> str | Literal[False]:
	UpperCamelCase__ :Any						=      list(lowercase__  )
	UpperCamelCase__ :Optional[Any]						=      list(lowercase__  )
	UpperCamelCase__ :Union[str, Any]						=      0
	for i in range(len(lowercase__  )  ):
		if lista[i] != lista[i]:
			count += 1
			UpperCamelCase__ :str						=      """_"""
	if count > 1:
		return False
	else:
		return "".join(lowercase__  )




def 				A		(					lowercase__  :  list[str]  )		-> list[str]:
	UpperCamelCase__ :int						=      []
	while True:
		UpperCamelCase__ :Tuple						=      ["""$"""] * len(lowercase__  )
		UpperCamelCase__ :Tuple						=      []
		for i in range(len(lowercase__  )  ):
			for j in range(i + 1 ,		len(lowercase__  )  ):
				UpperCamelCase__ :str						=      compare_string(binary[i] ,		binary[j]  )
				if k is False:
					UpperCamelCase__ :str						=      """*"""
					UpperCamelCase__ :Union[str, Any]						=      """*"""
					temp.append("""X"""  )
		for i in range(len(lowercase__  )  ):
			if checka[i] == "$":
				pi.append(binary[i]  )
		if len(lowercase__  ) == 0:
			return pi
		UpperCamelCase__ :Tuple						=      list(set(lowercase__  )  )




def 				A		(					lowercase__  :  int ,		lowercase__  :  Sequence[float]  )		-> list[str]:
	UpperCamelCase__ :int						=      []
	for minterm in minterms:
		UpperCamelCase__ :Any						=      """"""
		for _ in range(lowercase__  ):
			UpperCamelCase__ :Any						=      str(minterm % 2  ) + string
			minterm //= 2
		temp.append(lowercase__  )
	return temp




def 				A		(					lowercase__  :  str ,		lowercase__  :  str ,		lowercase__  :  int  )		-> bool:
	UpperCamelCase__ :Tuple						=      list(lowercase__  )
	UpperCamelCase__ :List[str]						=      list(lowercase__  )
	UpperCamelCase__ :Any						=      0
	for i in range(len(lowercase__  )  ):
		if lista[i] != lista[i]:
			count_n += 1
	return count_n == count




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




def 				A		(					lowercase__  :  list[str] ,		lowercase__  :  list[str]  )		-> list[list[int]]:
	UpperCamelCase__ :Union[str, Any]						=      [[0 for x in range(len(lowercase__  )  )] for x in range(len(lowercase__  )  )]
	for i in range(len(lowercase__  )  ):
		UpperCamelCase__ :Union[str, Any]						=      prime_implicants[i].count("""_"""  )
		for j in range(len(lowercase__  )  ):
			if is_for_table(prime_implicants[i] ,		binary[j] ,		lowercase__  ):
				UpperCamelCase__ :Union[str, Any]						=      1

	return chart




def 				A		(					)		-> None:
	UpperCamelCase__ :List[str]						=      int(input("""Enter the no. of variables\n"""  )  )
	UpperCamelCase__ :Union[str, Any]						=      [
	    float(lowercase__  )
	    for x in input(
	        """Enter the decimal representation of Minterms 'Spaces Separated'\n"""  ).split()
	]
	UpperCamelCase__ :List[Any]						=      decimal_to_binary(lowercase__ ,		lowercase__  )

	UpperCamelCase__ :int						=      check(lowercase__  )
	print("""Prime Implicants are:"""  )
	print(lowercase__  )
	UpperCamelCase__ :List[str]						=      prime_implicant_chart(lowercase__ ,		lowercase__  )

	UpperCamelCase__ :Tuple						=      selection(lowercase__ ,		lowercase__  )
	print("""Essential Prime Implicants are:"""  )
	print(lowercase__  )


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							main()



class     __UpperCAmelCase							:


     """simple docstring"""


     def __init__(	self  ,       __A    ):
        __a					=  set_counts
        __a					=  max(__A    )
        __a					=  len(__A    )
        __a					=  [1] * num_sets
        __a					=  list(range(__A    )    )


     def 	snake_case_  (	self  ,       __A  ,       __A    ):
        __a					=  self.get_parent(__A    )
        __a					=  self.get_parent(__A    )

        if src_parent == dst_parent:
           return False

        if self.ranks[dst_parent] >= self.ranks[src_parent]:
           self.set_counts[dst_parent] += self.set_counts[src_parent]
           __a					=  0
           __a					=  dst_parent
           if self.ranks[dst_parent] == self.ranks[src_parent]:
              self.ranks[dst_parent] += 1
           __a					=  self.set_counts[dst_parent]
        else:
           self.set_counts[src_parent] += self.set_counts[dst_parent]
           __a					=  0
           __a					=  src_parent
           __a					=  self.set_counts[src_parent]

        __a					=  max(self.max_set  ,       __A    )
        return True


     def 	snake_case_  (	self  ,       __A    ):
        if self.parents[disj_set] == disj_set:
           return disj_set
        __a					=  self.get_parent(self.parents[disj_set]    )
        return self.parents[disj_set]



