from __future__ import annotations

from collections.abc import Sequence
from typing import Literal
def  A      (       _lowercase						,    _lowercase		):
						SCREAMING_SNAKE_CASE				:       Optional[int]     							=				list(__snake_case		)
						SCREAMING_SNAKE_CASE				:       int     							=				list(__snake_case		)
						SCREAMING_SNAKE_CASE				:       List[str]     							=				0
						for i in range(len(__snake_case		)		):
												if lista[i] != lista[i]:
																		count += 1
																		SCREAMING_SNAKE_CASE				:       Tuple     							=				'_'
						if count > 1:
												return False
						else:
												return "".join(__snake_case		)
def  A      (       _lowercase		):
						SCREAMING_SNAKE_CASE				:       List[str]     							=				[]
						while True:
												SCREAMING_SNAKE_CASE				:       Optional[int]     							=				['$'] * len(__snake_case		)
												SCREAMING_SNAKE_CASE				:       Dict     							=				[]
												for i in range(len(__snake_case		)		):
																		for j in range(i + 1						,    len(__snake_case		)		):
																								SCREAMING_SNAKE_CASE				:       Any     							=				compare_string(binary[i]						,    binary[j]		)
																								if k is False:
																														SCREAMING_SNAKE_CASE				:       List[str]     							=				'*'
																														SCREAMING_SNAKE_CASE				:       List[str]     							=				'*'
																														temp.append('''X'''		)
												for i in range(len(__snake_case		)		):
																		if checka[i] == "$":
																								pi.append(binary[i]		)
												if len(__snake_case		) == 0:
																		return pi
												SCREAMING_SNAKE_CASE				:       Union[str, Any]     							=				list(set(__snake_case		)		)
def  A      (       _lowercase						,    _lowercase		):
						SCREAMING_SNAKE_CASE				:       Optional[int]     							=				[]
						for minterm in minterms:
												SCREAMING_SNAKE_CASE				:       Tuple     							=				''
												for _ in range(__snake_case		):
																		SCREAMING_SNAKE_CASE				:       int     							=				str(minterm % 2		) + string
																		minterm //= 2
												temp.append(__snake_case		)
						return temp
def  A      (       _lowercase						,    _lowercase						,    _lowercase		):
						SCREAMING_SNAKE_CASE				:       str     							=				list(__snake_case		)
						SCREAMING_SNAKE_CASE				:       List[Any]     							=				list(__snake_case		)
						SCREAMING_SNAKE_CASE				:       List[Any]     							=				0
						for i in range(len(__snake_case		)		):
												if lista[i] != lista[i]:
																		count_n += 1
						return count_n == count
def  A      (       _lowercase						,    _lowercase		):
						SCREAMING_SNAKE_CASE				:       List[str]     							=				[]
						SCREAMING_SNAKE_CASE				:       Any     							=				[0] * len(__snake_case		)
						for i in range(len(chart[0]		)		):
												SCREAMING_SNAKE_CASE				:       List[str]     							=				0
												SCREAMING_SNAKE_CASE				:       int     							=				-1
												for j in range(len(__snake_case		)		):
																		if chart[j][i] == 1:
																								count += 1
																								SCREAMING_SNAKE_CASE				:       Any     							=				j
												if count == 1:
																		SCREAMING_SNAKE_CASE				:       Dict     							=				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				:       Optional[Any]     							=				0
																		temp.append(prime_implicants[i]		)
						while True:
												SCREAMING_SNAKE_CASE				:       List[str]     							=				0
												SCREAMING_SNAKE_CASE				:       Optional[Any]     							=				-1
												SCREAMING_SNAKE_CASE				:       Tuple     							=				0
												for i in range(len(__snake_case		)		):
																		SCREAMING_SNAKE_CASE				:       Optional[Any]     							=				chart[i].count(1		)
																		if count_n > max_n:
																								SCREAMING_SNAKE_CASE				:       List[Any]     							=				count_n
																								SCREAMING_SNAKE_CASE				:       List[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  A      (       _lowercase						,    _lowercase		):
						SCREAMING_SNAKE_CASE				:       Union[str, Any]     							=				[[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				:       int     							=				1

						return chart
def  A      (       ):
						SCREAMING_SNAKE_CASE				:       Optional[Any]     							=				int(input('''Enter the no. of variables\n'''		)		)
						SCREAMING_SNAKE_CASE				:       Optional[int]     							=				[
						    float(__snake_case		)
						    for x in input(
						        '''Enter the decimal representation of Minterms \'Spaces Separated\'\n'''		).split()
						]
						SCREAMING_SNAKE_CASE				:       Optional[Any]     							=				decimal_to_binary(__snake_case						,    __snake_case		)

						SCREAMING_SNAKE_CASE				:       Dict     							=				check(__snake_case		)
						print('''Prime Implicants are:'''		)
						print(__snake_case		)
						SCREAMING_SNAKE_CASE				:       List[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()












'''simple docstring'''




import math
import sys






def 			_lowerCAmelCase     (    __snake_case    :					int     )	->	int:
     if number != int(__snake_case     ):
          raise ValueError('the value of input must be a natural number'     )
     if number < 0:
          raise ValueError('the value of input must not be a negative number'     )
     if number == 0:
          return 1
     __A		:					str						=			[-1] * (number + 1)
     __A		:					Dict						=			0
     for i in range(1					,				number + 1     ):
          __A		:					int						=			sys.maxsize
          __A		:					int						=			int(math.sqrt(__snake_case     )     )
          for j in range(1					,				root + 1     ):
               __A		:					str						=			1 + answers[i - (j**2)]
               __A		:					Dict						=			min(__snake_case					,				__snake_case     )
          __A		:					Union[str, Any]						=			answer
     return answers[number]


if __name__ == "__main__":
  import doctest

  doctest.testmod()