





"""simple docstring"""






from __future__ import annotations

from collections.abc import Sequence
from typing import Literal

def       __A (     a_  :str				,    a_  :str)						->						str | Literal[False]:
				__a	:  Any         =					list(_UpperCamelCase)
				__a	:  Optional[int]         =					list(_UpperCamelCase)
				__a	:  List[Any]         =					0
				for i in range(len(_UpperCamelCase)):
								if lista[i] != lista[i]:
												count += 1
												__a	:  Union[str, Any]         =					'''_'''
				if count > 1:
								return False
				else:
								return "".join(_UpperCamelCase)

def       __A (     a_  :list[str])						->						list[str]:
				__a	:  Tuple         =					[]
				while True:
								__a	:  List[str]         =					['''$'''] * len(_UpperCamelCase)
								__a	:  Optional[Any]         =					[]
								for i in range(len(_UpperCamelCase)):
												for j in range(i + 1				,    len(_UpperCamelCase)):
																__a	:  Tuple         =					compare_string(binary[i]				,    binary[j])
																if k is False:
																				__a	:  Optional[int]         =					'''*'''
																				__a	:  List[str]         =					'''*'''
																				temp.append('''X''')
								for i in range(len(_UpperCamelCase)):
												if checka[i] == "$":
																pi.append(binary[i])
								if len(_UpperCamelCase) == 0:
												return pi
								__a	:  Any         =					list(set(_UpperCamelCase))

def       __A (     a_  :int				,    a_  :Sequence[float])						->						list[str]:
				__a	:  Tuple         =					[]
				for minterm in minterms:
								__a	:  Tuple         =					''''''
								for _ in range(_UpperCamelCase):
												__a	:  Union[str, Any]         =					str(minterm % 2) + string
												minterm //= 2
								temp.append(_UpperCamelCase)
				return temp

def       __A (     a_  :str				,    a_  :str				,    a_  :int)						->						bool:
				__a	:  List[Any]         =					list(_UpperCamelCase)
				__a	:  Optional[Any]         =					list(_UpperCamelCase)
				__a	:  List[str]         =					0
				for i in range(len(_UpperCamelCase)):
								if lista[i] != lista[i]:
												count_n += 1
				return count_n == count

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

def       __A (     a_  :list[str]				,    a_  :list[str])						->						list[list[int]]:
				__a	:  Optional[Any]         =					[[0 for x in range(len(_UpperCamelCase))] for x in range(len(_UpperCamelCase))]
				for i in range(len(_UpperCamelCase)):
								__a	:  Union[str, Any]         =					prime_implicants[i].count('''_''')
								for j in range(len(_UpperCamelCase)):
												if is_for_table(prime_implicants[i]				,    binary[j]				,    _UpperCamelCase):
																__a	:  Union[str, Any]         =					1

				return chart

def       __A (     )						->						None:
				__a	:  Tuple         =					int(input('''Enter the no. of variables\n'''))
				__a	:  Optional[Any]         =					[
				    float(_UpperCamelCase)
				    for x in input(
				        '''Enter the decimal representation of Minterms \'Spaces Separated\'\n''').split()
				]
				__a	:  Optional[Any]         =					decimal_to_binary(_UpperCamelCase				,    _UpperCamelCase)

				__a	:  Tuple         =					check(_UpperCamelCase)
				print('''Prime Implicants are:''')
				print(_UpperCamelCase)
				__a	:  List[str]         =					prime_implicant_chart(_UpperCamelCase				,    _UpperCamelCase)

				__a	:  str         =					selection(_UpperCamelCase				,    _UpperCamelCase)
				print('''Essential Prime Implicants are:''')
				print(_UpperCamelCase)


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							main()






"""simple docstring"""






def       __A (     a_  :int)						->						Union[str, Any]:
				__a	:  int         =					[]
				__a	:  Dict         =					[]
				__a	:  str         =					{
				    '''^''': 3,
				    '''*''': 2,
				    '''/''': 2,
				    '''%''': 2,
				    '''+''': 1,
				    '''-''': 1,
				}  # Priority of each operator
				__a	:  Tuple         =					len(a_) if (len(a_) > 7) else 7

				# Print table header for output
				print(
				    '''Symbol'''.center(8)				,    '''Stack'''.center(a_)				,    '''Postfix'''.center(a_)				,    sep=''' | '''				,    )
				print('''-''' * (print_width * 3 + 7))

				for x in infix:
								if x.isalpha() or x.isdigit():
												post_fix.append(a_)  # if x is Alphabet / Digit, add it to Postfix
								elif x == "(":
												stack.append(a_)  # if x is "(" push to Stack
								elif x == ")":  # if x is ")" pop stack until "(" is encountered
												while stack[-1] != "(":
																post_fix.append(stack.pop())  # Pop stack & add the content to Postfix
												stack.pop()
								else:
												if len(a_) == 0:
																stack.append(a_)  # If stack is empty, push x to stack
												else:  # while priority of x is not > priority of element in the stack
																while len(a_) > 0 and priority[x] <= priority[stack[-1]]:
																				post_fix.append(stack.pop())  # pop stack & add to Postfix
																stack.append(a_)  # push x to stack

								print(
								    x.center(8)				,    (''''''.join(a_)).ljust(a_)				,    (''''''.join(a_)).ljust(a_)				,    sep=''' | '''				,    )  # Output in tabular format

				while len(a_) > 0:  # while stack is not empty
								post_fix.append(stack.pop())  # pop stack & add to Postfix
								print(
								    ''' '''.center(8)				,    (''''''.join(a_)).ljust(a_)				,    (''''''.join(a_)).ljust(a_)				,    sep=''' | '''				,    )  # Output in tabular format

				return "".join(a_)  # return Postfix as str

def       __A (     a_  :int)						->						List[Any]:
				__a	:  Dict         =					list(infix[::-1])  # reverse the infix equation

				for i in range(len(a_)):
								if infix[i] == "(":
												__a	:  Union[str, Any]         =					''')'''  # change "(" to ")"
								elif infix[i] == ")":
												__a	:  List[str]         =					'''('''  # change ")" to "("

				return (infix_2_postfix(''''''.join(a_)))[
				    ::-1
				]  # call infix_2_postfix on Infix, return reverse of Postfix


if __name__ == "__main__":
		A	     =					input('''\nEnter an Infix Equation = ''')  # Input an Infix equation
		A	     =					''''''.join(Infix.split())  # Remove spaces from the input
		print('''\n\t''', Infix, '''(Infix) -> ''', infix_2_prefix(Infix), '''(Prefix)''')