




"""simple docstring"""






from __future__ import annotations

from collections.abc import Sequence
from typing import Literal







def      _snake_case			(				lowercase__							,    lowercase__		):
				_lowerCamelCase     :			Optional[int]    =    list(lowerCamelCase_		)
				_lowerCamelCase     :			Tuple    =    list(lowerCamelCase_		)
				_lowerCamelCase     :			Optional[Any]    =    0
				for i in range(len(lowerCamelCase_		)		):
								if lista[i] != lista[i]:
												count += 1
												_lowerCamelCase     :			int    =    '_'
				if count > 1:
								return False
				else:
								return "".join(lowerCamelCase_		)







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







def      _snake_case			(				lowercase__							,    lowercase__		):
				_lowerCamelCase     :			int    =    []
				for minterm in minterms:
								_lowerCamelCase     :			Union[str, Any]    =    ''
								for _ in range(lowerCamelCase_		):
												_lowerCamelCase     :			Optional[int]    =    str(minterm % 2		) + string
												minterm //= 2
								temp.append(lowerCamelCase_		)
				return temp







def      _snake_case			(				lowercase__							,    lowercase__							,    lowercase__		):
				_lowerCamelCase     :			List[Any]    =    list(lowerCamelCase_		)
				_lowerCamelCase     :			Any    =    list(lowerCamelCase_		)
				_lowerCamelCase     :			List[str]    =    0
				for i in range(len(lowerCamelCase_		)		):
								if lista[i] != lista[i]:
												count_n += 1
				return count_n == count







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







def      _snake_case			(				lowercase__							,    lowercase__		):
				_lowerCamelCase     :			Any    =    [[0 for x in range(len(lowerCamelCase_		)		)] for x in range(len(lowerCamelCase_		)		)]
				for i in range(len(lowerCamelCase_		)		):
								_lowerCamelCase     :			Optional[Any]    =    prime_implicants[i].count('_'		)
								for j in range(len(lowerCamelCase_		)		):
												if is_for_table(prime_implicants[i]							,    binary[j]							,    lowerCamelCase_		):
																_lowerCamelCase     :			Tuple    =    1

				return chart







def      _snake_case			(				):
				_lowerCamelCase     :			Optional[Any]    =    int(input('Enter the no. of variables\n'		)		)
				_lowerCamelCase     :			Tuple    =    [
				    float(lowerCamelCase_		)
				    for x in input(
				        'Enter the decimal representation of Minterms \'Spaces Separated\'\n'		).split()
				]
				_lowerCamelCase     :			Dict    =    decimal_to_binary(lowerCamelCase_							,    lowerCamelCase_		)

				_lowerCamelCase     :			Optional[Any]    =    check(lowerCamelCase_		)
				print('Prime Implicants are:'		)
				print(lowerCamelCase_		)
				_lowerCamelCase     :			Any    =    prime_implicant_chart(lowerCamelCase_							,    lowerCamelCase_		)

				_lowerCamelCase     :			List[str]    =    selection(lowerCamelCase_							,    lowerCamelCase_		)
				print('Essential Prime Implicants are:'		)
				print(lowerCamelCase_		)


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			main()







def   a			(						lowerCamelCase_				):






				'''simple docstring'''
				lowercase__    =			[1]

				lowercase__ ,						lowercase__ ,						lowercase__    =			0, 0, 0
				lowercase__    =			ugly_nums[ia] * 2
				lowercase__    =			ugly_nums[ia] * 3
				lowercase__    =			ugly_nums[ia] * 5

				for _ in range(1		,   lowerCamelCase_				):
								lowercase__    =			min(lowerCamelCase_		,   lowerCamelCase_		,   lowerCamelCase_				)
								ugly_nums.append(lowerCamelCase_				)
								if next_num == next_a:
												ia += 1
												lowercase__    =			ugly_nums[ia] * 2
								if next_num == next_a:
												ia += 1
												lowercase__    =			ugly_nums[ia] * 3
								if next_num == next_a:
												ia += 1
												lowercase__    =			ugly_nums[ia] * 5
				return ugly_nums[-1]


if __name__ == "__main__":
							from doctest import testmod

							testmod(verbose=True)
							print(F"{ugly_numbers(2_00) = }")




