





'''simple docstring'''




from __future__ import annotations

from collections.abc import Callable
from typing import Any, Generic, TypeVar

a     :    List[str]      						=					TypeVar("""T""")

class     UpperCamelCase_				(							Generic[T]    ):





	def __init__(						self	,	A	,	A					)    ->    None:
								UpperCAmelCase  :	Any | T							  =	None

								UpperCAmelCase  :	int							  =	len(A					)
								UpperCAmelCase  :	list[T]							  =	[any_type for _ in range(self.N					)] + arr
								UpperCAmelCase  :	Optional[Any]							  =	fnc
								self.build()





	def 				_lowercase(						self					)    ->    None:
								for p in range(self.N - 1	,	0	,	-1					):
															UpperCAmelCase  :	Optional[Any]							  =	self.fn(self.st[p * 2]	,	self.st[p * 2 + 1]					)





	def 				_lowercase(						self	,	A	,	A					)    ->    None:
								p += self.N
								UpperCAmelCase  :	Optional[Any]							  =	v
								while p > 1:
															UpperCAmelCase  :	List[str]							  =	p // 2
															UpperCAmelCase  :	List[Any]							  =	self.fn(self.st[p * 2]	,	self.st[p * 2 + 1]					)






	def 				_lowercase(						self	,	A	,	A					)    ->    T | None:  # noqa: E741
								UpperCAmelCase  :	List[str]							  =	l + self.N, r + self.N

								UpperCAmelCase  :	T | None							  =	None
								while l <= r:
															if l % 2 == 1:
																						UpperCAmelCase  :	List[str]							  =	self.st[l] if res is None else self.fn(A	,	self.st[l]					)
															if r % 2 == 0:
																						UpperCAmelCase  :	Union[str, Any]							  =	self.st[r] if res is None else self.fn(A	,	self.st[r]					)
															UpperCAmelCase  :	List[str]							  =	(l + 1) // 2, (r - 1) // 2
								return res


if __name__ == "__main__":
							from functools import reduce

							a     :    Optional[Any]      						=					[1, 1_0, -2, 9, -3, 8, 4, -7, 5, 6, 1_1, -1_2]

							a     :    Dict      						=					{
							    0: 7,
							    1: 2,
							    2: 6,
							    3: -1_4,
							    4: 5,
							    5: 4,
							    6: 7,
							    7: -1_0,
							    8: 9,
							    9: 1_0,
							    1_0: 1_2,
							    1_1: 1,
							}

							a     :    Optional[int]      						=					SegmentTree(test_array, min)
							a     :    Dict      						=					SegmentTree(test_array, max)
							a     :    Dict      						=					SegmentTree(test_array, lambda a, b: a + b)



							def    __lowerCamelCase						(      )   ->    None:


														for i in range(len(__snake_case	)	):
																					for j in range(__snake_case			,       len(__snake_case	)	):
																												UpperCAmelCase  :	Optional[Any]							  =	reduce(__snake_case			,       test_array[i : j + 1]	)
																												UpperCAmelCase  :	str							  =	reduce(__snake_case			,       test_array[i : j + 1]	)
																												UpperCAmelCase  :	List[str]							  =	reduce(lambda _lowercase			,       _lowercase	: a + b			,       test_array[i : j + 1]	)
																												assert min_range == min_segment_tree.query(__snake_case			,       __snake_case	)
																												assert max_range == max_segment_tree.query(__snake_case			,       __snake_case	)
																												assert sum_range == sum_segment_tree.query(__snake_case			,       __snake_case	)

							test_all_segments()

							for index, value in test_updates.items():
														a     :    Optional[Any]      						=					value
														min_segment_tree.update(index, value)
														max_segment_tree.update(index, value)
														sum_segment_tree.update(index, value)
														test_all_segments()






'''simple docstring'''




from __future__ import annotations

from collections.abc import Sequence
from typing import Literal



def    __lowerCamelCase						(      _lowercase			,       _lowercase	)   ->    str | Literal[False]:
							UpperCAmelCase  :	Optional[int]							  =	list(_lowercase	)
							UpperCAmelCase  :	Dict							  =	list(_lowercase	)
							UpperCAmelCase  :	str							  =	0
							for i in range(len(_lowercase	)	):
														if lista[i] != lista[i]:
																					count += 1
																					UpperCAmelCase  :	Optional[Any]							  =	"""_"""
							if count > 1:
														return False
							else:
														return "".join(_lowercase	)



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



def    __lowerCamelCase						(      _lowercase			,       _lowercase	)   ->    list[str]:
							UpperCAmelCase  :	Dict							  =	[]
							for minterm in minterms:
														UpperCAmelCase  :	List[str]							  =	""""""
														for _ in range(_lowercase	):
																					UpperCAmelCase  :	Dict							  =	str(minterm % 2	) + string
																					minterm //= 2
														temp.append(_lowercase	)
							return temp



def    __lowerCamelCase						(      _lowercase			,       _lowercase			,       _lowercase	)   ->    bool:
							UpperCAmelCase  :	Optional[int]							  =	list(_lowercase	)
							UpperCAmelCase  :	Dict							  =	list(_lowercase	)
							UpperCAmelCase  :	Dict							  =	0
							for i in range(len(_lowercase	)	):
														if lista[i] != lista[i]:
																					count_n += 1
							return count_n == count



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



def    __lowerCamelCase						(      _lowercase			,       _lowercase	)   ->    list[list[int]]:
							UpperCAmelCase  :	Optional[int]							  =	[[0 for x in range(len(_lowercase	)	)] for x in range(len(_lowercase	)	)]
							for i in range(len(_lowercase	)	):
														UpperCAmelCase  :	Tuple							  =	prime_implicants[i].count("""_"""	)
														for j in range(len(_lowercase	)	):
																					if is_for_table(prime_implicants[i]			,       binary[j]			,       _lowercase	):
																												UpperCAmelCase  :	List[Any]							  =	1

							return chart



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

							UpperCAmelCase  :	Tuple							  =	check(_lowercase	)
							print("""Prime Implicants are:"""	)
							print(_lowercase	)
							UpperCAmelCase  :	Union[str, Any]							  =	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()

