


"""simple docstring"""







def      UpperCAmelCase__ (lowerCAmelCase_     ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE		     =       []
					if len(lowerCAmelCase_     ) == 1:
										return [nums.copy()]
					for _ in range(len(lowerCAmelCase_     )     ):
										__SCREAMING_SNAKE_CASE		     =       nums.pop(0     )
										__SCREAMING_SNAKE_CASE		     =       permute(lowerCAmelCase_     )
										for perm in permutations:
															perm.append(lowerCAmelCase_     )
										result.extend(lowerCAmelCase_     )
										nums.append(lowerCAmelCase_     )
					return result




def      UpperCAmelCase__ (lowerCAmelCase_     ):




					'''simple docstring'''


					def backtrack(lowerCAmelCase_     ):
										if start == len(lowerCAmelCase_     ) - 1:
															output.append(nums[:]     )
										else:
															for i in range(lowerCAmelCase_						,		len(lowerCAmelCase_     )     ):
																				__SCREAMING_SNAKE_CASE     ,						__SCREAMING_SNAKE_CASE		     =       nums[i], nums[start]
																				backtrack(start + 1     )
																				__SCREAMING_SNAKE_CASE     ,						__SCREAMING_SNAKE_CASE		     =       nums[i], nums[start]  # backtrack

					__SCREAMING_SNAKE_CASE		     =       []
					backtrack(0     )
					return output


if __name__ == "__main__":
		import doctest

		# use res to print the data in permute2 function
		a__       :							Union[str, Any]        =  permutea([1, 2, 3])
		print(res)
		doctest.testmod()




"""simple docstring"""







from __future__ import annotations

import math




class 				UpperCamelCase_			:

	"""simple docstring"""





	def __init__(				self    :       Union[str, Any]    ,    UpperCAmelCase__    :       int     ) ->			None:
						__SCREAMING_SNAKE_CASE		     =       size
						# approximate the overall size of segment tree with given value
						__SCREAMING_SNAKE_CASE		     =       [0 for i in range(0    ,    4 * size     )]
						# create array to store lazy update
						__SCREAMING_SNAKE_CASE		     =       [0 for i in range(0    ,    4 * size     )]
						__SCREAMING_SNAKE_CASE		     =       [0 for i in range(0    ,    4 * size     )]  # flag for lazy update




	def 						UpperCAmelCase_   (				self    :       str    ,    UpperCAmelCase__    :       int     ) ->			int:
						return idx * 2




	def 						UpperCAmelCase_   (				self    :       Any    ,    UpperCAmelCase__    :       int     ) ->			int:
						return idx * 2 + 1




	def 						UpperCAmelCase_   (				self    :       List[Any]    ,    UpperCAmelCase__    :       int    ,    UpperCAmelCase__    :       int    ,    UpperCAmelCase__    :       int    ,    UpperCAmelCase__    :       list[int]     ) ->			None:
						if left_element == right_element:
											__SCREAMING_SNAKE_CASE		     =       a[left_element - 1]
						else:
											__SCREAMING_SNAKE_CASE		     =       (left_element + right_element) // 2
											self.build(self.left(UpperCAmelCase__     )    ,    UpperCAmelCase__    ,    UpperCAmelCase__    ,    UpperCAmelCase__     )
											self.build(self.right(UpperCAmelCase__     )    ,    mid + 1    ,    UpperCAmelCase__    ,    UpperCAmelCase__     )
											__SCREAMING_SNAKE_CASE		     =       max(
											    self.segment_tree[self.left(UpperCAmelCase__     )]    ,    self.segment_tree[self.right(UpperCAmelCase__     )]     )




	def 						UpperCAmelCase_   (				self    :       Tuple    ,    UpperCAmelCase__    :       int    ,    UpperCAmelCase__    :       int    ,    UpperCAmelCase__    :       int    ,    UpperCAmelCase__    :       int    ,    UpperCAmelCase__    :       int    ,    UpperCAmelCase__    :       int     ) ->			bool:
						if self.flag[idx] is True:
											__SCREAMING_SNAKE_CASE		     =       self.lazy[idx]
											__SCREAMING_SNAKE_CASE		     =       False
											if left_element != right_element:
																__SCREAMING_SNAKE_CASE		     =       self.lazy[idx]
																__SCREAMING_SNAKE_CASE		     =       self.lazy[idx]
																__SCREAMING_SNAKE_CASE		     =       True
																__SCREAMING_SNAKE_CASE		     =       True

						if right_element < a or left_element > b:
											return True
						if left_element >= a and right_element <= b:
											__SCREAMING_SNAKE_CASE		     =       val
											if left_element != right_element:
																__SCREAMING_SNAKE_CASE		     =       val
																__SCREAMING_SNAKE_CASE		     =       val
																__SCREAMING_SNAKE_CASE		     =       True
																__SCREAMING_SNAKE_CASE		     =       True
											return True
						__SCREAMING_SNAKE_CASE		     =       (left_element + right_element) // 2
						self.update(self.left(UpperCAmelCase__     )    ,    UpperCAmelCase__    ,    UpperCAmelCase__    ,    UpperCAmelCase__    ,    UpperCAmelCase__    ,    UpperCAmelCase__     )
						self.update(self.right(UpperCAmelCase__     )    ,    mid + 1    ,    UpperCAmelCase__    ,    UpperCAmelCase__    ,    UpperCAmelCase__    ,    UpperCAmelCase__     )
						__SCREAMING_SNAKE_CASE		     =       max(
						    self.segment_tree[self.left(UpperCAmelCase__     )]    ,    self.segment_tree[self.right(UpperCAmelCase__     )]     )
						return True




	def 						UpperCAmelCase_   (				self    :       int    ,    UpperCAmelCase__    :       int    ,    UpperCAmelCase__    :       int    ,    UpperCAmelCase__    :       int    ,    UpperCAmelCase__    :       int    ,    UpperCAmelCase__    :       int     ) ->			int | float:
						if self.flag[idx] is True:
											__SCREAMING_SNAKE_CASE		     =       self.lazy[idx]
											__SCREAMING_SNAKE_CASE		     =       False
											if left_element != right_element:
																__SCREAMING_SNAKE_CASE		     =       self.lazy[idx]
																__SCREAMING_SNAKE_CASE		     =       self.lazy[idx]
																__SCREAMING_SNAKE_CASE		     =       True
																__SCREAMING_SNAKE_CASE		     =       True
						if right_element < a or left_element > b:
											return -math.inf
						if left_element >= a and right_element <= b:
											return self.segment_tree[idx]
						__SCREAMING_SNAKE_CASE		     =       (left_element + right_element) // 2
						__SCREAMING_SNAKE_CASE		     =       self.query(self.left(UpperCAmelCase__     )    ,    UpperCAmelCase__    ,    UpperCAmelCase__    ,    UpperCAmelCase__    ,    UpperCAmelCase__     )
						__SCREAMING_SNAKE_CASE		     =       self.query(self.right(UpperCAmelCase__     )    ,    mid + 1    ,    UpperCAmelCase__    ,    UpperCAmelCase__    ,    UpperCAmelCase__     )
						return max(UpperCAmelCase__    ,    UpperCAmelCase__     )




	def __str__(				self    :       int     ) ->			str:
						return str([self.query(1    ,    1    ,    self.size    ,    UpperCAmelCase__    ,    UpperCAmelCase__     ) for i in range(1    ,    self.size + 1     )]     )


if __name__ == "__main__":
		a__       :							Tuple        =  [1, 2, -4, 7, 3, -5, 6, 1_1, -2_0, 9, 1_4, 1_5, 5, 2, -8]
		a__       :							Dict        =  1_5
		a__       :							int        =  SegmentTree(size)
		segt.build(1, 1, size, A)
		print(segt.query(1, 1, size, 4, 6))
		print(segt.query(1, 1, size, 7, 1_1))
		print(segt.query(1, 1, size, 7, 1_2))
		segt.update(1, 1, size, 1, 3, 1_1_1)
		print(segt.query(1, 1, size, 1, 1_5))
		segt.update(1, 1, size, 7, 8, 2_3_5)
		print(segt)
