





'''simple docstring'''




from __future__ import annotations

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

_SCREAMING_SNAKE_CASE							     =			TypeVar("T")
class 			_lowerCAmelCase		(			Generic[T]	):






     """simple docstring"""






     def __init__(   self							:			List[str]   ,       __snake_case							:			list[T]   ,       __snake_case							:			Callable[[T, T], T]						)->	None:
        snake_case 						=   None

        snake_case 						=   len(lowerCAmelCase_						)
        snake_case 						=   [any_type for _ in range(self.N						)] + arr
        snake_case 						=   fnc
        self.build()



     def      lowerCAmelCase			(   self							:			int						)->	None:
        for p in range(self.N - 1   ,       0   ,       -1						):
           snake_case 						=   self.fn(self.st[p * 2]   ,       self.st[p * 2 + 1]						)



     def      lowerCAmelCase			(   self							:			Optional[int]   ,       __snake_case							:			int   ,       __snake_case							:			T						)->	None:
        p += self.N
        snake_case 						=   v
        while p > 1:
           snake_case 						=   p // 2
           snake_case 						=   self.fn(self.st[p * 2]   ,       self.st[p * 2 + 1]						)



     def      lowerCAmelCase			(   self							:			Optional[int]   ,       __snake_case							:			int   ,       __snake_case							:			int						)->	T | None:  # noqa: E741
        snake_case						,    snake_case 						=   l + self.N, r + self.N

        snake_case 						=   None
        while l <= r:
           if l % 2 == 1:
              snake_case 						=   self.st[l] if res is None else self.fn(lowerCAmelCase_   ,       self.st[l]						)
           if r % 2 == 0:
              snake_case 						=   self.st[r] if res is None else self.fn(lowerCAmelCase_   ,       self.st[r]						)
           snake_case						,    snake_case 						=   (l + 1) // 2, (r - 1) // 2
        return res


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

 _SCREAMING_SNAKE_CASE							     =			[1, 10, -2, 9, -3, 8, 4, -7, 5, 6, 11, -12]

 _SCREAMING_SNAKE_CASE							     =			{
     0: 7,
     1: 2,
     2: 6,
     3: -14,
     4: 5,
     5: 4,
     6: 7,
     7: -10,
     8: 9,
     9: 10,
     10: 12,
     11: 1,
 }

 _SCREAMING_SNAKE_CASE							     =			SegmentTree(test_array, min)
 _SCREAMING_SNAKE_CASE							     =			SegmentTree(test_array, max)
 _SCREAMING_SNAKE_CASE							     =			SegmentTree(test_array, lambda a, b: a + b)





 def 	__lowerCamelCase			(      )		->  Dict:




    for i in range(len(_SCREAMING_SNAKE_CASE		)		):
       for j in range(_SCREAMING_SNAKE_CASE      ,    len(_SCREAMING_SNAKE_CASE		)		):
          snake_case 						=   reduce(_SCREAMING_SNAKE_CASE      ,    test_array[i : j + 1]		)
          snake_case 						=   reduce(_SCREAMING_SNAKE_CASE      ,    test_array[i : j + 1]		)
          snake_case 						=   reduce(lambda __lowerCAmelCase      ,    __lowerCAmelCase		: a + b      ,    test_array[i : j + 1]		)
          assert min_range == min_segment_tree.query(_SCREAMING_SNAKE_CASE      ,    _SCREAMING_SNAKE_CASE		)
          assert max_range == max_segment_tree.query(_SCREAMING_SNAKE_CASE      ,    _SCREAMING_SNAKE_CASE		)
          assert sum_range == sum_segment_tree.query(_SCREAMING_SNAKE_CASE      ,    _SCREAMING_SNAKE_CASE		)

 test_all_segments()

 for index, value in test_updates.items():
  _SCREAMING_SNAKE_CASE							     =			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

import math

UpperCAmelCase__  			=				'''2020.9.26'''
UpperCAmelCase__  			=				'''xcodz-dot, cclaus, dhruvmanila'''






def 						UpperCAmelCase__(				_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float ):






			"""simple docstring"""




			if not all(isinstance(_SCREAMING_SNAKE_CASE,(float, int) ) for val in locals().values() ):
						__A=	f"""Input values must either be float or int: {list(locals().values() )}"""
						raise TypeError(_SCREAMING_SNAKE_CASE )
			__A=	((x * distance) / (z + distance)) * scale
			__A=	((y * distance) / (z + distance)) * scale
			return projected_x, projected_y






def 						UpperCAmelCase__(				_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: str,_SCREAMING_SNAKE_CASE					: float ):






			"""simple docstring"""




			if not isinstance(_SCREAMING_SNAKE_CASE,_SCREAMING_SNAKE_CASE ):
						raise TypeError('Axis must be a str' )
			__A=	locals()
			del input_variables["axis"]
			if not all(isinstance(_SCREAMING_SNAKE_CASE,(float, int) ) for val in input_variables.values() ):
						__A=	(
						    'Input values except axis must either be float or int: '
						    f"""{list(input_variables.values() )}"""
						)
						raise TypeError(_SCREAMING_SNAKE_CASE )
			__A=	(angle % 360) / 450 * 180 / math.pi
			if axis == "z":
						__A=	x * math.cos(_SCREAMING_SNAKE_CASE ) - y * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	y * math.cos(_SCREAMING_SNAKE_CASE ) + x * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	z
			elif axis == "x":
						__A=	y * math.cos(_SCREAMING_SNAKE_CASE ) - z * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	z * math.cos(_SCREAMING_SNAKE_CASE ) + y * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	x
			elif axis == "y":
						__A=	x * math.cos(_SCREAMING_SNAKE_CASE ) - z * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	z * math.cos(_SCREAMING_SNAKE_CASE ) + x * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	y
			else:
						raise ValueError('not a valid axis, choose one of \'x\', \'y\', \'z\'' )

			return new_x, new_y, new_z


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					print(F"""{convert_to_ad(1.0, 2.0, 3.0, 10.0, 10.0) = }""")
					print(F"""{rotate(1.0, 2.0, 3.0, 'y', 90.0) = }""")



