

import math


class 					A		:







    """simple docstring"""





    def __init__( self					:			Dict,lowercase_					:			List[Any]						)->       Dict:





        '''simple docstring'''







        A__        =  len(lowercase_						)
        A__        =  [0] * (
            4 * self.N
        )  # approximate the overall size of segment tree with array N
        self.build(1,0,self.N - 1						)


    def 		snake_case__	( self					:			str,lowercase_					:			Optional[int]						)->       List[Any]:





        '''simple docstring'''







        return idx * 2


    def 		snake_case__	( self					:			Optional[Any],lowercase_					:			Dict						)->       Union[str, Any]:





        '''simple docstring'''







        return idx * 2 + 1


    def 		snake_case__	( self					:			Optional[int],lowercase_					:			Optional[Any],lowercase_					:			Optional[int],lowercase_					:			int						)->       str:  # noqa: E741





        '''simple docstring'''







        if l == r:
            A__        =  A[l]
        else:
            A__        =  (l + r) // 2
            self.build(self.left(lowercase_						),lowercase_,lowercase_						)
            self.build(self.right(lowercase_						),mid + 1,lowercase_						)
            A__        =  max(self.st[self.left(lowercase_						)],self.st[self.right(lowercase_						)]						)


    def 		snake_case__	( self					:			List[Any],lowercase_					:			int,lowercase_					:			Tuple,lowercase_					:			List[str]						)->       List[str]:





        '''simple docstring'''







        return self.update_recursive(1,0,self.N - 1,a - 1,b - 1,lowercase_						)


    def 		snake_case__	( self					:			Union[str, Any],lowercase_					:			Any,lowercase_					:			Dict,lowercase_					:			Union[str, Any],lowercase_					:			Tuple,lowercase_					:			Optional[int],lowercase_					:			List[Any]						)->       List[str]:  # noqa: E741





        '''simple docstring'''







        if r < a or l > b:
            return True
        if l == r:
            A__        =  val
            return True
        A__        =  (l + r) // 2
        self.update_recursive(self.left(lowercase_						),lowercase_,lowercase_,lowercase_,lowercase_,lowercase_						)
        self.update_recursive(self.right(lowercase_						),mid + 1,lowercase_,lowercase_,lowercase_,lowercase_						)
        A__        =  max(self.st[self.left(lowercase_						)],self.st[self.right(lowercase_						)]						)
        return True


    def 		snake_case__	( self					:			Tuple,lowercase_					:			Dict,lowercase_					:			Tuple						)->       str:





        '''simple docstring'''







        return self.query_recursive(1,0,self.N - 1,a - 1,b - 1						)


    def 		snake_case__	( self					:			Dict,lowercase_					:			Dict,lowercase_					:			str,lowercase_					:			int,lowercase_					:			List[str],lowercase_					:			Tuple						)->       int:  # noqa: E741





        '''simple docstring'''







        if r < a or l > b:
            return -math.inf
        if l >= a and r <= b:
            return self.st[idx]
        A__        =  (l + r) // 2
        A__        =  self.query_recursive(self.left(lowercase_						),lowercase_,lowercase_,lowercase_,lowercase_						)
        A__        =  self.query_recursive(self.right(lowercase_						),mid + 1,lowercase_,lowercase_,lowercase_						)
        return max(lowercase_,lowercase_						)


    def 		snake_case__	( self					:			Any						)->       str:





        '''simple docstring'''







        A__        =  []
        for i in range(1,N + 1						):
            show_list += [self.query(lowercase_,lowercase_						)]
        print(lowercase_						)


if __name__ == "__main__":
     lowercase_									=    [1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
     lowercase_									=    15
     lowercase_									=    SegmentTree(A)
     print(segt.query(4, 6))
     print(segt.query(7, 11))
     print(segt.query(7, 12))
     segt.update(1, 3, 111)
     print(segt.query(1, 15))
     segt.update(7, 8, 235)
     segt.show_data()







from __future__ import annotations

from math import pi, pow



def     lowerCAmelCase		(		_lowerCAmelCase				: int | float						):




 """simple docstring"""







 if side_length < 0:
  raise ValueError("vol_cube() only accepts non-negative values"						)
 return pow(_lowerCAmelCase    ,				3						)



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if height < 0 or radius < 0:
  raise ValueError("vol_spherical_cap() only accepts non-negative values"						)
 # Volume is 1/3 pi * height squared * (3 * radius - height)
 return 1 / 3 * pi * pow(_lowerCAmelCase    ,				2						) * (3 * radius - height)



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if radius_a < 0 or radius_a < 0 or centers_distance < 0:
  raise ValueError("vol_spheres_intersect() only accepts non-negative values"						)
 if centers_distance == 0:
  return vol_sphere(min(_lowerCAmelCase    ,				_lowerCAmelCase						)						)

 UpperCAmelCase__							=    (
     (radius_a - radius_a + centers_distance)
     * (radius_a + radius_a - centers_distance)
     / (2 * centers_distance)
 )
 UpperCAmelCase__							=    (
     (radius_a - radius_a + centers_distance)
     * (radius_a + radius_a - centers_distance)
     / (2 * centers_distance)
 )

 return vol_spherical_cap(_lowerCAmelCase    ,				_lowerCAmelCase						) + vol_spherical_cap(_lowerCAmelCase    ,				_lowerCAmelCase						)



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if radius_a <= 0 or radius_a <= 0 or centers_distance < 0:
  raise ValueError(
      "vol_spheres_union() only accepts non-negative values, non-zero radius"						)

 if centers_distance == 0:
  return vol_sphere(max(_lowerCAmelCase    ,				_lowerCAmelCase						)						)

 return (
     vol_sphere(_lowerCAmelCase						)
     + vol_sphere(_lowerCAmelCase						)
     - vol_spheres_intersect(_lowerCAmelCase    ,				_lowerCAmelCase    ,				_lowerCAmelCase						)
 )



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if width < 0 or height < 0 or length < 0:
  raise ValueError("vol_cuboid() only accepts non-negative values"						)
 return float(width * height * length						)



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if height < 0 or area_of_base < 0:
  raise ValueError("vol_cone() only accepts non-negative values"						)
 return area_of_base * height / 3.0



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if height < 0 or radius < 0:
  raise ValueError("vol_right_circ_cone() only accepts non-negative values"						)
 return pi * pow(_lowerCAmelCase    ,				2						) * height / 3.0



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if height < 0 or area_of_base < 0:
  raise ValueError("vol_prism() only accepts non-negative values"						)
 return float(area_of_base * height						)



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if height < 0 or area_of_base < 0:
  raise ValueError("vol_pyramid() only accepts non-negative values"						)
 return area_of_base * height / 3.0



def     lowerCAmelCase		(		_lowerCAmelCase				: float						):




 """simple docstring"""







 if radius < 0:
  raise ValueError("vol_sphere() only accepts non-negative values"						)
 # Volume is 4/3 * pi * radius cubed
 return 4 / 3 * pi * pow(_lowerCAmelCase    ,				3						)



def     lowerCAmelCase		(		_lowerCAmelCase				: float						):




 """simple docstring"""







 if radius < 0:
  raise ValueError("vol_hemisphere() only accepts non-negative values"						)
 # Volume is radius cubed * pi * 2/3
 return pow(_lowerCAmelCase    ,				3						) * pi * 2 / 3



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if height < 0 or radius < 0:
  raise ValueError("vol_circular_cylinder() only accepts non-negative values"						)
 # Volume is radius squared * height * pi
 return pow(_lowerCAmelCase    ,				2						) * height * pi



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if inner_radius < 0 or outer_radius < 0 or height < 0:
  raise ValueError(
      "vol_hollow_circular_cylinder() only accepts non-negative values"						)
 if outer_radius <= inner_radius:
  raise ValueError("outer_radius must be greater than inner_radius"						)
 return pi * (pow(_lowerCAmelCase    ,				2						) - pow(_lowerCAmelCase    ,				2						)) * height



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if radius_a < 0 or radius_a < 0 or height < 0:
  raise ValueError("vol_conical_frustum() only accepts non-negative values"						)
 return (
     1
     / 3
     * pi
     * height
     * (pow(_lowerCAmelCase    ,				2						) + pow(_lowerCAmelCase    ,				2						) + radius_a * radius_a)
 )



def     lowerCAmelCase		(		_lowerCAmelCase				: float    ,				_lowerCAmelCase				: float						):




 """simple docstring"""







 if torus_radius < 0 or tube_radius < 0:
  raise ValueError("vol_torus() only accepts non-negative values"						)
 return 2 * pow(_lowerCAmelCase    ,				2						) * torus_radius * pow(_lowerCAmelCase    ,				2						)



def     lowerCAmelCase		(		):




 """simple docstring"""







 print("Volumes:"						)
 print(F'''Cube: {vol_cube(2						) = }'''						)  # = 8
 print(F'''Cuboid: {vol_cuboid(2    ,				2    ,				2						) = }'''						)  # = 8
 print(F'''Cone: {vol_cone(2    ,				2						) = }'''						)  # ~= 1.33
 print(F'''Right Circular Cone: {vol_right_circ_cone(2    ,				2						) = }'''						)  # ~= 8.38
 print(F'''Prism: {vol_prism(2    ,				2						) = }'''						)  # = 4
 print(F'''Pyramid: {vol_pyramid(2    ,				2						) = }'''						)  # ~= 1.33
 print(F'''Sphere: {vol_sphere(2						) = }'''						)  # ~= 33.5
 print(F'''Hemisphere: {vol_hemisphere(2						) = }'''						)  # ~= 16.75
 print(F'''Circular Cylinder: {vol_circular_cylinder(2    ,				2						) = }'''						)  # ~= 25.1
 print(F'''Torus: {vol_torus(2    ,				2						) = }'''						)  # ~= 157.9
 print(F'''Conical Frustum: {vol_conical_frustum(2    ,				2    ,				4						) = }'''						)  # ~= 58.6
 print(F'''Spherical cap: {vol_spherical_cap(1    ,				2						) = }'''						)  # ~= 5.24
 print(F'''Spheres intersetion: {vol_spheres_intersect(2    ,				2    ,				1						) = }'''						)  # ~= 21.21
 print(F'''Spheres union: {vol_spheres_union(2    ,				2    ,				1						) = }'''						)  # ~= 45.81
 print(
     F'''Hollow Circular Cylinder: {vol_hollow_circular_cylinder(1    ,				2    ,				3						) = }'''						)  # ~= 28.3


if __name__ == "__main__":
  main()





