


'''simple docstring'''



from __future__ import annotations

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

__A	=TypeVar('T')


class 		_snake_case					(     Generic[T]	):




     def __init__(      self							,							_lowerCamelCase							,							_lowerCamelCase):
        UpperCAmelCase__  :					Any | T        =     None

        UpperCAmelCase__  :					int        =     len(_lowerCamelCase)
        UpperCAmelCase__  :					list[T]        =     [any_type for _ in range(self.N)] + arr
        UpperCAmelCase__  :					List[Any]        =     fnc
        self.build()




     def 				snake_case__						(      self):
        for p in range(self.N - 1							,							0							,							-1):
           UpperCAmelCase__  :					Union[str, Any]        =     self.fn(self.st[p * 2]							,							self.st[p * 2 + 1])




     def 				snake_case__						(      self							,							_lowerCamelCase							,							_lowerCamelCase):
        p += self.N
        UpperCAmelCase__  :					Union[str, Any]        =     v
        while p > 1:
           UpperCAmelCase__  :					Tuple        =     p // 2
           UpperCAmelCase__  :					str        =     self.fn(self.st[p * 2]							,							self.st[p * 2 + 1])




     def 				snake_case__						(      self							,							_lowerCamelCase							,							_lowerCamelCase):  # noqa: E741
        UpperCAmelCase__  :					List[str]        =     l + self.N, r + self.N

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


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

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

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

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







  def     _UpperCamelCase      (		):


     for i in range(len(lowerCamelCase__					)					):
        for j in range(lowerCamelCase__ ,      len(lowerCamelCase__					)					):
           UpperCAmelCase__  :					str        =     reduce(lowerCamelCase__ ,      test_array[i : j + 1]					)
           UpperCAmelCase__  :					Union[str, Any]        =     reduce(lowerCamelCase__ ,      test_array[i : j + 1]					)
           UpperCAmelCase__  :					str        =     reduce(lambda UpperCamelCase__ ,      UpperCamelCase__					: a + b ,      test_array[i : j + 1]					)
           assert min_range == min_segment_tree.query(lowerCamelCase__ ,      lowerCamelCase__					)
           assert max_range == max_segment_tree.query(lowerCamelCase__ ,      lowerCamelCase__					)
           assert sum_range == sum_segment_tree.query(lowerCamelCase__ ,      lowerCamelCase__					)

  test_all_segments()

  for index, value in test_updates.items():
    __A	=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 collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean







def     _UpperCamelCase      (		UpperCamelCase__					):

			# A local function to see if a dot lands in the circle.
			def is_in_circle(UpperCamelCase__ ,      UpperCamelCase__					) -> bool:
						UpperCAmelCase__  :					List[str]        =     sqrt((x**2) + (y**2)					)
						# Our circle has a radius of 1, so a distance
						# greater than 1 would land outside the circle.
						return distance_from_centre <= 1

			# The proportion of guesses that landed in the circle
			UpperCAmelCase__  :					Optional[Any]        =     mean(
			    int(is_in_circle(uniform(-1.0 ,      1.0					) ,      uniform(-1.0 ,      1.0					)					)					)
			    for _ in range(UpperCamelCase__					)					)
			# The ratio of the area for circle to square is pi/4.
			UpperCAmelCase__  :					int        =     proportion * 4
			print(f'''The estimated value of pi is {pi_estimate}'''					)
			print(f'''The numpy value of pi is {pi}'''					)
			print(f'''The total error is {abs(pi - pi_estimate					)}'''					)







def     _UpperCamelCase      (		UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__ = 0.0 ,      UpperCamelCase__ = 1.0 ,      ):
			return mean(
			    function_to_integrate(uniform(UpperCamelCase__ ,      UpperCamelCase__					)					) for _ in range(UpperCamelCase__					)					) * (max_value - min_value)







def     _UpperCamelCase      (		UpperCamelCase__ ,      UpperCamelCase__ = 0.0 ,      UpperCamelCase__ = 1.0					):

			def identity_function(UpperCamelCase__					) -> float:
						return x

			UpperCAmelCase__  :					List[str]        =     area_under_curve_estimator(
			    UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__					)
			UpperCAmelCase__  :					Optional[int]        =     (max_value * max_value - min_value * min_value) / 2

			print("""******************"""					)
			print(f'''Estimating area under y=x where x varies from {min_value} to {max_value}'''					)
			print(f'''Estimated value is {estimated_value}'''					)
			print(f'''Expected value is {expected_value}'''					)
			print(f'''Total error is {abs(estimated_value - expected_value					)}'''					)
			print("""******************"""					)







def     _UpperCamelCase      (		UpperCamelCase__					):

			def function_to_integrate(UpperCamelCase__					) -> float:
						return sqrt(4.0 - x * x					)

			UpperCAmelCase__  :					Dict        =     area_under_curve_estimator(
			    UpperCamelCase__ ,      UpperCamelCase__ ,      0.0 ,      2.0					)

			print("""******************"""					)
			print("""Estimating pi using area_under_curve_estimator"""					)
			print(f'''Estimated value is {estimated_value}'''					)
			print(f'''Expected value is {pi}'''					)
			print(f'''Total error is {abs(estimated_value - pi					)}'''					)
			print("""******************"""					)


if __name__ == "__main__":
		import doctest

		doctest.testmod()