


'''simple docstring'''



from __future__ import annotations

import math


class 		_snake_case					:




					def __init__(      self							,							_lowerCamelCase):
								UpperCAmelCase__  :					int        =     size
								# approximate the overall size of segment tree with given value
								UpperCAmelCase__  :					Any        =     [0 for i in range(0							,							4 * size)]
								# create array to store lazy update
								UpperCAmelCase__  :					str        =     [0 for i in range(0							,							4 * size)]
								UpperCAmelCase__  :					Tuple        =     [0 for i in range(0							,							4 * size)]  # flag for lazy update




					def 				snake_case__						(      self							,							_lowerCamelCase):
								return idx * 2




					def 				snake_case__						(      self							,							_lowerCamelCase):
								return idx * 2 + 1




					def 				snake_case__						(      self							,							_lowerCamelCase							,							_lowerCamelCase							,							_lowerCamelCase							,							_lowerCamelCase):
								if left_element == right_element:
											UpperCAmelCase__  :					List[Any]        =     a[left_element - 1]
								else:
											UpperCAmelCase__  :					Union[str, Any]        =     (left_element + right_element) // 2
											self.build(self.left(_lowerCamelCase)							,							_lowerCamelCase							,							_lowerCamelCase							,							_lowerCamelCase)
											self.build(self.right(_lowerCamelCase)							,							mid + 1							,							_lowerCamelCase							,							_lowerCamelCase)
											UpperCAmelCase__  :					List[Any]        =     max(
											    self.segment_tree[self.left(_lowerCamelCase)]							,							self.segment_tree[self.right(_lowerCamelCase)])




					def 				snake_case__						(      self							,							_lowerCamelCase							,							_lowerCamelCase							,							_lowerCamelCase							,							_lowerCamelCase							,							_lowerCamelCase							,							_lowerCamelCase):
								if self.flag[idx] is True:
											UpperCAmelCase__  :					int        =     self.lazy[idx]
											UpperCAmelCase__  :					Optional[int]        =     False
											if left_element != right_element:
														UpperCAmelCase__  :					Optional[int]        =     self.lazy[idx]
														UpperCAmelCase__  :					Any        =     self.lazy[idx]
														UpperCAmelCase__  :					Optional[int]        =     True
														UpperCAmelCase__  :					Optional[Any]        =     True

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




					def 				snake_case__						(      self							,							_lowerCamelCase							,							_lowerCamelCase							,							_lowerCamelCase							,							_lowerCamelCase							,							_lowerCamelCase):
								if self.flag[idx] is True:
											UpperCAmelCase__  :					Any        =     self.lazy[idx]
											UpperCAmelCase__  :					List[Any]        =     False
											if left_element != right_element:
														UpperCAmelCase__  :					int        =     self.lazy[idx]
														UpperCAmelCase__  :					int        =     self.lazy[idx]
														UpperCAmelCase__  :					str        =     True
														UpperCAmelCase__  :					Tuple        =     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]
								UpperCAmelCase__  :					str        =     (left_element + right_element) // 2
								UpperCAmelCase__  :					Dict        =     self.query(self.left(_lowerCamelCase)							,							_lowerCamelCase							,							_lowerCamelCase							,							_lowerCamelCase							,							_lowerCamelCase)
								UpperCAmelCase__  :					List[str]        =     self.query(self.right(_lowerCamelCase)							,							mid + 1							,							_lowerCamelCase							,							_lowerCamelCase							,							_lowerCamelCase)
								return max(_lowerCamelCase							,							_lowerCamelCase)




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


if __name__ == "__main__":
		__A	=[1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
		__A	=15
		__A	=SegmentTree(size)
		segt.build(1, 1, size, A)
		print(segt.query(1, 1, size, 4, 6))
		print(segt.query(1, 1, size, 7, 11))
		print(segt.query(1, 1, size, 7, 12))
		segt.update(1, 1, size, 1, 3, 1_11)
		print(segt.query(1, 1, size, 1, 15))
		segt.update(1, 1, size, 7, 8, 2_35)
		print(segt)



'''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()