



"""simple docstring"""


from __future__ import annotations

__A   :							Optional[Any]										=   []







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						list[list[int]]					,     _SCREAMING_SNAKE_CASE   :						int					,     _SCREAMING_SNAKE_CASE   :						int				):






				'''simple docstring'''



				for i in range(len(_SCREAMING_SNAKE_CASE				)				):
								if board[row][i] == 1:
												return False
				for i in range(len(_SCREAMING_SNAKE_CASE				)				):
								if board[i][column] == 1:
												return False
				for i, j in zip(range(_SCREAMING_SNAKE_CASE					,     -1					,     -1				)					,     range(_SCREAMING_SNAKE_CASE					,     -1					,     -1				)				):
								if board[i][j] == 1:
												return False
				for i, j in zip(range(_SCREAMING_SNAKE_CASE					,     -1					,     -1				)					,     range(_SCREAMING_SNAKE_CASE					,     len(_SCREAMING_SNAKE_CASE				)				)				):
								if board[i][j] == 1:
												return False
				return True







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						list[list[int]]					,     _SCREAMING_SNAKE_CASE   :						int				):






				'''simple docstring'''



				if row >= len(_SCREAMING_SNAKE_CASE				):
								solution.append(_SCREAMING_SNAKE_CASE				)
								printboard(_SCREAMING_SNAKE_CASE				)
								print()
								return True
				for i in range(len(_SCREAMING_SNAKE_CASE				)				):
								if is_safe(_SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE				):
												_UpperCAmelCase					=    1
												solve(_SCREAMING_SNAKE_CASE					,     row + 1				)
												_UpperCAmelCase					=    0
				return False







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						list[list[int]]				):






				'''simple docstring'''



				for i in range(len(_SCREAMING_SNAKE_CASE				)				):
								for j in range(len(_SCREAMING_SNAKE_CASE				)				):
												if board[i][j] == 1:
																print('''Q'''					,     end=''' '''				)
												else:
																print('''.'''					,     end=''' '''				)
								print()


# n=int(input("The no. of queens"))
__A   :							Optional[Any]										=   8
__A   :							Dict										=   [[0 for i in range(n)] for j in range(n)]
solve(board, 0)
print("The total no. of solutions are :", len(solution))








"""simple docstring"""


from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						int				):






				'''simple docstring'''



				def is_in_circle(_SCREAMING_SNAKE_CASE   :						float					,     _SCREAMING_SNAKE_CASE   :						float				) -> bool:
								_UpperCAmelCase					=    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					=    mean(
				    int(is_in_circle(uniform(-1.0					,     1.0				)					,     uniform(-1.0					,     1.0				)				)				)
				    for _ in range(_SCREAMING_SNAKE_CASE				)				)
				# The ratio of the area for circle to square is pi/4.
				_UpperCAmelCase					=    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  lowercase	(      _SCREAMING_SNAKE_CASE   :						int					,     _SCREAMING_SNAKE_CASE   :						Callable[[float], float]					,     _SCREAMING_SNAKE_CASE   :						float = 0.0					,     _SCREAMING_SNAKE_CASE   :						float = 1.0					,     ):






				'''simple docstring'''



				return mean(
				    function_to_integrate(uniform(_SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE				)				) for _ in range(_SCREAMING_SNAKE_CASE				)				) * (max_value - min_value)







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						int					,     _SCREAMING_SNAKE_CASE   :						float = 0.0					,     _SCREAMING_SNAKE_CASE   :						float = 1.0				):






				'''simple docstring'''



				def identity_function(_SCREAMING_SNAKE_CASE   :						float				) -> float:
								return x

				_UpperCAmelCase					=    area_under_curve_estimator(
				    _SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE				)
				_UpperCAmelCase					=    (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  lowercase	(      _SCREAMING_SNAKE_CASE   :						int				):






				'''simple docstring'''



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

				_UpperCAmelCase					=    area_under_curve_estimator(
				    _SCREAMING_SNAKE_CASE					,     _SCREAMING_SNAKE_CASE					,     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()



