


'''simple docstring'''



from itertools import permutations







def     _UpperCamelCase      (		UpperCamelCase__					):
			if num[3] % 2 != 0:
						return False

			if (num[2] + num[3] + num[4]) % 3 != 0:
						return False

			if num[5] % 5 != 0:
						return False

			UpperCAmelCase__  :					Optional[int]        =     [7, 1_1, 1_3, 1_7]
			for i, test in enumerate(UpperCamelCase__					):
						if (num[i + 4] * 1_0_0 + num[i + 5] * 1_0 + num[i + 6]) % test != 0:
									return False
			return True







def     _UpperCamelCase      (		UpperCamelCase__ = 1_0					):
			return sum(
			    int("""""".join(map(UpperCamelCase__ ,      UpperCamelCase__					)					)					)
			    for num in permutations(range(UpperCamelCase__					)					)
			    if is_substring_divisible(UpperCamelCase__					)					)


if __name__ == "__main__":
		print(f"""{solution() = }""")



'''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()