





from itertools import count
from math import asin, pi, sqrt
def 			__UpperCamelCase				(			lowercase__	:       str		)	->      float:
    '''simple docstring'''





    return (
        (1 - 2 * point) * sqrt(point - point**2		) + 2 * point + asin(sqrt(1 - point		)		)
    ) / 4
def 			__UpperCamelCase				(			lowercase__	:       str		)	->      float:
    '''simple docstring'''





    lowerCAmelCase_					:	Optional[int]						=   (circles_number + 1 - sqrt(2 * circles_number		)) / (
        2 * (circles_number**2 + 1)
    )
    lowerCAmelCase_					:	Union[str, Any]						=   circles_number * intersection_y

    lowerCAmelCase_					:	int						=   intersection_x * intersection_y / 2
    lowerCAmelCase_					:	Dict						=   circle_bottom_arc_integral(
        1 / 2		) - circle_bottom_arc_integral(snake_case_		)

    return triangle_area + concave_region_area
def 			__UpperCamelCase				(			lowercase__	:       int = 1 / 1000		)	->      int:
    '''simple docstring'''





    lowerCAmelCase_					:	Optional[Any]						=   (1 - pi / 4) / 4

    for n in count(1		):
        if concave_triangle_area(snake_case_		) / l_section_area < fraction:
            return n

    return -1


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









from __future__ import annotations

import math
from itertools import permutations
def 			__UpperCamelCase				(			lowercase__	:       int		)	->      bool:
    '''simple docstring'''





    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
        return False

    # All primes number are in format of 6k +/- 1
    for i in range(5		,    int(math.sqrt(lowercase__		) + 1		)		,    6		):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True
def 			__UpperCamelCase				(			lowercase__	:       int = 7		)	->      int:
    '''simple docstring'''





    lowerCAmelCase_					:	str						=   """""".join(str(lowercase__		) for i in range(1		,    n + 1		)		)
    lowerCAmelCase_					:	Any						=   [int("""""".join(lowercase__		)		) for i in permutations(lowercase__		,    lowercase__		)]
    lowerCAmelCase_					:	List[Any]						=   [num for num in perm_list if is_prime(lowercase__		)]
    return max(lowercase__		) if pandigitals else 0


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


