
'''simple docstring'''




from decimal import Decimal, getcontext
from math import ceil, factorial







def 		lowerCAmelCase_				(   snake_case__						):




    '''simple docstring'''



    if not isinstance(snake_case__		,				snake_case__						):
        raise TypeError('''Undefined for non-integers'''						)
    elif precision < 1:
        raise ValueError('''Undefined for non-natural numbers'''						)

    A       :   Optional[int]					=						precision
    A       :   str					=						ceil(precision / 14						)
    A       :   List[str]					=						42_6880 * Decimal(1_0005						).sqrt()
    A       :   List[str]					=						1
    A       :   Tuple					=						1359_1409
    A       :   List[Any]					=						Decimal(snake_case__						)
    for k in range(1		,				snake_case__						):
        A       :   List[Any]					=						factorial(6 * k						) // (factorial(3 * k						) * factorial(snake_case__						) ** 3)
        linear_term += 5_4514_0134
        exponential_term *= -26_2537_4126_4076_8000
        partial_sum += Decimal(multinomial_term * linear_term						) / exponential_term
    return str(constant_term / partial_sum						)[:-1]


if __name__ == "__main__":
      lowercase			:				int    		=			50
      print(f'''The first {n} digits of pi is: {pi(n)}''')











'''simple docstring'''


def 							UpperCAmelCase_  (						__lowerCamelCase					:					int	,__lowerCamelCase					:					int ):
   return int((input_a, input_a).count(0 ) == 0 )
def 							UpperCAmelCase_  (						):
   assert and_gate(0	,0 ) == 0
   assert and_gate(0	,1 ) == 0
   assert and_gate(1	,0 ) == 0
   assert and_gate(1	,1 ) == 1


if __name__ == "__main__":
 test_and_gate()
 print(and_gate(1, 0))
 print(and_gate(0, 0))
 print(and_gate(0, 1))
 print(and_gate(1, 1))


