






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





def    __lowerCAmelCase   (    __snake_case							):

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

     __lowerCAmelCase             =       precision
     __lowerCAmelCase             =       ceil(precision / 14							)
     __lowerCAmelCase             =       42_6880 * Decimal(1_0005							).sqrt()
     __lowerCAmelCase             =       1
     __lowerCAmelCase             =       1359_1409
     __lowerCAmelCase             =       Decimal(__snake_case							)
     for k in range(1       ,			__snake_case							):
          __lowerCAmelCase             =       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__":
 lowerCamelCase      :       int    =						50
 print(F'''The first {n} digits of pi is: {pi(n)}''')














lowerCamelCase      :       List[Any]    =						{
    '''meter''': '''m''',
    '''kilometer''': '''km''',
    '''megametre''': '''Mm''',
    '''gigametre''': '''Gm''',
    '''terametre''': '''Tm''',
    '''petametre''': '''Pm''',
    '''exametre''': '''Em''',
    '''zettametre''': '''Zm''',
    '''yottametre''': '''Ym''',
}
# Exponent of the factor(meter)
lowerCamelCase      :       Union[str, Any]    =						{
    '''m''': 0,
    '''km''': 3,
    '''Mm''': 6,
    '''Gm''': 9,
    '''Tm''': 12,
    '''Pm''': 15,
    '''Em''': 18,
    '''Zm''': 21,
    '''Ym''': 24,
}





def    __lowerCAmelCase   (    __snake_case       ,			__snake_case       ,			__snake_case							):
     __lowerCAmelCase             =       from_type.lower().strip("s"							)
     __lowerCAmelCase             =       to_type.lower().strip("s"							)

     __lowerCAmelCase             =       UNIT_SYMBOL.get(__snake_case       ,			__snake_case							)
     __lowerCAmelCase             =       UNIT_SYMBOL.get(__snake_case       ,			__snake_case							)

     if from_sanitized not in METRIC_CONVERSION:
          __lowerCAmelCase             =       (
              F"""Invalid 'from_type' value: {from_type!r}.\n"""
              F"""Conversion abbreviations are: {", ".join(__snake_case							)}"""
          )
          raise ValueError(__snake_case							)
     if to_sanitized not in METRIC_CONVERSION:
          __lowerCAmelCase             =       (
              F"""Invalid 'to_type' value: {to_type!r}.\n"""
              F"""Conversion abbreviations are: {", ".join(__snake_case							)}"""
          )
          raise ValueError(__snake_case							)
     __lowerCAmelCase             =       METRIC_CONVERSION[from_sanitized]
     __lowerCAmelCase             =       METRIC_CONVERSION[to_sanitized]
     __lowerCAmelCase             =       1

     if from_exponent > to_exponent:
          __lowerCAmelCase             =       from_exponent - to_exponent
     else:
          __lowerCAmelCase             =       -(to_exponent - from_exponent)

     return value * pow(10       ,			__snake_case							)


if __name__ == "__main__":
 from doctest import testmod

 testmod()






