


"""simple docstring"""


from __future__ import annotations


def    _lowerCamelCase   (     lowerCamelCase__	:							int       ,		lowerCamelCase__	:							int  ):
 lowercase__       :       list[list[int]]				=						[]
 create_all_state(1       ,		lowerCamelCase__       ,		lowerCamelCase__       ,		[]       ,		lowerCamelCase__  )
 return result


def    _lowerCamelCase   (     lowerCamelCase__	:							int       ,		lowerCamelCase__	:							int       ,		lowerCamelCase__	:							int       ,		lowerCamelCase__	:							list[int]       ,		lowerCamelCase__	:							list[list[int]]       ,		):
 if level == 0:
  total_list.append(current_list[:]  )
  return

 for i in range(lowerCamelCase__       ,		total_number - level + 2  ):
  current_list.append(lowerCamelCase__  )
  create_all_state(i + 1       ,		lowerCamelCase__       ,		level - 1       ,		lowerCamelCase__       ,		lowerCamelCase__  )
  current_list.pop()


def    _lowerCamelCase   (     lowerCamelCase__	:							list[list[int]]  ):
 for i in total_list:
  print(*lowerCamelCase__  )


if __name__ == "__main__":
   __snake_case    					=					4
   __snake_case    					=					2
   __snake_case    					=					generate_all_combinations(n, k)
   print_all_state(total_list)



"""simple docstring"""


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


def    _lowerCamelCase   (     lowerCamelCase__	:							int  ):

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

 lowercase__       :       List[str]				=						precision
 lowercase__       :       Optional[int]				=						ceil(precision / 14  )
 lowercase__       :       Union[str, Any]				=						42_68_80 * Decimal(1_00_05  ).sqrt()
 lowercase__       :       Optional[Any]				=						1
 lowercase__       :       Optional[Any]				=						13_59_14_09
 lowercase__       :       List[Any]				=						Decimal(lowerCamelCase__  )
 for k in range(1       ,		lowerCamelCase__  ):
  lowercase__       :       Optional[int]				=						factorial(6 * k  ) // (factorial(3 * k  ) * factorial(lowerCamelCase__  ) ** 3)
  linear_term += 5_45_14_01_34
  exponential_term *= -26_25_37_41_26_40_76_80_00
  partial_sum += Decimal(multinomial_term * linear_term  ) / exponential_term
 return str(constant_term / partial_sum  )[:-1]


if __name__ == "__main__":
   __snake_case    					=					50
   print(F"The first {n} digits of pi is: {pi(n)}")