


'''simple docstring'''




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





def 	a_					( lowerCamelCase	:     int				):

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

   lowerCAmelCase     =			precision
   lowerCAmelCase     =			ceil(precision / 14				)
   lowerCAmelCase     =			426880 * Decimal(10005				).sqrt()
   lowerCAmelCase     =			1
   lowerCAmelCase     =			13591409
   lowerCAmelCase     =			Decimal(lowerCamelCase				)
   for k in range(1	, lowerCamelCase				):
      lowerCAmelCase     =			factorial(6 * k				) // (factorial(3 * k				) * factorial(lowerCamelCase				) ** 3)
      linear_term += 545140134
      exponential_term *= -262537412640768000
      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)}''')









'''simple docstring'''




from __future__ import annotations

from bisect import bisect_left
from functools import total_ordering
from heapq import merge

@total_ordering
class 		UpperCAmelCase_      (  __lowercase		):





     def __lt__( self       :      Optional[int]    ,      UpperCAmelCase__       :      List[str]    )				->  List[Any]:
        return self[-1] < other[-1]





     def __eq__( self       :      str    ,      UpperCAmelCase__       :      List[str]    )				->  Tuple:
        return self[-1] == other[-1]





def 	a_					( lowerCamelCase	:     list				):
   lowerCAmelCase     =			[]
   # sort into stacks
   for element in collection:
      lowerCAmelCase     =			Stack([element]				)
      lowerCAmelCase     =			bisect_left(lowerCamelCase	, lowerCamelCase				)
      if i != len(lowerCamelCase				):
         stacks[i].append(lowerCamelCase				)
      else:
         stacks.append(lowerCamelCase				)

    # use a heap-based merge to merge stack efficiently
   lowerCAmelCase     =			merge(*(reversed(lowerCamelCase				) for stack in stacks)				)
   return collection


if __name__ == "__main__":
       __snake_case    						=input("""Enter numbers separated by a comma:\n""").strip()
       __snake_case    						=[int(item) for item in user_input.split(""",""")]
       print(patience_sort(unsorted))





