


'''simple docstring'''






from __future__ import annotations

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






@total_ordering
class   __snake_case			(  _SCREAMING_SNAKE_CASE):







    """simple docstring"""



    def __lt__(  self       :    Tuple       ,		lowerCamelCase       :    Optional[int]						)  ->    int:
      return self[-1] < other[-1]





    def __eq__(  self       :    Any       ,		lowerCamelCase       :    int						)  ->    Optional[int]:
      return self[-1] == other[-1]







def 							UpperCamelCase_     (       A__   :  list   ):
  '''simple docstring'''





  lowerCAmelCase_     : list[Stack]     =  []
  # sort into stacks
  for element in collection:
    lowerCAmelCase_     : List[Any]     =  Stack([element]   )
    lowerCAmelCase_     : Optional[Any]     =  bisect_left(A__				,       A__   )
    if i != len(A__   ):
      stacks[i].append(A__   )
    else:
      stacks.append(A__   )

    # use a heap-based merge to merge stack efficiently
  lowerCAmelCase_     : Optional[Any]     =  merge(*(reversed(A__   ) for stack in stacks)   )
  return collection


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







'''simple docstring'''






from math import factorial

__A   :    dict[str, int]											= {str(digit): factorial(digit) for digit in range(10)}







def 							UpperCamelCase_     (       A__   :  int   ):
  '''simple docstring'''





  if not isinstance(A__				,       A__   ):
    raise TypeError("""Parameter number must be int"""   )

  if number < 0:
    raise ValueError("""Parameter number must be greater than or equal to 0"""   )

  # Converts number in string to iterate on its digits and adds its factorial.
  return sum(DIGIT_FACTORIAL[digit] for digit in str(A__   )   )







def 							UpperCamelCase_     (       A__   :  int = 60				,       A__   :  int = 1_00_00_00   ):
  '''simple docstring'''





  if not isinstance(A__				,       A__   ) or not isinstance(A__				,       A__   ):
    raise TypeError("""Parameters chain_length and number_limit must be int"""   )

  if chain_length <= 0 or number_limit <= 0:
    raise ValueError(
        """Parameters chain_length and number_limit must be greater than 0"""   )

  # the counter for the chains with the exact desired length
  lowerCAmelCase_     : Optional[int]     =  0
  # the cached sizes of the previous chains
  lowerCAmelCase_     : dict[int, int]     =  {}

  for start_chain_element in range(1				,       A__   ):
    # The temporary set will contain the elements of the chain
    lowerCAmelCase_     : List[str]     =  set()
    lowerCAmelCase_     : Optional[int]     =  0

    # Stop computing the chain when you find a cached size, a repeating item or the
    # length is greater then the desired one.
    lowerCAmelCase_     : int     =  start_chain_element
    while (
        chain_element not in chain_sets_lengths
        and chain_element not in chain_set
        and chain_set_length <= chain_length
    ):
      chain_set.add(A__   )
      chain_set_length += 1
      lowerCAmelCase_     : Union[str, Any]     =  digit_factorial_sum(A__   )

    if chain_element in chain_sets_lengths:
      chain_set_length += chain_sets_lengths[chain_element]

    lowerCAmelCase_     : int     =  chain_set_length

    # If chain contains the exact amount of elements increase the counter
    if chain_set_length == chain_length:
      chains_counter += 1

  return chains_counter


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  print(F'''{solution()}''')



