
'''simple docstring'''

from math import factorial

snake_case									=    {str(digit): factorial(digit) for digit in range(10)}


def        UpperCAmelCase_ (  lowerCamelCase_			):







 """simple docstring"""


 if not isinstance(lowerCamelCase_      ,			lowerCamelCase_			):
  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(lowerCamelCase_			)			)


def        UpperCAmelCase_ (  lowerCamelCase_ = 6_0      ,			lowerCamelCase_ = 1_0_0_0_0_0_0			):







 """simple docstring"""


 if not isinstance(lowerCamelCase_      ,			lowerCamelCase_			) or not isinstance(lowerCamelCase_      ,			lowerCamelCase_			):
  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__     :   str     		=	0
 # the cached sizes of the previous chains
 lowerCAmelCase__     :   dict[int, int]     		=	{}

 for start_chain_element in range(1      ,			lowerCamelCase_			):
  # The temporary set will contain the elements of the chain
  lowerCAmelCase__     :   Any     		=	set()
  lowerCAmelCase__     :   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__     :   Dict     		=	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(lowerCamelCase_			)
   chain_set_length += 1
   lowerCAmelCase__     :   Dict     		=	digit_factorial_sum(lowerCamelCase_			)

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

  lowerCAmelCase__     :   Optional[Any]     		=	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()}')







'''simple docstring'''

def        UpperCAmelCase_ (  lowerCamelCase_			):







 """simple docstring"""


 lowerCAmelCase__     :   str     		=	len(lowerCamelCase_			)
 lowerCAmelCase__     :   Optional[Any]     		=	len(matrix[0]			)
 lowerCAmelCase__     :   Any     		=	min(lowerCamelCase_      ,			lowerCamelCase_			)

 for row in range(lowerCamelCase_			):
  # Check if diagonal element is not zero
  if matrix[row][row] != 0:
   # Eliminate all the elements below the diagonal
   for col in range(row + 1      ,			lowerCamelCase_			):
    lowerCAmelCase__     :   Tuple     		=	matrix[col][row] / matrix[row][row]
    for i in range(lowerCamelCase_      ,			lowerCamelCase_			):
     matrix[col][i] -= multiplier * matrix[row][i]
  else:
   # Find a non-zero diagonal element to swap rows
   lowerCAmelCase__     :   Dict     		=	True
   for i in range(row + 1      ,			lowerCamelCase_			):
    if matrix[i][row] != 0:
     lowerCAmelCase__		,     lowerCAmelCase__     :   Optional[Any]     		=	matrix[i], matrix[row]
     lowerCAmelCase__     :   Optional[Any]     		=	False
     break
   if reduce:
    rank -= 1
    for i in range(lowerCamelCase_			):
     lowerCAmelCase__     :   Union[str, Any]     		=	matrix[i][rank]

            # Reduce the row pointer by one to stay on the same row
   row -= 1

 return rank


if __name__ == "__main__":
     import doctest

     doctest.testmod()





