
'''simple docstring'''





from math import factorial

SCREAMING_SNAKE_CASE     =       {str(digit): factorial(digit) for digit in range(1_0)}







def snake_case_     (					lowercase__		):
  if not isinstance(lowercase__   ,       lowercase__		):
    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(lowercase__		)		)







def snake_case_     (					lowercase__ = 6_0   ,       lowercase__ = 1_0_0_0_0_0_0		):

  if not isinstance(lowercase__   ,       lowercase__		) or not isinstance(lowercase__   ,       lowercase__		):
    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
  UpperCAmelCase__      :					Union[str, Any]				       =							0
  # the cached sizes of the previous chains
  UpperCAmelCase__      :					dict[int, int]				       =							{}

  for start_chain_element in range(1   ,       lowercase__		):
    # The temporary set will contain the elements of the chain
    UpperCAmelCase__      :					Any				       =							set()
    UpperCAmelCase__      :					int				       =							0

    # Stop computing the chain when you find a cached size, a repeating item or the
    # length is greater then the desired one.
    UpperCAmelCase__      :					List[str]				       =							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(lowercase__		)
      chain_set_length += 1
      UpperCAmelCase__      :					List[str]				       =							digit_factorial_sum(lowercase__		)

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

    UpperCAmelCase__      :					List[str]				       =							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'''





import unittest

from transformers.testing_utils import CaptureStdout
from transformers.tools.python_interpreter import evaluate







def snake_case_     (					lowercase__		):
  return x + 2






class 							UpperCAmelCase_							(    unittest.TestCase				):

 '''simple docstring'''







 def 							UpperCamelCase  (					self		:  Optional[int] ):



   '''simple docstring'''




   UpperCAmelCase__      :					List[str]				       =							"x = 3"
   UpperCAmelCase__      :					List[str]				       =							{}
   UpperCAmelCase__      :					Tuple				       =							evaluate(snake_case__			,				{}			,				state=snake_case__ )
   assert result == 3
   self.assertDictEqual(snake_case__			,				{"x": 3} )

   UpperCAmelCase__      :					Any				       =							"x = y"
   UpperCAmelCase__      :					List[str]				       =							{"y": 5}
   UpperCAmelCase__      :					Dict				       =							evaluate(snake_case__			,				{}			,				state=snake_case__ )
   # evaluate returns the value of the last assignment.
   assert result == 5
   self.assertDictEqual(snake_case__			,				{"x": 5, "y": 5} )







 def 							UpperCamelCase  (					self		:  Union[str, Any] ):



   '''simple docstring'''




   UpperCAmelCase__      :					int				       =							"y = add_two(x)"
   UpperCAmelCase__      :					Tuple				       =							{"x": 3}
   UpperCAmelCase__      :					Union[str, Any]				       =							evaluate(snake_case__			,				{"add_two": add_two}			,				state=snake_case__ )
   assert result == 5
   self.assertDictEqual(snake_case__			,				{"x": 3, "y": 5} )

   # Won't work without the tool
   with CaptureStdout() as out:
     UpperCAmelCase__      :					Any				       =							evaluate(snake_case__			,				{}			,				state=snake_case__ )
   assert result is None
   assert "tried to execute add_two" in out.out







 def 							UpperCamelCase  (					self		:  List[str] ):



   '''simple docstring'''




   UpperCAmelCase__      :					Tuple				       =							"x = 3"
   UpperCAmelCase__      :					List[Any]				       =							{}
   UpperCAmelCase__      :					Tuple				       =							evaluate(snake_case__			,				{}			,				state=snake_case__ )
   assert result == 3
   self.assertDictEqual(snake_case__			,				{"x": 3} )







 def 							UpperCamelCase  (					self		:  Dict ):



   '''simple docstring'''




   UpperCAmelCase__      :					int				       =							"test_dict = {'x': x, 'y': add_two(x)}"
   UpperCAmelCase__      :					List[Any]				       =							{"x": 3}
   UpperCAmelCase__      :					int				       =							evaluate(snake_case__			,				{"add_two": add_two}			,				state=snake_case__ )
   self.assertDictEqual(snake_case__			,				{"x": 3, "y": 5} )
   self.assertDictEqual(snake_case__			,				{"x": 3, "test_dict": {"x": 3, "y": 5}} )







 def 							UpperCamelCase  (					self		:  List[str] ):



   '''simple docstring'''




   UpperCAmelCase__      :					int				       =							"x = 3\ny = 5"
   UpperCAmelCase__      :					Dict				       =							{}
   UpperCAmelCase__      :					Union[str, Any]				       =							evaluate(snake_case__			,				{}			,				state=snake_case__ )
   # evaluate returns the value of the last assignment.
   assert result == 5
   self.assertDictEqual(snake_case__			,				{"x": 3, "y": 5} )







 def 							UpperCamelCase  (					self		:  Union[str, Any] ):



   '''simple docstring'''




   UpperCAmelCase__      :					Dict				       =							"text = f'This is x: {x}.'"
   UpperCAmelCase__      :					Dict				       =							{"x": 3}
   UpperCAmelCase__      :					Dict				       =							evaluate(snake_case__			,				{}			,				state=snake_case__ )
   # evaluate returns the value of the last assignment.
   assert result == "This is x: 3."
   self.assertDictEqual(snake_case__			,				{"x": 3, "text": "This is x: 3."} )







 def 							UpperCamelCase  (					self		:  List[Any] ):



   '''simple docstring'''




   UpperCAmelCase__      :					List[str]				       =							"if x <= 3:\n    y = 2\nelse:\n    y = 5"
   UpperCAmelCase__      :					Dict				       =							{"x": 3}
   UpperCAmelCase__      :					Dict				       =							evaluate(snake_case__			,				{}			,				state=snake_case__ )
   # evaluate returns the value of the last assignment.
   assert result == 2
   self.assertDictEqual(snake_case__			,				{"x": 3, "y": 2} )

   UpperCAmelCase__      :					Optional[Any]				       =							{"x": 8}
   UpperCAmelCase__      :					str				       =							evaluate(snake_case__			,				{}			,				state=snake_case__ )
   # evaluate returns the value of the last assignment.
   assert result == 5
   self.assertDictEqual(snake_case__			,				{"x": 8, "y": 5} )







 def 							UpperCamelCase  (					self		:  str ):



   '''simple docstring'''




   UpperCAmelCase__      :					Optional[int]				       =							"test_list = [x, add_two(x)]"
   UpperCAmelCase__      :					Any				       =							{"x": 3}
   UpperCAmelCase__      :					Any				       =							evaluate(snake_case__			,				{"add_two": add_two}			,				state=snake_case__ )
   self.assertListEqual(snake_case__			,				[3, 5] )
   self.assertDictEqual(snake_case__			,				{"x": 3, "test_list": [3, 5]} )







 def 							UpperCamelCase  (					self		:  str ):



   '''simple docstring'''




   UpperCAmelCase__      :					str				       =							"y = x"
   UpperCAmelCase__      :					str				       =							{"x": 3}
   UpperCAmelCase__      :					Any				       =							evaluate(snake_case__			,				{}			,				state=snake_case__ )
   assert result == 3
   self.assertDictEqual(snake_case__			,				{"x": 3, "y": 3} )







 def 							UpperCamelCase  (					self		:  int ):



   '''simple docstring'''




   UpperCAmelCase__      :					Optional[int]				       =							"test_list = [x, add_two(x)]\ntest_list[1]"
   UpperCAmelCase__      :					List[Any]				       =							{"x": 3}
   UpperCAmelCase__      :					List[Any]				       =							evaluate(snake_case__			,				{"add_two": add_two}			,				state=snake_case__ )
   assert result == 5
   self.assertDictEqual(snake_case__			,				{"x": 3, "test_list": [3, 5]} )

   UpperCAmelCase__      :					Union[str, Any]				       =							"test_dict = {'x': x, 'y': add_two(x)}\ntest_dict['y']"
   UpperCAmelCase__      :					str				       =							{"x": 3}
   UpperCAmelCase__      :					Any				       =							evaluate(snake_case__			,				{"add_two": add_two}			,				state=snake_case__ )
   assert result == 5
   self.assertDictEqual(snake_case__			,				{"x": 3, "test_dict": {"x": 3, "y": 5}} )







 def 							UpperCamelCase  (					self		:  Union[str, Any] ):



   '''simple docstring'''




   UpperCAmelCase__      :					List[Any]				       =							"x = 0\nfor i in range(3):\n    x = i"
   UpperCAmelCase__      :					List[Any]				       =							{}
   UpperCAmelCase__      :					Any				       =							evaluate(snake_case__			,				{"range": range}			,				state=snake_case__ )
   assert result == 2
   self.assertDictEqual(snake_case__			,				{"x": 2, "i": 2} )



