




'''simple docstring'''





from math import factorial

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







def 			_a   (		SCREAMING_SNAKE_CASE_							:       int  ):
					if not isinstance(SCREAMING_SNAKE_CASE_   ,   SCREAMING_SNAKE_CASE_  ):
										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(SCREAMING_SNAKE_CASE_  )  )







def 			_a   (		SCREAMING_SNAKE_CASE_							:       int = 60   ,   SCREAMING_SNAKE_CASE_							:       int = 1_00_00_00  ):

					if not isinstance(SCREAMING_SNAKE_CASE_   ,   SCREAMING_SNAKE_CASE_  ) or not isinstance(SCREAMING_SNAKE_CASE_   ,   SCREAMING_SNAKE_CASE_  ):
										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            = 0
					# the cached sizes of the previous chains
					__lowerCAmelCase            = {}

					for start_chain_element in range(1   ,   SCREAMING_SNAKE_CASE_  ):
										# The temporary set will contain the elements of the chain
										__lowerCAmelCase            = set()
										__lowerCAmelCase            = 0

										# Stop computing the chain when you find a cached size, a repeating item or the
										# length is greater then the desired one.
										__lowerCAmelCase            = 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(SCREAMING_SNAKE_CASE_  )
															chain_set_length += 1
															__lowerCAmelCase            = digit_factorial_sum(SCREAMING_SNAKE_CASE_  )

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

										__lowerCAmelCase            = 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()}''')










from __future__ import annotations

from collections.abc import Iterator
from typing import Any
class     a__					:






						def __init__(     self	,    _A    ):




											"""simple docstring"""



											__lowerCAmelCase            = data
											__lowerCAmelCase            = None






class     a__					:






						def __init__(     self    ):




											"""simple docstring"""



											__lowerCAmelCase            = None
											__lowerCAmelCase            = None






						def __iter__(     self    ):




											"""simple docstring"""



											__lowerCAmelCase            = self.head
											while self.head:
																yield node.data
																__lowerCAmelCase            = node.next
																if node == self.head:
																					break






						def __len__(     self    ):




											"""simple docstring"""



											return sum(1 for _ in self    )






						def __repr__(     self    ):




											"""simple docstring"""



											return "->".join(str(_A    ) for item in iter(self    )    )






						def        __SCREAMING_SNAKE_CASE(     self	,    _A    ):




											"""simple docstring"""



											self.insert_nth(len(self    )	,    _A    )






						def        __SCREAMING_SNAKE_CASE(     self	,    _A    ):




											"""simple docstring"""



											self.insert_nth(0	,    _A    )






						def        __SCREAMING_SNAKE_CASE(     self	,    _A	,    _A    ):




											"""simple docstring"""



											if index < 0 or index > len(self    ):
																raise IndexError("list index out of range."    )
											__lowerCAmelCase            = Node(_A    )
											if self.head is None:
																__lowerCAmelCase            = new_node  # first node points itself
																__lowerCAmelCase            = __lowerCAmelCase            = new_node
											elif index == 0:  # insert at head
																__lowerCAmelCase            = self.head
																__lowerCAmelCase            = __lowerCAmelCase            = new_node
											else:
																__lowerCAmelCase            = self.head
																for _ in range(index - 1    ):
																					__lowerCAmelCase            = temp.next
																__lowerCAmelCase            = temp.next
																__lowerCAmelCase            = new_node
																if index == len(self    ) - 1:  # insert at tail
																					__lowerCAmelCase            = new_node






						def        __SCREAMING_SNAKE_CASE(     self    ):




											"""simple docstring"""



											return self.delete_nth(0    )






						def        __SCREAMING_SNAKE_CASE(     self    ):




											"""simple docstring"""



											return self.delete_nth(len(self    ) - 1    )






						def        __SCREAMING_SNAKE_CASE(     self	,    _A = 0    ):




											"""simple docstring"""



											if not 0 <= index < len(self    ):
																raise IndexError("list index out of range."    )
											__lowerCAmelCase            = self.head
											if self.head == self.tail:  # just one node
																__lowerCAmelCase            = __lowerCAmelCase            = None
											elif index == 0:  # delete head node
																__lowerCAmelCase            = self.tail.next.next
																__lowerCAmelCase            = self.head.next
											else:
																__lowerCAmelCase            = self.head
																for _ in range(index - 1    ):
																					__lowerCAmelCase            = temp.next
																__lowerCAmelCase            = temp.next
																__lowerCAmelCase            = temp.next.next
																if index == len(self    ) - 1:  # delete at tail
																					__lowerCAmelCase            = temp
											return delete_node.data






						def        __SCREAMING_SNAKE_CASE(     self    ):




											"""simple docstring"""



											return len(self    ) == 0







def 			_a   (		):
					__lowerCAmelCase            = CircularLinkedList()
					assert len(SCREAMING_SNAKE_CASE_  ) == 0
					assert circular_linked_list.is_empty() is True
					assert str(SCREAMING_SNAKE_CASE_  ) == ""

					try:
										circular_linked_list.delete_front()
										raise AssertionError  # This should not happen
					except IndexError:
										assert True  # This should happen

					try:
										circular_linked_list.delete_tail()
										raise AssertionError  # This should not happen
					except IndexError:
										assert True  # This should happen

					try:
										circular_linked_list.delete_nth(-1  )
										raise AssertionError
					except IndexError:
										assert True

					try:
										circular_linked_list.delete_nth(0  )
										raise AssertionError
					except IndexError:
										assert True

					assert circular_linked_list.is_empty() is True
					for i in range(5  ):
										assert len(SCREAMING_SNAKE_CASE_  ) == i
										circular_linked_list.insert_nth(SCREAMING_SNAKE_CASE_   ,   i + 1  )
					assert str(SCREAMING_SNAKE_CASE_  ) == "->".join(str(SCREAMING_SNAKE_CASE_  ) for i in range(1   ,   6  )  )

					circular_linked_list.insert_tail(6  )
					assert str(SCREAMING_SNAKE_CASE_  ) == "->".join(str(SCREAMING_SNAKE_CASE_  ) for i in range(1   ,   7  )  )
					circular_linked_list.insert_head(0  )
					assert str(SCREAMING_SNAKE_CASE_  ) == "->".join(str(SCREAMING_SNAKE_CASE_  ) for i in range(0   ,   7  )  )

					assert circular_linked_list.delete_front() == 0
					assert circular_linked_list.delete_tail() == 6
					assert str(SCREAMING_SNAKE_CASE_  ) == "->".join(str(SCREAMING_SNAKE_CASE_  ) for i in range(1   ,   6  )  )
					assert circular_linked_list.delete_nth(2  ) == 3

					circular_linked_list.insert_nth(2   ,   3  )
					assert str(SCREAMING_SNAKE_CASE_  ) == "->".join(str(SCREAMING_SNAKE_CASE_  ) for i in range(1   ,   6  )  )

					assert circular_linked_list.is_empty() is False


if __name__ == "__main__":
					import doctest

					doctest.testmod()




