


"""simple docstring"""







import functools
from typing import Any




def        UpperCAmelCase__	(lowerCAmelCase_  ,						lowerCAmelCase_       ):




					'''simple docstring'''


					if not isinstance(lowerCAmelCase_  ,						lowerCAmelCase_       ) or len(lowerCAmelCase_       ) == 0:
										raise ValueError("the string should be not empty string"       )

					if not isinstance(lowerCAmelCase_  ,						lowerCAmelCase_       ) or not all(
					    isinstance(lowerCAmelCase_  ,						lowerCAmelCase_       ) and len(lowerCAmelCase_       ) > 0 for item in words       ):
										raise ValueError("the words should be a list of non-empty strings"       )

					# Build trie
					__SCREAMING_SNAKE_CASE						       =    {}
					__SCREAMING_SNAKE_CASE						       =    "WORD_KEEPER"

					for word in words:
										__SCREAMING_SNAKE_CASE						       =    trie
										for c in word:
															if c not in trie_node:
																				__SCREAMING_SNAKE_CASE						       =    {}

															__SCREAMING_SNAKE_CASE						       =    trie_node[c]

										__SCREAMING_SNAKE_CASE						       =    True

					__SCREAMING_SNAKE_CASE						       =    len(lowerCAmelCase_       )

					# Dynamic programming method
					@functools.cache
					def is_breakable(lowerCAmelCase_       ) -> bool:
										if index == len_string:
															return True

										__SCREAMING_SNAKE_CASE						       =    trie
										for i in range(lowerCAmelCase_  ,						lowerCAmelCase_       ):
															__SCREAMING_SNAKE_CASE						       =    trie_node.get(string[i]  ,						lowerCAmelCase_       )

															if trie_node is None:
																				return False

															if trie_node.get(lowerCAmelCase_  ,						lowerCAmelCase_       ) and is_breakable(i + 1       ):
																				return True

										return False

					return is_breakable(0       )


if __name__ == "__main__":
		import doctest

		doctest.testmod()




"""simple docstring"""







def        UpperCAmelCase__	(lowerCAmelCase_  ,						lowerCAmelCase_       ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						       =    [0 for i in range(r + 1       )]
					# nc0 = 1
					__SCREAMING_SNAKE_CASE						       =    1
					for i in range(1  ,						n + 1       ):
										# to compute current row from previous row.
										__SCREAMING_SNAKE_CASE						       =    min(lowerCAmelCase_  ,						lowerCAmelCase_       )
										while j > 0:
															c[j] += c[j - 1]
															j -= 1
					return c[r]



print(binomial_coefficient(n=1_0, r=5))
