


import functools
from typing import Any




def     UpperCamelCase    (      _a       ,		_a		)					->							List[Any]:
					'''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
					lowercase_       :dict[str, Any]     =       {}
					lowercase_       :Dict     =       'WORD_KEEPER'

					for word in words:
										lowercase_       :List[Any]     =       trie
										for c in word:
															if c not in trie_node:
																				lowercase_       :str     =       {}

															lowercase_       :Any     =       trie_node[c]

										lowercase_       :Optional[int]     =       True

					lowercase_       :List[str]     =       len(lowerCAmelCase__		)

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

										lowercase_       :Tuple     =       trie
										for i in range(lowerCAmelCase__       ,		lowerCAmelCase__		):
															lowercase_       :Dict     =       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()





def     UpperCamelCase    (      _a       ,		_a       ,		_a		)					->							int:
     '''simple docstring'''





     def count_of_possible_combinations(_a		) -> int:
          if target < 0:
               return 0
          if target == 0:
               return 1
          return sum(count_of_possible_combinations(target - item		) for item in array		)

     return count_of_possible_combinations(_a		)




def     UpperCamelCase    (      _a       ,		_a       ,		_a		)					->							int:
     '''simple docstring'''





     def count_of_possible_combinations_with_dp_array(
         _a       ,		_a		) -> int:
          if target < 0:
               return 0
          if target == 0:
               return 1
          if dp_array[target] != -1:
               return dp_array[target]
          lowercase_       :Optional[int]     =       sum(
              count_of_possible_combinations_with_dp_array(target - item       ,		_a		)
              for item in array		)
          lowercase_       :List[Any]     =       answer
          return answer

     lowercase_       :Dict     =       [-1] * (target + 1)
     return count_of_possible_combinations_with_dp_array(_a       ,		_a		)




def     UpperCamelCase    (      _a       ,		_a       ,		_a		)					->							int:
     '''simple docstring'''





     lowercase_       :Optional[int]     =       [0] * (target + 1)
     lowercase_       :int     =       1

     for i in range(1       ,		target + 1		):
          for j in range(_a		):
               if i - array[j] >= 0:
                    dp_array[i] += dp_array[i - array[j]]

     return dp_array[target]


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   SCREAMING_SNAKE_CASE       :		Optional[Any]         =				3
   SCREAMING_SNAKE_CASE       :		Tuple         =				5
   SCREAMING_SNAKE_CASE       :		List[Any]         =				[1, 2, 5]
   print(combination_sum_iv(n, array, target))

