



"""simple docstring"""
from __future__ import annotations





def      __magic_name__				(							lowercase							,			lowercase = None ):
   SCREAMING_SNAKE_CASE_: Optional[int]     			=word_bank or []
   # create a table
   SCREAMING_SNAKE_CASE_: int     			=len(lowercase ) + 1

   SCREAMING_SNAKE_CASE_: list[list[list[str]]]     			=[]
   for _ in range(lowercase ):
      table.append([] )
   # seed value
   SCREAMING_SNAKE_CASE_: Dict     			=[[]]  # because empty string has empty combination

   # iterate through the indices
   for i in range(lowercase ):
      # condition
      if table[i] != []:
         for word in word_bank:
            # slice condition
            if target[i : i + len(lowercase )] == word:
               SCREAMING_SNAKE_CASE_: list[list[str]]     			=[
                   [word, *way] for way in table[i]
               ]
               # adds the word to every combination the current position holds
               # now,push that combination to the table[i+len(word)]
               table[i + len(lowercase )] += new_combinations

    # combinations are in reverse order so reverse for better output
   for combination in table[len(lowercase )]:
      combination.reverse()

   return table[len(lowercase )]


if __name__ == "__main__":
   print(all_construct("""jwajalapa""", ["""jwa""", """j""", """w""", """a""", """la""", """lapa"""]))
   print(all_construct("""rajamati""", ["""s""", """raj""", """amat""", """raja""", """ma""", """i""", """t"""]))
   print(
       all_construct(
           """hexagonosaurus""",
           ["""h""", """ex""", """hex""", """ag""", """ago""", """ru""", """auru""", """rus""", """go""", """no""", """o""", """s"""],
       )
   )








"""simple docstring"""
def      __magic_name__				(							lowercase ):
   if upper_limit < 0:
      raise ValueError("""Limit for the Catalan sequence must be ≥ 0""" )

   SCREAMING_SNAKE_CASE_: Tuple     			=[0] * (upper_limit + 1)

   # Base case: C(0) = C(1) = 1
   SCREAMING_SNAKE_CASE_: Any     			=1
   if upper_limit > 0:
      SCREAMING_SNAKE_CASE_: List[str]     			=1

   # Recurrence relation: C(i) = sum(C(j).C(i-j-1)), from j = 0 to i
   for i in range(2							,			upper_limit + 1 ):
      for j in range(lowercase ):
         catalan_list[i] += catalan_list[j] * catalan_list[i - j - 1]

   return catalan_list


if __name__ == "__main__":
   print("""\n********* Catalan Numbers Using Dynamic Programming ************\n""")
   print("""\n*** Enter -1 at any time to quit ***""")
   print("""\nEnter the upper limit (≥ 0) for the Catalan number sequence: """, end="""""")
   try:
      while True:
         _UpperCAmelCase     =			int(input().strip())
         if N < 0:
            print("""\n********* Goodbye!! ************""")
            break
         else:
            print(f"""The Catalan numbers from 0 through {N} are:""")
            print(catalan_numbers(N))
            print("""Try another upper limit for the sequence: """, end="""""")
   except (NameError, ValueError):
      print("""\n********* Invalid input, goodbye! ************\n""")

   import doctest

   doctest.testmod()



