

def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__      )  ->					"list[int]":
 if upper_limit < 0:
  raise ValueError('Limit for the Catalan sequence must be ≥ 0'      )

 __lowerCamelCase    :    List[str] 	=			[0] * (upper_limit + 1)

 # Base case: C(0) = C(1) = 1
 __lowerCamelCase    :    Dict 	=			1
 if upper_limit > 0:
  __lowerCamelCase    :    int 	=			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(lowerCamelCase__      ):
   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:
               a		=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()







from __future__ import annotations






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__      )  ->					bool:
	if len(lowerCamelCase__      ) == 0:
		return False
	__lowerCamelCase    :    List[Any] 	=			len(lowerCamelCase__      ) // 2
	if a_list[midpoint] == item:
		return True
	if item < a_list[midpoint]:
		return binary_search(a_list[:midpoint]     ,			lowerCamelCase__      )
	else:
		return binary_search(a_list[midpoint + 1 :]     ,			lowerCamelCase__      )


if __name__ == "__main__":
					a		=input("""Enter numbers separated by comma:\n""").strip()
					a		=[int(item.strip()) for item in user_input.split(""",""")]
					a		=int(input("""Enter the number to be found in the list:\n""").strip())
					a		="""""" if binary_search(sequence, target) else """not """
					print(F"""{target} was {not_str}found in {sequence}""")




