




def SCREAMING_SNAKE_CASE				(       lowercase_						)   ->       "list[int]":



       """simple docstring"""

       if upper_limit < 0:
              raise ValueError('''Limit for the Catalan sequence must be ≥ 0'''						)

       A__       =    [0] * (upper_limit + 1)

       # Base case: C(0) = C(1) = 1
       A__       =    1
       if upper_limit > 0:
              A__       =    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:
      _lowerCamelCase	:		List[Any]							       =   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				(       lowercase_ ,				lowercase_ ,				lowercase_						)   ->       tuple[float, list[float]]:



       """simple docstring"""

       A__       =    list(range(len(lowercase_						)						)						)
       A__       =    [v / w for v, w in zip(lowercase_ ,				lowercase_						)]
       index.sort(key=lambda lowercase_						: ratio[i] ,				reverse=lowercase_						)

       A__       =    0
       A__       =    [0] * len(lowercase_						)
       for i in index:
              if weight[i] <= capacity:
                     A__       =    1
                     max_value += value[i]
                     capacity -= weight[i]
              else:
                     A__       =    capacity / weight[i]
                     max_value += value[i] * capacity / weight[i]
                     break

       return max_value, fractions


if __name__ == "__main__":
  import doctest

  doctest.testmod()


