




def  snake_case(    __magic_name__   )			->							"list[int]":





     '''simple docstring'''


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

     lowercase :       Union[str, Any]       =			[0] * (upper_limit + 1)

     # Base case: C(0) = C(1) = 1
     lowercase :       Optional[Any]       =			1
     if upper_limit > 0:
          lowercase :       Dict       =			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(__magic_name__   ):
               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_						=			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()









def  snake_case(    __magic_name__			,		__magic_name__			,		__magic_name__   )			->							int:





     '''simple docstring'''


     if len(__magic_name__   ) != len(__magic_name__   ):
          raise ValueError('''The length of profit and weight must be same.'''   )
     if max_weight <= 0:
          raise ValueError('''max_weight must greater than zero.'''   )
     if any(p < 0 for p in profit   ):
          raise ValueError('''Profit can not be negative.'''   )
     if any(w < 0 for w in weight   ):
          raise ValueError('''Weight can not be negative.'''   )

     # List created to store profit gained for the 1kg in case of each weight
     # respectively.  Calculate and append profit/weight for each element.
     lowercase :       str       =			[p / w for p, w in zip(__magic_name__			,		__magic_name__   )]

     # Creating a copy of the list and sorting profit/weight in ascending order
     lowercase :       str       =			sorted(__magic_name__   )

     # declaring useful variables
     lowercase :       Union[str, Any]       =			len(__magic_name__   )
     lowercase :       Optional[int]       =			0
     lowercase :       Optional[int]       =			0
     lowercase :       int       =			0

     # loop till the total weight do not reach max limit e.g. 15 kg and till i<length
     while limit <= max_weight and i < length:
          # flag value for encountered greatest element in sorted_profit_by_weight
          lowercase :       Optional[int]       =			sorted_profit_by_weight[length - i - 1]
          lowercase :       Union[str, Any]       =			profit_by_weight.index(__magic_name__   )
          lowercase :       Any       =			-1

          # check if the weight encountered is less than the total weight
          # encountered before.
          if max_weight - limit >= weight[index]:
               limit += weight[index]
               # Adding profit gained for the given weight 1 ===
               # weight[index]/weight[index]
               gain += 1 * profit[index]
          else:
               # Since the weight encountered is greater than limit, therefore take the
               # required number of remaining kgs and calculate profit for it.
               # weight remaining / weight[index]
               gain += (max_weight - limit) / weight[index] * profit[index]
               break
          i += 1
     return gain


if __name__ == "__main__":
 print(
     'Input profits, weights, and then max_weight (all positive ints) separated by '
     'spaces.'
 )

 lowerCAmelCase_						=			[int(x) for x in input('Input profits separated by spaces: ').split()]
 lowerCAmelCase_						=			[int(x) for x in input('Input weights separated by spaces: ').split()]
 lowerCAmelCase_						=			int(input('Max weight allowed: '))

 # Function Call
 calc_profit(profit, weight, max_weight)