






from itertools import count







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase = 50      )			->     int:
     UpperCamelCase__      :       Dict	    =  [1] * min_block_length

     for n in count(__lowerCAmelCase      ):
          fill_count_functions.append(1      )

          for block_length in range(__lowerCAmelCase ,   n + 1      ):
               for block_start in range(n - block_length      ):
                    fill_count_functions[n] += fill_count_functions[
                        n - block_start - block_length - 1
                    ]

               fill_count_functions[n] += 1

          if fill_count_functions[n] > 100_0000:
               break

     return n


if __name__ == "__main__":
 print(F"""{solution() = }""")







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase      )			->     int:
     assert isinstance(__lowerCAmelCase ,   __lowerCAmelCase      ), f'The input value of [n={number}] is not an integer'

     if number == 1:
          return 2
     elif number < 1:
          UpperCamelCase__      :       List[Any]	    =  f'The input value of [n={number}] has to be > 0'
          raise ValueError(__lowerCAmelCase      )
     else:
          UpperCamelCase__      :       Optional[Any]	    =  sylvester(number - 1      )
          UpperCamelCase__      :       str	    =  num - 1
          UpperCamelCase__      :       int	    =  num
          return lower * upper + 1


if __name__ == "__main__":
 print(F"""The 8th number in Sylvester's sequence: {sylvester(8)}""")