





def 							_lowerCAmelCase (  _a   :					int = 50			)	->			int:
     lowerCAmelCase_					:       Optional[int]    =		[1] * (length + 1)

     for row_length in range(3					,   length + 1			):
          for block_length in range(3					,   row_length + 1			):
               for block_start in range(row_length - block_length			):
                    ways_number[row_length] += ways_number[
                        row_length - block_start - block_length - 1
                    ]

               ways_number[row_length] += 1

     return ways_number[length]


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







from collections import namedtuple

UpperCAmelCase_					:   Union[str, Any] 							=						namedtuple("""from_to""", """from_ to""")

UpperCAmelCase_					:   int 							=						{
    """cubicmeter""": from_to(1, 1),
    """litre""": from_to(0.0_01, 10_00),
    """kilolitre""": from_to(1, 1),
    """gallon""": from_to(0.0_04_54, 2_64.1_72),
    """cubicyard""": from_to(0.7_64_55, 1.3_07_95),
    """cubicfoot""": from_to(0.0_28, 35.31_47),
    """cup""": from_to(0.0_00_23_65_88, 42_26.75),
}






def 							_lowerCAmelCase (  _a   :					float					,   _a   :					str					,   _a   :					str			)	->			float:
     if from_type not in METRIC_CONVERSION:
          raise ValueError(
              F'Invalid \'from_type\' value: {from_type!r}  Supported values are:\n'
              + """, """.join(_a			)			)
     if to_type not in METRIC_CONVERSION:
          raise ValueError(
              F'Invalid \'to_type\' value: {to_type!r}.  Supported values are:\n'
              + """, """.join(_a			)			)
     return value * METRIC_CONVERSION[from_type].from_ * METRIC_CONVERSION[to_type].to


if __name__ == "__main__":
      import doctest

      doctest.testmod()
