



def       _lowerCAmelCase			(_lowerCAmelCase = 50):
					UpperCamelCase_						     =      [[0] * 3 for _ in range(length + 1)]

					for row_length in range(length + 1):
										for tile_length in range(2      ,		5):
															for tile_start in range(row_length - tile_length + 1):
																				different_colour_ways_number[row_length][tile_length - 2] += (
																				    different_colour_ways_number[row_length - tile_start - tile_length][
																				        tile_length - 2
																				    ]
																				    + 1
																				)

					return sum(different_colour_ways_number[length])


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





import pytest

from datasets.utils.sharding import _distribute_shards, _number_of_shards_in_gen_kwargs, _split_gen_kwargs






@pytest.mark.parametrize(
    "kwargs, expected"				, [
        ({"num_shards": 0, "max_num_jobs": 1}, []),
        ({"num_shards": 10, "max_num_jobs": 1}, [range(10  )]),
        ({"num_shards": 10, "max_num_jobs": 10}, [range(_lowerCamelCase				, i + 1  ) for i in range(10  )]),
        ({"num_shards": 1, "max_num_jobs": 10}, [range(1  )]),
        ({"num_shards": 10, "max_num_jobs": 3}, [range(0				, 4  ), range(4				, 7  ), range(7				, 10  )]),
        ({"num_shards": 3, "max_num_jobs": 10}, [range(0				, 1  ), range(1				, 2  ), range(2				, 3  )]),
    ]				, )
def 				A				(					_lowerCamelCase				, _lowerCamelCase  ):





							'''simple docstring'''




							_lowerCAmelCase     :							List[Any]    =    _distribute_shards(**_lowerCamelCase  )
							assert out == expected






@pytest.mark.parametrize(
    "gen_kwargs, max_num_jobs, expected"				, [
        ({"foo": 0}, 10, [{"foo": 0}]),
        ({"shards": [0, 1, 2, 3]}, 1, [{"shards": [0, 1, 2, 3]}]),
        ({"shards": [0, 1, 2, 3]}, 4, [{"shards": [0]}, {"shards": [1]}, {"shards": [2]}, {"shards": [3]}]),
        ({"shards": [0, 1]}, 4, [{"shards": [0]}, {"shards": [1]}]),
        ({"shards": [0, 1, 2, 3]}, 2, [{"shards": [0, 1]}, {"shards": [2, 3]}]),
    ]				, )
def 				A				(					_lowerCamelCase				, _lowerCamelCase				, _lowerCamelCase  ):





							'''simple docstring'''




							_lowerCAmelCase     :							Optional[int]    =    _split_gen_kwargs(_lowerCamelCase				, _lowerCamelCase  )
							assert out == expected






@pytest.mark.parametrize(
    "gen_kwargs, expected"				, [
        ({"foo": 0}, 1),
        ({"shards": [0]}, 1),
        ({"shards": [0, 1, 2, 3]}, 4),
        ({"shards": [0, 1, 2, 3], "foo": 0}, 4),
        ({"shards": [0, 1, 2, 3], "other": (0, 1)}, 4),
        ({"shards": [0, 1, 2, 3], "shards2": [0, 1]}, RuntimeError),
    ]				, )
def 				A				(					_lowerCamelCase				, _lowerCamelCase  ):





							'''simple docstring'''




							if expected is RuntimeError:
														with pytest.raises(_lowerCamelCase  ):
																					_number_of_shards_in_gen_kwargs(_lowerCamelCase  )
							else:
														_lowerCAmelCase     :							Optional[int]    =    _number_of_shards_in_gen_kwargs(_lowerCamelCase  )
														assert out == expected
