






from typing import List

import numpy as np





def 					lowercase_ (    __snake_case     :							dict      )     -> str:





				'''simple docstring'''


				snake_case__      :Optional[Any]         =   {key: len(__a      ) for key, value in gen_kwargs.items() if isinstance(__a	,	__a      )}
				if len(set(lists_lengths.values()      )      ) > 1:
								raise RuntimeError(
								    (
								        "Sharding is ambiguous for this dataset: "
								        + "we found several data sources lists of different lengths, and we don't know over which list we should parallelize:\n"
								        + "\n".join(F'\t- key {key} has length {length}' for key, length in lists_lengths.items()      )
								        + "\nTo fix this, check the 'gen_kwargs' and make sure to use lists only for data sources, "
								        + "and use tuples otherwise. In the end there should only be one single list, or several lists with the same length."
								    )      )
				snake_case__      :Optional[Any]         =   max(lists_lengths.values()	,	default=0      )
				return max(1	,	__a      )





def 					lowercase_ (    __snake_case     :							int	,	__snake_case     :							int      )     -> Union[str, Any]:





				'''simple docstring'''


				snake_case__      :str         =   []
				for group_idx in range(__a      ):
								snake_case__      :Union[str, Any]         =   num_shards // max_num_jobs + (group_idx < (num_shards % max_num_jobs))
								if num_shards_to_add == 0:
												break
								snake_case__      :Tuple         =   shards_indices_per_group[-1].stop if shards_indices_per_group else 0
								snake_case__      :List[Any]         =   range(__a	,	start + num_shards_to_add      )
								shards_indices_per_group.append(__a      )
				return shards_indices_per_group





def 					lowercase_ (    __snake_case     :							dict	,	__snake_case     :							int      )     -> List[str]:





				'''simple docstring'''


				snake_case__      :Union[str, Any]         =   _number_of_shards_in_gen_kwargs(__a      )
				if num_shards == 1:
								return [dict(__a      )]
				else:
								snake_case__      :Optional[Any]         =   _distribute_shards(num_shards=__a	,	max_num_jobs=__a      )
								return [
								    {
								        key: [value[shard_idx] for shard_idx in shard_indices_per_group[group_idx]]
								        if isinstance(__a	,	__a      )
								        else value
								        for key, value in gen_kwargs.items()
								    }
								    for group_idx in range(len(__a      )      )
								]





def 					lowercase_ (    __snake_case     :							List[dict]      )     -> Optional[Any]:





				'''simple docstring'''


				return {
				    key: [value for gen_kwargs in gen_kwargs_list for value in gen_kwargs[key]]
				    if isinstance(gen_kwargs_list[0][key]	,	__a      )
				    else gen_kwargs_list[0][key]
				    for key in gen_kwargs_list[0]
				}





def 					lowercase_ (    __snake_case     :							np.random.Generator	,	__snake_case     :							dict      )     -> str:





				'''simple docstring'''


				snake_case__      :List[Any]         =   {len(__a      ) for value in gen_kwargs.values() if isinstance(__a	,	__a      )}
				snake_case__      :Tuple         =   {}
				for size in list_sizes:
								snake_case__      :int         =   list(range(__a      )      )
								rng.shuffle(indices_per_size[size]      )
				# Now let's copy the gen_kwargs and shuffle the lists based on their sizes
				snake_case__      :Dict         =   dict(__a      )
				for key, value in shuffled_kwargs.items():
								if isinstance(__a	,	__a      ):
												snake_case__      :Union[str, Any]         =   [value[i] for i in indices_per_size[len(__a      )]]
				return shuffled_kwargs







def 					lowercase_ (    __snake_case     :							list      )     -> list:





				'''simple docstring'''


				if any(not isinstance(__snake_case	,	__snake_case      ) or x < 0 for x in sequence      ):
								raise TypeError("Sequence must be list of non-negative integers"      )
				for _ in range(len(__snake_case      )      ):
								for i, (rod_upper, rod_lower) in enumerate(zip(__snake_case	,	sequence[1:]      )      ):
												if rod_upper > rod_lower:
																sequence[i] -= rod_upper - rod_lower
																sequence[i + 1] += rod_upper - rod_lower
				return sequence


if __name__ == "__main__":
	assert bead_sort([5, 4, 3, 2, 1]) == [1, 2, 3, 4, 5]
	assert bead_sort([7, 9, 4, 3, 5]) == [3, 4, 5, 7, 9]