
"""simple docstring"""







def    __lowerCAmelCase    (_UpperCamelCase = 100_0000		):
	__lowerCAmelCase      :						int						      =				[i - 1 for i in range(limit + 1		)]

	for i in range(2	,  limit + 1		):
		if phi[i] == i - 1:
			for j in range(2 * i	,  limit + 1	,  _UpperCamelCase		):
				phi[j] -= phi[j] // i

	return sum(phi[2 : limit + 1]		)


if __name__ == "__main__":
							print(solution())

"""simple docstring"""







lowerCamelCase__        =		"""0.21.0"""

from .accelerator import Accelerator
from .big_modeling import (
    cpu_offload,
    cpu_offload_with_hook,
    disk_offload,
    dispatch_model,
    init_empty_weights,
    init_on_device,
    load_checkpoint_and_dispatch,
)
from .data_loader import skip_first_batches
from .launchers import debug_launcher, notebook_launcher
from .state import PartialState
from .utils import (
    DeepSpeedPlugin,
    DistributedDataParallelKwargs,
    DistributedType,
    FullyShardedDataParallelPlugin,
    GradScalerKwargs,
    InitProcessGroupKwargs,
    find_executable_batch_size,
    infer_auto_device_map,
    is_rich_available,
    load_checkpoint_in_model,
    synchronize_rng_states,
)


if is_rich_available():
							from .utils import rich