






'''simple docstring'''







from __future__ import annotations

import math





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase       ,    UpperCamelCase   )   -> float:
							lowerCamelCase__      :			Union[str, Any] 						= u
							for i in range(1       ,    UpperCamelCase   ):
														lowerCamelCase__      :			Optional[Any] 						= temp * (u - i)
							return temp





def 				SCREAMING_SNAKE_CASE_ ()   -> None:
							lowerCamelCase__      :			int 						= int(input("""enter the numbers of values: """   )   )
							lowerCamelCase__      :			list[list[float]] 						= []
							for _ in range(UpperCamelCase   ):
														y.append([]   )
							for i in range(UpperCamelCase   ):
														for j in range(UpperCamelCase   ):
																					y[i].append(UpperCamelCase   )
																					lowerCamelCase__      :			int 						= 0

							print("""enter the values of parameters in a list: """   )
							lowerCamelCase__      :			Dict 						= list(map(UpperCamelCase       ,    input().split()   )   )

							print("""enter the values of corresponding parameters: """   )
							for i in range(UpperCamelCase   ):
														lowerCamelCase__      :			List[Any] 						= float(input()   )

							lowerCamelCase__      :			Union[str, Any] 						= int(input("""enter the value to interpolate: """   )   )
							lowerCamelCase__      :			List[str] 						= (value - x[0]) / (x[1] - x[0])

							# for calculating forward difference table

							for i in range(1       ,    UpperCamelCase   ):
														for j in range(n - i   ):
																					lowerCamelCase__      :			Union[str, Any] 						= y[j + 1][i - 1] - y[j][i - 1]

							lowerCamelCase__      :			Any 						= y[0][0]
							for i in range(1       ,    UpperCamelCase   ):
														summ += (ucal(UpperCamelCase       ,    UpperCamelCase   ) * y[0][i]) / math.factorial(UpperCamelCase   )

							print(f'''the value at {value} is {summ}'''   )


if __name__ == "__main__":
			main()









'''simple docstring'''







_A			:    List[str]					  ='''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

