
'''simple docstring'''
from math import pow






def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, ):
							if current_sum == needed_sum:
														# If the sum of the powers is equal to needed_sum, then we have a solution.
														solutions_count += 1
														return current_sum, solutions_count

							_snake_case       =  int(pow(_SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				)				)
							if current_sum + i_to_n <= needed_sum:
														# If the sum of the powers is less than needed_sum, then continue adding powers.
														current_sum += i_to_n
														_snake_case,							_snake_case       =  backtrack(
														    _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, current_number + 1							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				)
														current_sum -= i_to_n
							if i_to_n < needed_sum:
														# If the power of i is less than needed_sum, then try with the next power.
														_snake_case,							_snake_case       =  backtrack(
														    _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, current_number + 1							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				)
							return current_sum, solutions_count






def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				):
							if not (1 <= needed_sum <= 1000 and 2 <= power <= 10):
														raise ValueError(
														    """Invalid input\n"""
														    """needed_sum must be between 1 and 1000, power between 2 and 10."""				)

							return backtrack(_SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, 1							, 0							, 0				)[1]  # Return the solutions_count


if __name__ == "__main__":
				import doctest

				doctest.testmod()




'''simple docstring'''
from ...configuration_utils import PretrainedConfig
from ...utils import logging
from ...utils.backbone_utils import BackboneConfigMixin, get_aligned_output_features_output_indices


__lowerCAmelCase												=	logging.get_logger(__name__)

__lowerCAmelCase												=	{
    'shi-labs/nat-mini-in1k-224': 'https://huggingface.co/shi-labs/nat-mini-in1k-224/resolve/main/config.json',
    # See all Nat models at https://huggingface.co/models?filter=nat
}


class       _lowerCAmelCase   (   __snake_case					,							__snake_case				):







							'''simple docstring'''

							lowerCAmelCase_ 						=						"nat"

							lowerCAmelCase_ 						=						{
							    "num_attention_heads": "num_heads",
							    "num_hidden_layers": "num_layers",
							}

							def __init__(self  ,  UpperCAmelCase=4  ,  UpperCAmelCase=3  ,  UpperCAmelCase=64  ,  UpperCAmelCase=[3, 4, 6, 5]  ,  UpperCAmelCase=[2, 4, 8, 16]  ,  UpperCAmelCase=7  ,  UpperCAmelCase=3.0  ,  UpperCAmelCase=True  ,  UpperCAmelCase=0.0  ,  UpperCAmelCase=0.0  ,  UpperCAmelCase=0.1  ,  UpperCAmelCase="gelu"  ,  UpperCAmelCase=0.02  ,  UpperCAmelCase=1e-5  ,  UpperCAmelCase=0.0  ,  UpperCAmelCase=None  ,  UpperCAmelCase=None  ,  **UpperCAmelCase  ,  )					->       str:
														super().__init__(**UpperCAmelCase  )

														_snake_case       =  patch_size
														_snake_case       =  num_channels
														_snake_case       =  embed_dim
														_snake_case       =  depths
														_snake_case       =  len(UpperCAmelCase  )
														_snake_case       =  num_heads
														_snake_case       =  kernel_size
														_snake_case       =  mlp_ratio
														_snake_case       =  qkv_bias
														_snake_case       =  hidden_dropout_prob
														_snake_case       =  attention_probs_dropout_prob
														_snake_case       =  drop_path_rate
														_snake_case       =  hidden_act
														_snake_case       =  layer_norm_eps
														_snake_case       =  initializer_range
														# we set the hidden_size attribute in order to make Nat work with VisionEncoderDecoderModel
														# this indicates the channel dimension after the last stage of the model
														_snake_case       =  int(embed_dim * 2 ** (len(UpperCAmelCase  ) - 1)  )
														_snake_case       =  layer_scale_init_value
														_snake_case       =  ["""stem"""] + [f"""stage{idx}""" for idx in range(1  ,  len(UpperCAmelCase  ) + 1  )]
														_snake_case,							_snake_case       =  get_aligned_output_features_output_indices(
														    out_features=UpperCAmelCase  ,  out_indices=UpperCAmelCase  ,  stage_names=self.stage_names  )