

from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt






def 					lowerCamelCase_     (							UpperCAmelCase_							:     int	)						->				bool:




	'''simple docstring'''




	_UpperCamelCase   :		int			=						int(number**0.5	)
	return number == sq * sq






def 					lowerCamelCase_     (							UpperCAmelCase_							:     int							,       UpperCAmelCase_							:     int							,       UpperCAmelCase_							:     int							,       UpperCAmelCase_							:     int							,       UpperCAmelCase_							:     int							,       UpperCAmelCase_							:     int	)						->				tuple[int, int]:




	'''simple docstring'''




	_UpperCamelCase   :		int			=						x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
	_UpperCamelCase   :		int			=						x_den * y_den * z_den
	_UpperCamelCase   :		int			=						gcd(UpperCAmelCase_							,       UpperCAmelCase_	)
	top //= hcf
	bottom //= hcf
	return top, bottom






def 					lowerCamelCase_     (							UpperCAmelCase_							:     int = 3_5	)						->				int:




	'''simple docstring'''




	_UpperCamelCase   :		set			=						set()
	_UpperCamelCase   :		int
	_UpperCamelCase   :		Fraction			=						Fraction(0	)
	_UpperCamelCase   :		tuple[int, int]

	for x_num in range(1							,       order + 1	):
		for x_den in range(x_num + 1							,       order + 1	):
			for y_num in range(1							,       order + 1	):
				for y_den in range(y_num + 1							,       order + 1	):
					# n=1
					_UpperCamelCase   :		Dict			=						x_num * y_den + x_den * y_num
					_UpperCamelCase   :		int			=						x_den * y_den
					_UpperCamelCase   :		int			=						gcd(UpperCAmelCase_							,       UpperCAmelCase_	)
					z_num //= hcf
					z_den //= hcf
					if 0 < z_num < z_den <= order:
						_UpperCamelCase   :		Any			=						add_three(
						    UpperCAmelCase_							,       UpperCAmelCase_							,       UpperCAmelCase_							,       UpperCAmelCase_							,       UpperCAmelCase_							,       UpperCAmelCase_	)
						unique_s.add(UpperCAmelCase_	)

					# n=2
					_UpperCamelCase   :		List[str]			=						(
					    x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
					)
					_UpperCamelCase   :		List[str]			=						x_den * x_den * y_den * y_den
					if is_sq(UpperCAmelCase_	) and is_sq(UpperCAmelCase_	):
						_UpperCamelCase   :		List[str]			=						int(sqrt(UpperCAmelCase_	)	)
						_UpperCamelCase   :		Optional[Any]			=						int(sqrt(UpperCAmelCase_	)	)
						_UpperCamelCase   :		List[Any]			=						gcd(UpperCAmelCase_							,       UpperCAmelCase_	)
						z_num //= hcf
						z_den //= hcf
						if 0 < z_num < z_den <= order:
							_UpperCamelCase   :		str			=						add_three(
							    UpperCAmelCase_							,       UpperCAmelCase_							,       UpperCAmelCase_							,       UpperCAmelCase_							,       UpperCAmelCase_							,       UpperCAmelCase_	)
							unique_s.add(UpperCAmelCase_	)

                    # n=-1
					_UpperCamelCase   :		Optional[int]			=						x_num * y_num
					_UpperCamelCase   :		int			=						x_den * y_num + x_num * y_den
					_UpperCamelCase   :		Tuple			=						gcd(UpperCAmelCase_							,       UpperCAmelCase_	)
					z_num //= hcf
					z_den //= hcf
					if 0 < z_num < z_den <= order:
						_UpperCamelCase   :		List[str]			=						add_three(
						    UpperCAmelCase_							,       UpperCAmelCase_							,       UpperCAmelCase_							,       UpperCAmelCase_							,       UpperCAmelCase_							,       UpperCAmelCase_	)
						unique_s.add(UpperCAmelCase_	)

					# n=2
					_UpperCamelCase   :		List[Any]			=						x_num * x_num * y_num * y_num
					_UpperCamelCase   :		Optional[Any]			=						(
					    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
					)
					if is_sq(UpperCAmelCase_	) and is_sq(UpperCAmelCase_	):
						_UpperCamelCase   :		Any			=						int(sqrt(UpperCAmelCase_	)	)
						_UpperCamelCase   :		Tuple			=						int(sqrt(UpperCAmelCase_	)	)
						_UpperCamelCase   :		List[Any]			=						gcd(UpperCAmelCase_							,       UpperCAmelCase_	)
						z_num //= hcf
						z_den //= hcf
						if 0 < z_num < z_den <= order:
							_UpperCamelCase   :		Optional[Any]			=						add_three(
							    UpperCAmelCase_							,       UpperCAmelCase_							,       UpperCAmelCase_							,       UpperCAmelCase_							,       UpperCAmelCase_							,       UpperCAmelCase_	)
							unique_s.add(UpperCAmelCase_	)

	for num, den in unique_s:
		total += Fraction(UpperCAmelCase_							,       UpperCAmelCase_	)

	return total.denominator + total.numerator


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







from ...configuration_utils import PretrainedConfig
from ...utils import logging


lowerCAmelCase__								=		logging.get_logger(__name__)

lowerCAmelCase__								=		{
    """facebook/vit-mae-base""": """https://huggingface.co/facebook/vit-mae-base/resolve/main/config.json""",
    # See all ViT MAE models at https://huggingface.co/models?filter=vit-mae
}







class 	lowercase    (				_lowercase							):


		"""simple docstring"""




		a__					       =  "vit_mae"


		def __init__(				self	,       __snake_case=7_68	,       __snake_case=12	,       __snake_case=12	,       __snake_case=30_72	,       __snake_case="gelu"	,       __snake_case=0.0	,       __snake_case=0.0	,       __snake_case=0.0_2	,       __snake_case=1e-12	,       __snake_case=2_24	,       __snake_case=16	,       __snake_case=3	,       __snake_case=True	,       __snake_case=16	,       __snake_case=5_12	,       __snake_case=8	,       __snake_case=20_48	,       __snake_case=0.7_5	,       __snake_case=False	,       **__snake_case	,       ):
			super().__init__(**__snake_case)

			_UpperCamelCase   :		Optional[int]			=						hidden_size
			_UpperCamelCase   :		Optional[int]			=						num_hidden_layers
			_UpperCamelCase   :		Tuple			=						num_attention_heads
			_UpperCamelCase   :		List[str]			=						intermediate_size
			_UpperCamelCase   :		str			=						hidden_act
			_UpperCamelCase   :		List[str]			=						hidden_dropout_prob
			_UpperCamelCase   :		List[Any]			=						attention_probs_dropout_prob
			_UpperCamelCase   :		str			=						initializer_range
			_UpperCamelCase   :		Any			=						layer_norm_eps
			_UpperCamelCase   :		int			=						image_size
			_UpperCamelCase   :		Any			=						patch_size
			_UpperCamelCase   :		List[Any]			=						num_channels
			_UpperCamelCase   :		Union[str, Any]			=						qkv_bias
			_UpperCamelCase   :		str			=						decoder_num_attention_heads
			_UpperCamelCase   :		Union[str, Any]			=						decoder_hidden_size
			_UpperCamelCase   :		Union[str, Any]			=						decoder_num_hidden_layers
			_UpperCamelCase   :		Any			=						decoder_intermediate_size
			_UpperCamelCase   :		int			=						mask_ratio
			_UpperCamelCase   :		List[Any]			=						norm_pix_loss




