

from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt


def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		Optional[Any]       ):





				"""simple docstring"""


				SCREAMING_SNAKE_CASE_									=						int(number**0.5       )
				return number == sq * sq


def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		Optional[int] ,   _SCREAMING_SNAKE_CASE					:		str ,   _SCREAMING_SNAKE_CASE					:		Optional[int] ,   _SCREAMING_SNAKE_CASE					:		List[Any] ,   _SCREAMING_SNAKE_CASE					:		Tuple ,   _SCREAMING_SNAKE_CASE					:		Optional[Any]       ):





				"""simple docstring"""


				SCREAMING_SNAKE_CASE_									=						x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
				SCREAMING_SNAKE_CASE_									=						x_den * y_den * z_den
				SCREAMING_SNAKE_CASE_									=						gcd(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       )
				top //= hcf
				bottom //= hcf
				return top, bottom


def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		List[str] = 35       ):





				"""simple docstring"""


				SCREAMING_SNAKE_CASE_									=						set()
				SCREAMING_SNAKE_CASE_									=						42
				SCREAMING_SNAKE_CASE_									=						Fraction(0       )
				SCREAMING_SNAKE_CASE_									=						42

				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
																				SCREAMING_SNAKE_CASE_									=						x_num * y_den + x_den * y_num
																				SCREAMING_SNAKE_CASE_									=						x_den * y_den
																				SCREAMING_SNAKE_CASE_									=						gcd(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       )
																				z_num //= hcf
																				z_den //= hcf
																				if 0 < z_num < z_den <= order:
																								SCREAMING_SNAKE_CASE_									=						add_three(
																								    _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       )
																								unique_s.add(_SCREAMING_SNAKE_CASE       )

																				# n=2
																				SCREAMING_SNAKE_CASE_									=						(
																				    x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
																				)
																				SCREAMING_SNAKE_CASE_									=						x_den * x_den * y_den * y_den
																				if is_sq(_SCREAMING_SNAKE_CASE       ) and is_sq(_SCREAMING_SNAKE_CASE       ):
																								SCREAMING_SNAKE_CASE_									=						int(sqrt(_SCREAMING_SNAKE_CASE       )       )
																								SCREAMING_SNAKE_CASE_									=						int(sqrt(_SCREAMING_SNAKE_CASE       )       )
																								SCREAMING_SNAKE_CASE_									=						gcd(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       )
																								z_num //= hcf
																								z_den //= hcf
																								if 0 < z_num < z_den <= order:
																												SCREAMING_SNAKE_CASE_									=						add_three(
																												    _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       )
																												unique_s.add(_SCREAMING_SNAKE_CASE       )

                    # n=-1
																				SCREAMING_SNAKE_CASE_									=						x_num * y_num
																				SCREAMING_SNAKE_CASE_									=						x_den * y_num + x_num * y_den
																				SCREAMING_SNAKE_CASE_									=						gcd(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       )
																				z_num //= hcf
																				z_den //= hcf
																				if 0 < z_num < z_den <= order:
																								SCREAMING_SNAKE_CASE_									=						add_three(
																								    _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       )
																								unique_s.add(_SCREAMING_SNAKE_CASE       )

																				# n=2
																				SCREAMING_SNAKE_CASE_									=						x_num * x_num * y_num * y_num
																				SCREAMING_SNAKE_CASE_									=						(
																				    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
																				)
																				if is_sq(_SCREAMING_SNAKE_CASE       ) and is_sq(_SCREAMING_SNAKE_CASE       ):
																								SCREAMING_SNAKE_CASE_									=						int(sqrt(_SCREAMING_SNAKE_CASE       )       )
																								SCREAMING_SNAKE_CASE_									=						int(sqrt(_SCREAMING_SNAKE_CASE       )       )
																								SCREAMING_SNAKE_CASE_									=						gcd(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       )
																								z_num //= hcf
																								z_den //= hcf
																								if 0 < z_num < z_den <= order:
																												SCREAMING_SNAKE_CASE_									=						add_three(
																												    _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       )
																												unique_s.add(_SCREAMING_SNAKE_CASE       )

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

				return total.denominator + total.numerator


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





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


UpperCamelCase__  :      str			=    logging.get_logger(__name__)

UpperCamelCase__  :      Optional[int]			=    {
    "facebook/dpr-ctx_encoder-single-nq-base": (
        "https://huggingface.co/facebook/dpr-ctx_encoder-single-nq-base/resolve/main/config.json"
    ),
    "facebook/dpr-question_encoder-single-nq-base": (
        "https://huggingface.co/facebook/dpr-question_encoder-single-nq-base/resolve/main/config.json"
    ),
    "facebook/dpr-reader-single-nq-base": (
        "https://huggingface.co/facebook/dpr-reader-single-nq-base/resolve/main/config.json"
    ),
    "facebook/dpr-ctx_encoder-multiset-base": (
        "https://huggingface.co/facebook/dpr-ctx_encoder-multiset-base/resolve/main/config.json"
    ),
    "facebook/dpr-question_encoder-multiset-base": (
        "https://huggingface.co/facebook/dpr-question_encoder-multiset-base/resolve/main/config.json"
    ),
    "facebook/dpr-reader-multiset-base": (
        "https://huggingface.co/facebook/dpr-reader-multiset-base/resolve/main/config.json"
    ),
}



class       __snake_case  (    lowerCAmelCase__       ):
  __lowerCAmelCase     :	Optional[int]						 =  'dpr'

  def __init__(					self						,		_A=30522						,		_A=768						,		_A=12						,		_A=12						,		_A=3072						,		_A="gelu"						,		_A=0.1						,		_A=0.1						,		_A=512						,		_A=2						,		_A=0.0_2						,		_A=1E-12						,		_A=0						,		_A="absolute"						,		_A = 0						,		**_A						,		):
      super().__init__(pad_token_id=_A						,		**_A)

      SCREAMING_SNAKE_CASE_									=						vocab_size
      SCREAMING_SNAKE_CASE_									=						hidden_size
      SCREAMING_SNAKE_CASE_									=						num_hidden_layers
      SCREAMING_SNAKE_CASE_									=						num_attention_heads
      SCREAMING_SNAKE_CASE_									=						hidden_act
      SCREAMING_SNAKE_CASE_									=						intermediate_size
      SCREAMING_SNAKE_CASE_									=						hidden_dropout_prob
      SCREAMING_SNAKE_CASE_									=						attention_probs_dropout_prob
      SCREAMING_SNAKE_CASE_									=						max_position_embeddings
      SCREAMING_SNAKE_CASE_									=						type_vocab_size
      SCREAMING_SNAKE_CASE_									=						initializer_range
      SCREAMING_SNAKE_CASE_									=						layer_norm_eps
      SCREAMING_SNAKE_CASE_									=						projection_dim
      SCREAMING_SNAKE_CASE_									=						position_embedding_type


