
"""simple docstring"""




from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt



def     __magic_name__		(					UpperCamelCase     :		int     )     ->						bool:
    a__		=			int(number**0.5     )
    return number == sq * sq



def     __magic_name__		(					UpperCamelCase     :		int							,		UpperCamelCase     :		int							,		UpperCamelCase     :		int							,		UpperCamelCase     :		int							,		UpperCamelCase     :		int							,		UpperCamelCase     :		int     )     ->						tuple[int, int]:
    a__		=			x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
    a__		=			x_den * y_den * z_den
    a__		=			gcd(UpperCamelCase							,		UpperCamelCase     )
    top //= hcf
    bottom //= hcf
    return top, bottom



def     __magic_name__		(					UpperCamelCase     :		int = 35     )     ->						int:
    a__		=			set()
    a__		=			42
    a__		=			Fraction(0     )
    a__		=			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
                    a__		=			x_num * y_den + x_den * y_num
                    a__		=			x_den * y_den
                    a__		=			gcd(UpperCamelCase							,		UpperCamelCase     )
                    z_num //= hcf
                    z_den //= hcf
                    if 0 < z_num < z_den <= order:
                        a__		=			add_three(
                            UpperCamelCase							,		UpperCamelCase							,		UpperCamelCase							,		UpperCamelCase							,		UpperCamelCase							,		UpperCamelCase     )
                        unique_s.add(UpperCamelCase     )

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

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

                    # n=2
                    a__		=			x_num * x_num * y_num * y_num
                    a__		=			(
                        x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
                    )
                    if is_sq(UpperCamelCase     ) and is_sq(UpperCamelCase     ):
                        a__		=			int(sqrt(UpperCamelCase     )     )
                        a__		=			int(sqrt(UpperCamelCase     )     )
                        a__		=			gcd(UpperCamelCase							,		UpperCamelCase     )
                        z_num //= hcf
                        z_den //= hcf
                        if 0 < z_num < z_den <= order:
                            a__		=			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() = }''')




"""simple docstring"""




import io
import json
import unittest

from parameterized import parameterized

from transformers import FSMTForConditionalGeneration, FSMTTokenizer
from transformers.testing_utils import get_tests_dir, require_torch, slow, torch_device
from utils import calculate_bleu


a		:       Any     						=       get_tests_dir() + '/test_data/fsmt/fsmt_val_data.json'
with io.open(filename, 'r', encoding='utf-8') as f:
    a		:       Tuple     						=       json.load(f)







@require_torch
class     lowercase(unittest.TestCase       ):



     def 			lowercase__  (							self     ,				__SCREAMING_SNAKE_CASE   )		->     Optional[Any]:







         """simple docstring"""



         return FSMTTokenizer.from_pretrained(__SCREAMING_SNAKE_CASE   )



     def 			lowercase__  (							self     ,				__SCREAMING_SNAKE_CASE   )		->     int:







         """simple docstring"""



         a__		=			FSMTForConditionalGeneration.from_pretrained(__SCREAMING_SNAKE_CASE   ).to(__SCREAMING_SNAKE_CASE   )
         if torch_device == "cuda":
             model.half()
         return model




     @parameterized.expand(
         [
             ['en-ru', 26.0],
             ['ru-en', 22.0],
             ['en-de', 22.0],
             ['de-en', 29.0],
         ]   )
     @slow
     def 			lowercase__  (							self     ,				__SCREAMING_SNAKE_CASE     ,				__SCREAMING_SNAKE_CASE   )		->     Tuple:







         """simple docstring"""



         a__		=			f'facebook/wmt19-{pair}'
         a__		=			self.get_tokenizer(__SCREAMING_SNAKE_CASE   )
         a__		=			self.get_model(__SCREAMING_SNAKE_CASE   )

         a__		=			bleu_data[pair]['src']
         a__		=			bleu_data[pair]['tgt']

         a__		=			tokenizer(__SCREAMING_SNAKE_CASE     ,				return_tensors='pt'     ,				truncation=__SCREAMING_SNAKE_CASE     ,				padding='longest'   ).to(__SCREAMING_SNAKE_CASE   )
         a__		=			model.generate(
             input_ids=batch.input_ids     ,				num_beams=8     ,				)
         a__		=			tokenizer.batch_decode(
             __SCREAMING_SNAKE_CASE     ,				skip_special_tokens=__SCREAMING_SNAKE_CASE     ,				clean_up_tokenization_spaces=__SCREAMING_SNAKE_CASE   )
         a__		=			calculate_bleu(__SCREAMING_SNAKE_CASE     ,				__SCREAMING_SNAKE_CASE   )
         print(__SCREAMING_SNAKE_CASE   )
         self.assertGreaterEqual(scores['bleu']     ,				__SCREAMING_SNAKE_CASE   )


