




"""simple docstring"""






import unittest

import numpy as np

from transformers.testing_utils import require_torch, require_vision
from transformers.utils import is_torch_available, is_vision_available

from ...test_image_processing_common import ImageProcessingSavingTestMixin, prepare_image_inputs


if is_torch_available():
			import torch

if is_vision_available():
			from PIL import Image

			from transformers import MobileNetVaImageProcessor






class lowerCAmelCase__      (	unittest.TestCase		):






			'''simple docstring'''



			def __init__(    self    , lowercase    , lowercase=7    , lowercase=3    , lowercase=18    , lowercase=30    , lowercase=400    , lowercase=True    , lowercase=None    , lowercase=True    , lowercase=None    , ):
							_lowerCamelCase	:     Union[str, Any]       =       size if size is not None else {'shortest_edge': 20}
							_lowerCamelCase	:     str       =       crop_size if crop_size is not None else {'height': 18, 'width': 18}
							_lowerCamelCase	:     Optional[Any]       =       parent
							_lowerCamelCase	:     str       =       batch_size
							_lowerCamelCase	:     List[Any]       =       num_channels
							_lowerCamelCase	:     Tuple       =       image_size
							_lowerCamelCase	:     Union[str, Any]       =       min_resolution
							_lowerCamelCase	:     Any       =       max_resolution
							_lowerCamelCase	:     str       =       do_resize
							_lowerCamelCase	:     Tuple       =       size
							_lowerCamelCase	:     int       =       do_center_crop
							_lowerCamelCase	:     List[Any]       =       crop_size






			def    A_       (    self    ):
							return {
							    "do_resize": self.do_resize,
							    "size": self.size,
							    "do_center_crop": self.do_center_crop,
							    "crop_size": self.crop_size,
							}






@require_torch
@require_vision
class lowerCAmelCase__      (	lowercase,      unittest.TestCase		):






			'''simple docstring'''



			lowerCamelCase__ =     MobileNetVaImageProcessor if is_vision_available() else None
			def    A_       (    self    ):
							_lowerCamelCase	:     List[Any]       =       MobileNetVaImageProcessingTester(self    )
			@property
			def    A_       (    self    ):
							return self.image_processor_tester.prepare_image_processor_dict()
			def    A_       (    self    ):
							_lowerCamelCase	:     Any       =       self.image_processing_class(**self.image_processor_dict    )
							self.assertTrue(hasattr(lowercase    , 'do_resize'    )    )
							self.assertTrue(hasattr(lowercase    , 'size'    )    )
							self.assertTrue(hasattr(lowercase    , 'do_center_crop'    )    )
							self.assertTrue(hasattr(lowercase    , 'crop_size'    )    )
			def    A_       (    self    ):
							_lowerCamelCase	:     Tuple       =       self.image_processing_class.from_dict(self.image_processor_dict    )
							self.assertEqual(image_processor.size    , {'shortest_edge': 20}    )
							self.assertEqual(image_processor.crop_size    , {'height': 18, 'width': 18}    )

							_lowerCamelCase	:     Union[str, Any]       =       self.image_processing_class.from_dict(self.image_processor_dict    , size=42    , crop_size=84    )
							self.assertEqual(image_processor.size    , {'shortest_edge': 42}    )
							self.assertEqual(image_processor.crop_size    , {'height': 84, 'width': 84}    )
			def    A_       (    self    ):
							pass
			def    A_       (    self    ):
							# Initialize image_processing
							_lowerCamelCase	:     Tuple       =       self.image_processing_class(**self.image_processor_dict    )
							# create random PIL images
							_lowerCamelCase	:     List[str]       =       prepare_image_inputs(self.image_processor_tester    , equal_resolution=lowercase    )
							for image in image_inputs:
											self.assertIsInstance(lowercase    , Image.Image    )

							# Test not batched input
							_lowerCamelCase	:     Optional[int]       =       image_processing(image_inputs[0]    , return_tensors='pt'    ).pixel_values
							self.assertEqual(
							    encoded_images.shape    , (
							        1,
							        self.image_processor_tester.num_channels,
							        self.image_processor_tester.crop_size['height'],
							        self.image_processor_tester.crop_size['width'],
							    )    , )

							# Test batched
							_lowerCamelCase	:     List[Any]       =       image_processing(lowercase    , return_tensors='pt'    ).pixel_values
							self.assertEqual(
							    encoded_images.shape    , (
							        self.image_processor_tester.batch_size,
							        self.image_processor_tester.num_channels,
							        self.image_processor_tester.crop_size['height'],
							        self.image_processor_tester.crop_size['width'],
							    )    , )
			def    A_       (    self    ):
							# Initialize image_processing
							_lowerCamelCase	:     List[str]       =       self.image_processing_class(**self.image_processor_dict    )
							# create random numpy tensors
							_lowerCamelCase	:     Optional[Any]       =       prepare_image_inputs(self.image_processor_tester    , equal_resolution=lowercase    , numpify=lowercase    )
							for image in image_inputs:
											self.assertIsInstance(lowercase    , np.ndarray    )

							# Test not batched input
							_lowerCamelCase	:     Tuple       =       image_processing(image_inputs[0]    , return_tensors='pt'    ).pixel_values
							self.assertEqual(
							    encoded_images.shape    , (
							        1,
							        self.image_processor_tester.num_channels,
							        self.image_processor_tester.crop_size['height'],
							        self.image_processor_tester.crop_size['width'],
							    )    , )

							# Test batched
							_lowerCamelCase	:     str       =       image_processing(lowercase    , return_tensors='pt'    ).pixel_values
							self.assertEqual(
							    encoded_images.shape    , (
							        self.image_processor_tester.batch_size,
							        self.image_processor_tester.num_channels,
							        self.image_processor_tester.crop_size['height'],
							        self.image_processor_tester.crop_size['width'],
							    )    , )






			def    A_       (    self    ):
							# Initialize image_processing
							_lowerCamelCase	:     Optional[Any]       =       self.image_processing_class(**self.image_processor_dict    )
							# create random PyTorch tensors
							_lowerCamelCase	:     List[str]       =       prepare_image_inputs(self.image_processor_tester    , equal_resolution=lowercase    , torchify=lowercase    )
							for image in image_inputs:
											self.assertIsInstance(lowercase    , torch.Tensor    )

							# Test not batched input
							_lowerCamelCase	:     int       =       image_processing(image_inputs[0]    , return_tensors='pt'    ).pixel_values
							self.assertEqual(
							    encoded_images.shape    , (
							        1,
							        self.image_processor_tester.num_channels,
							        self.image_processor_tester.crop_size['height'],
							        self.image_processor_tester.crop_size['width'],
							    )    , )

							# Test batched
							_lowerCamelCase	:     Union[str, Any]       =       image_processing(lowercase    , return_tensors='pt'    ).pixel_values
							self.assertEqual(
							    encoded_images.shape    , (
							        self.image_processor_tester.batch_size,
							        self.image_processor_tester.num_channels,
							        self.image_processor_tester.crop_size['height'],
							        self.image_processor_tester.crop_size['width'],
							    )    , )





"""simple docstring"""






from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt







def 	_snake_case     (							lowercase__						):
				_lowerCamelCase	:     int       =       int(number**0.5						)
				return number == sq * sq







def 	_snake_case     (							lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__						):
				_lowerCamelCase	:     int       =       x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
				_lowerCamelCase	:     int       =       x_den * y_den * z_den
				_lowerCamelCase	:     int       =       gcd(lowercase__				,       lowercase__						)
				top //= hcf
				bottom //= hcf
				return top, bottom







def 	_snake_case     (							lowercase__ = 35						):
				_lowerCamelCase	:     set       =       set()
				_lowerCamelCase	:     int
				_lowerCamelCase	:     Fraction       =       Fraction(0						)
				_lowerCamelCase	:     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
																				_lowerCamelCase	:     int       =       x_num * y_den + x_den * y_num
																				_lowerCamelCase	:     List[Any]       =       x_den * y_den
																				_lowerCamelCase	:     int       =       gcd(lowercase__				,       lowercase__						)
																				z_num //= hcf
																				z_den //= hcf
																				if 0 < z_num < z_den <= order:
																								_lowerCamelCase	:     Optional[Any]       =       add_three(
																								    lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__						)
																								unique_s.add(lowercase__						)

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

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

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

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

				return total.denominator + total.numerator


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