


import inspect
import unittest

import torch
import torch.nn as nn

from accelerate.hooks import (
    AlignDevicesHook,
    ModelHook,
    SequentialHook,
    add_hook_to_module,
    attach_align_device_hook,
    remove_hook_from_module,
    remove_hook_from_submodules,
)
from accelerate.test_utils import require_multi_gpu


class   a__	(						nn.Module    ):

       def __init__(   self      :     Any    ):
            super().__init__()
            a_    :     Union[str, Any]										=    nn.Linear(3      ,							4    )
            a_    :     Optional[Any]										=    nn.BatchNormad(4    )
            a_    :     Optional[Any]										=    nn.Linear(4      ,							5    )

       def 						UpperCAmelCase(   self      :     List[str]      ,							lowerCamelCase_      :     int    ):
            return self.lineara(self.batchnorm(self.lineara(lowerCamelCase_    )    )    )


class   a__	(						lowerCAmelCase_    ):

       def 						UpperCAmelCase(   self      :     Dict      ,							lowerCamelCase_      :     Tuple      ,							*lowerCamelCase_      :     Dict      ,							**lowerCamelCase_      :     int    ):
            return (args[0] + 1,) + args[1:], kwargs


class   a__	(						lowerCAmelCase_    ):

       def 						UpperCAmelCase(   self      :     Optional[int]      ,							lowerCamelCase_      :     Optional[int]      ,							lowerCamelCase_      :     Any    ):
            return output + 1


class   a__	(						unittest.TestCase    ):

       def 						UpperCAmelCase(   self      :     Optional[Any]    ):
            a_    :     List[Any]										=    ModelForTest()
            a_    :     Optional[Any]										=    ModelHook()

            add_hook_to_module(lowerCamelCase_      ,							lowerCamelCase_    )
            self.assertEqual(test_model._hf_hook      ,							lowerCamelCase_    )
            self.assertTrue(hasattr(lowerCamelCase_      ,							"""_old_forward"""    )    )

            # Check adding the hook did not change the name or the signature
            self.assertEqual(test_model.forward.__name__      ,							"""forward"""    )
            self.assertListEqual(list(inspect.signature(test_model.forward    ).parameters    )      ,							["""x"""]    )

            remove_hook_from_module(lowerCamelCase_    )
            self.assertFalse(hasattr(lowerCamelCase_      ,							"""_hf_hook"""    )    )
            self.assertFalse(hasattr(lowerCamelCase_      ,							"""_old_forward"""    )    )

       def 						UpperCAmelCase(   self      :     int    ):
            a_    :     List[Any]										=    ModelForTest()
            a_    :     List[str]										=    ModelHook()

            add_hook_to_module(lowerCamelCase_      ,							lowerCamelCase_    )
            add_hook_to_module(lowerCamelCase_      ,							lowerCamelCase_      ,							append=lowerCamelCase_    )

            self.assertEqual(isinstance(test_model._hf_hook      ,							lowerCamelCase_    )      ,							lowerCamelCase_    )
            self.assertEqual(len(test_model._hf_hook.hooks    )      ,							2    )
            self.assertTrue(hasattr(lowerCamelCase_      ,							"""_old_forward"""    )    )

            # Check adding the hook did not change the name or the signature
            self.assertEqual(test_model.forward.__name__      ,							"""forward"""    )
            self.assertListEqual(list(inspect.signature(test_model.forward    ).parameters    )      ,							["""x"""]    )

            remove_hook_from_module(lowerCamelCase_    )
            self.assertFalse(hasattr(lowerCamelCase_      ,							"""_hf_hook"""    )    )
            self.assertFalse(hasattr(lowerCamelCase_      ,							"""_old_forward"""    )    )

       def 						UpperCAmelCase(   self      :     Any    ):
            a_    :     List[str]										=    ModelForTest()
            a_    :     Any										=    torch.randn(2      ,							3    )
            a_    :     Union[str, Any]										=    test_model(x + 1    )
            a_    :     Optional[int]										=    test_model(x + 2    )

            a_    :     Any										=    PreForwardHook()
            add_hook_to_module(lowerCamelCase_      ,							lowerCamelCase_    )
            a_    :     Optional[Any]										=    test_model(lowerCamelCase_    )
            self.assertTrue(torch.allclose(lowerCamelCase_      ,							lowerCamelCase_      ,							atol=1E-5    )    )

            # Attaching a hook to a model when it already has one replaces, does not chain
            a_    :     Tuple										=    PreForwardHook()
            add_hook_to_module(lowerCamelCase_      ,							lowerCamelCase_    )
            a_    :     List[str]										=    test_model(lowerCamelCase_    )
            self.assertTrue(torch.allclose(lowerCamelCase_      ,							lowerCamelCase_      ,							atol=1E-5    )    )

            # You need to use the sequential hook to chain two or more hooks
            a_    :     int										=    SequentialHook(PreForwardHook()      ,							PreForwardHook()    )
            add_hook_to_module(lowerCamelCase_      ,							lowerCamelCase_    )

            a_    :     int										=    test_model(lowerCamelCase_    )
            assert torch.allclose(lowerCamelCase_      ,							lowerCamelCase_      ,							atol=1E-5    )

       def 						UpperCAmelCase(   self      :     Dict    ):
            a_    :     List[str]										=    ModelForTest()
            a_    :     List[str]										=    torch.randn(2      ,							3    )
            a_    :     int										=    test_model(lowerCamelCase_    )

            a_    :     List[Any]										=    PostForwardHook()
            add_hook_to_module(lowerCamelCase_      ,							lowerCamelCase_    )
            a_    :     int										=    test_model(lowerCamelCase_    )
            self.assertTrue(torch.allclose(lowerCamelCase_      ,							output + 1      ,							atol=1E-5    )    )

            # Attaching a hook to a model when it already has one replaces, does not chain
            a_    :     Tuple										=    PostForwardHook()
            add_hook_to_module(lowerCamelCase_      ,							lowerCamelCase_    )
            a_    :     Optional[int]										=    test_model(lowerCamelCase_    )
            self.assertTrue(torch.allclose(lowerCamelCase_      ,							output + 1      ,							atol=1E-5    )    )

            # You need to use the sequential hook to chain two or more hooks
            a_    :     Any										=    SequentialHook(PostForwardHook()      ,							PostForwardHook()    )
            add_hook_to_module(lowerCamelCase_      ,							lowerCamelCase_    )

            a_    :     int										=    test_model(lowerCamelCase_    )
            assert torch.allclose(lowerCamelCase_      ,							output + 2      ,							atol=1E-5    )

       def 						UpperCAmelCase(   self      :     Optional[int]    ):
            a_    :     str										=    ModelForTest()
            a_    :     str										=    torch.randn(2      ,							3    )
            a_    :     List[Any]										=    test_model(lowerCamelCase_    )

            a_    :     Dict										=    PostForwardHook()
            add_hook_to_module(lowerCamelCase_      ,							lowerCamelCase_    )
            a_    :     Any										=    test_model(lowerCamelCase_    )
            self.assertTrue(torch.allclose(lowerCamelCase_      ,							output + 1    )    )
            self.assertTrue(outputa.requires_grad    )

            a_    :     Any										=    True
            a_    :     Any										=    test_model(lowerCamelCase_    )
            self.assertFalse(outputa.requires_grad    )

       @require_multi_gpu
       def 						UpperCAmelCase(   self      :     Optional[int]    ):
            a_    :     Tuple										=    ModelForTest()
            # Everything is on CPU
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )

            # This will move each submodule on different devices
            add_hook_to_module(model.lineara      ,							AlignDevicesHook(execution_device=0    )    )
            add_hook_to_module(model.batchnorm      ,							AlignDevicesHook(execution_device=0    )    )
            add_hook_to_module(model.lineara      ,							AlignDevicesHook(execution_device=1    )    )

            self.assertEqual(model.lineara.weight.device      ,							torch.device(0    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device(0    )    )
            self.assertEqual(model.batchnorm.running_mean.device      ,							torch.device(0    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device(1    )    )

            # We can still make a forward pass. The input does not need to be on any particular device
            a_    :     List[Any]										=    torch.randn(2      ,							3    )
            a_    :     Dict										=    model(lowerCamelCase_    )
            self.assertEqual(output.device      ,							torch.device(1    )    )

            # We can add a general hook to put back output on same device as input.
            add_hook_to_module(lowerCamelCase_      ,							AlignDevicesHook(io_same_device=lowerCamelCase_    )    )
            a_    :     Any										=    torch.randn(2      ,							3    ).to(0    )
            a_    :     Dict										=    model(lowerCamelCase_    )
            self.assertEqual(output.device      ,							torch.device(0    )    )

       def 						UpperCAmelCase(   self      :     Dict    ):
            a_    :     Optional[Any]										=    ModelForTest()

            # Everything is on CPU
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )

            # This will move each submodule on different devices
            a_    :     int										=    {"""execution_device""": 0 if torch.cuda.is_available() else """cpu""", """offload""": True}

            add_hook_to_module(model.lineara      ,							AlignDevicesHook(**lowerCamelCase_    )    )
            add_hook_to_module(model.batchnorm      ,							AlignDevicesHook(**lowerCamelCase_    )    )
            add_hook_to_module(model.lineara      ,							AlignDevicesHook(**lowerCamelCase_    )    )

            # Parameters have been offloaded, so on the meta device
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""meta"""    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device("""meta"""    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""meta"""    )    )
            # Buffers are not included in the offload by default, so are on the execution device
            a_    :     Optional[int]										=    torch.device(hook_kwargs["""execution_device"""]    )
            self.assertEqual(model.batchnorm.running_mean.device      ,							lowerCamelCase_    )

            a_    :     Any										=    torch.randn(2      ,							3    )
            a_    :     str										=    model(lowerCamelCase_    )
            self.assertEqual(output.device      ,							lowerCamelCase_    )

            # Removing hooks loads back the weights in the model.
            remove_hook_from_module(model.lineara    )
            remove_hook_from_module(model.batchnorm    )
            remove_hook_from_module(model.lineara    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )

            # Now test with buffers included in the offload
            a_    :     List[Any]										=    {
                """execution_device""": 0 if torch.cuda.is_available() else """cpu""",
                """offload""": True,
                """offload_buffers""": True,
            }

            add_hook_to_module(model.lineara      ,							AlignDevicesHook(**lowerCamelCase_    )    )
            add_hook_to_module(model.batchnorm      ,							AlignDevicesHook(**lowerCamelCase_    )    )
            add_hook_to_module(model.lineara      ,							AlignDevicesHook(**lowerCamelCase_    )    )

            # Parameters have been offloaded, so on the meta device, buffers included
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""meta"""    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device("""meta"""    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""meta"""    )    )
            self.assertEqual(model.batchnorm.running_mean.device      ,							torch.device("""meta"""    )    )

            a_    :     Any										=    torch.randn(2      ,							3    )
            a_    :     Optional[int]										=    model(lowerCamelCase_    )
            self.assertEqual(output.device      ,							lowerCamelCase_    )

            # Removing hooks loads back the weights in the model.
            remove_hook_from_module(model.lineara    )
            remove_hook_from_module(model.batchnorm    )
            remove_hook_from_module(model.lineara    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )

       def 						UpperCAmelCase(   self      :     Dict    ):
            a_    :     int										=    ModelForTest()

            # Everything is on CPU
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )

            # This will move each submodule on different devices
            a_    :     Any										=    0 if torch.cuda.is_available() else """cpu"""
            attach_align_device_hook(lowerCamelCase_      ,							execution_device=lowerCamelCase_      ,							offload=lowerCamelCase_    )

            # Parameters have been offloaded, so on the meta device
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""meta"""    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device("""meta"""    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""meta"""    )    )
            # Buffers are not included in the offload by default, so are on the execution device
            a_    :     int										=    torch.device(lowerCamelCase_    )
            self.assertEqual(model.batchnorm.running_mean.device      ,							lowerCamelCase_    )

            a_    :     Optional[int]										=    torch.randn(2      ,							3    )
            a_    :     Tuple										=    model(lowerCamelCase_    )
            self.assertEqual(output.device      ,							lowerCamelCase_    )

            # Removing hooks loads back the weights in the model.
            remove_hook_from_submodules(lowerCamelCase_    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )

            # Now test with buffers included in the offload
            attach_align_device_hook(lowerCamelCase_      ,							execution_device=lowerCamelCase_      ,							offload=lowerCamelCase_      ,							offload_buffers=lowerCamelCase_    )

            # Parameters have been offloaded, so on the meta device, buffers included
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""meta"""    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device("""meta"""    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""meta"""    )    )
            self.assertEqual(model.batchnorm.running_mean.device      ,							torch.device("""meta"""    )    )

            a_    :     List[str]										=    torch.randn(2      ,							3    )
            a_    :     Union[str, Any]										=    model(lowerCamelCase_    )
            self.assertEqual(output.device      ,							lowerCamelCase_    )

            # Removing hooks loads back the weights in the model.
            remove_hook_from_submodules(lowerCamelCase_    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )

       def 						UpperCAmelCase(   self      :     int    ):
            a_    :     str										=    ModelForTest()

            # Everything is on CPU
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )

            # This will move each submodule on different devices
            a_    :     List[str]										=    0 if torch.cuda.is_available() else """cpu"""
            attach_align_device_hook(
                lowerCamelCase_      ,							execution_device=lowerCamelCase_      ,							offload=lowerCamelCase_      ,							weights_map=model.state_dict()    )

            # Parameters have been offloaded, so on the meta device
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""meta"""    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device("""meta"""    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""meta"""    )    )
            # Buffers are not included in the offload by default, so are on the execution device
            a_    :     Dict										=    torch.device(lowerCamelCase_    )
            self.assertEqual(model.batchnorm.running_mean.device      ,							lowerCamelCase_    )

            a_    :     int										=    torch.randn(2      ,							3    )
            a_    :     Tuple										=    model(lowerCamelCase_    )
            self.assertEqual(output.device      ,							lowerCamelCase_    )

            # Removing hooks loads back the weights in the model.
            remove_hook_from_submodules(lowerCamelCase_    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )

            # Now test with buffers included in the offload
            attach_align_device_hook(
                lowerCamelCase_      ,							execution_device=lowerCamelCase_      ,							offload=lowerCamelCase_      ,							weights_map=model.state_dict()      ,							offload_buffers=lowerCamelCase_      ,							)

            # Parameters have been offloaded, so on the meta device, buffers included
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""meta"""    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device("""meta"""    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""meta"""    )    )
            self.assertEqual(model.batchnorm.running_mean.device      ,							torch.device("""meta"""    )    )

            a_    :     Tuple										=    torch.randn(2      ,							3    )
            a_    :     Dict										=    model(lowerCamelCase_    )
            self.assertEqual(output.device      ,							lowerCamelCase_    )

            # Removing hooks loads back the weights in the model.
            remove_hook_from_submodules(lowerCamelCase_    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.batchnorm.weight.device      ,							torch.device("""cpu"""    )    )
            self.assertEqual(model.lineara.weight.device      ,							torch.device("""cpu"""    )    )







from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt



def  _a			(						__UpperCamelCase ):
     a_    :     int										=    int(number**0.5 )
     return number == sq * sq



def  _a			(						__UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase ):
     a_    :     int										=    x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
     a_    :     int										=    x_den * y_den * z_den
     a_    :     int										=    gcd(__UpperCamelCase  ,  __UpperCamelCase )
     top //= hcf
     bottom //= hcf
     return top, bottom



def  _a			(						__UpperCamelCase = 3_5 ):
     a_    :     set										=    set()
     a_    :     int
     a_    :     Fraction										=    Fraction(0 )
     a_    :     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
                         a_    :     int										=    x_num * y_den + x_den * y_num
                         a_    :     Optional[int]										=    x_den * y_den
                         a_    :     Optional[Any]										=    gcd(__UpperCamelCase  ,  __UpperCamelCase )
                         z_num //= hcf
                         z_den //= hcf
                         if 0 < z_num < z_den <= order:
                              a_    :     Optional[int]										=    add_three(
                                  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase )
                              unique_s.add(__UpperCamelCase )

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

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

                         # n=2
                         a_    :     Union[str, Any]										=    x_num * x_num * y_num * y_num
                         a_    :     Dict										=    (
                             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_    :     Dict										=    int(sqrt(__UpperCamelCase ) )
                              a_    :     Union[str, Any]										=    int(sqrt(__UpperCamelCase ) )
                              a_    :     Dict										=    gcd(__UpperCamelCase  ,  __UpperCamelCase )
                              z_num //= hcf
                              z_den //= hcf
                              if 0 < z_num < z_den <= order:
                                   a_    :     List[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() = }''')



