
from __future__ import annotations





def        lowerCAmelCase       (				snake_case__   :      int )->			int | None:
    for r in range(1				,					snake_case__ ):
        A_								=					[]
        for x in range(n - 1 ):
            A_								=					pow(snake_case__				,					snake_case__				,					snake_case__ )
            if val in li:
                break
            li.append(snake_case__ )
        else:
            return r
    return None


if __name__ == "__main__":
     __magic_name__  :  int     			=   int(input('Enter a prime number q: '))
     __magic_name__  :  Tuple     			=   find_primitive(q)
     if a is None:
          print(f"""Cannot find the primitive for the value: {a!r}""")
     else:
          __magic_name__  :  Dict     			=   int(input('Enter private key of A: '))
          __magic_name__  :  Optional[int]     			=   pow(a, a_private, q)
          __magic_name__  :  str     			=   int(input('Enter private key of B: '))
          __magic_name__  :  Dict     			=   pow(a, b_private, q)

          __magic_name__  :  Union[str, Any]     			=   pow(b_public, a_private, q)
          __magic_name__  :  Optional[int]     			=   pow(a_public, b_private, q)

          print('The key value generated by A is: ', a_secret)
          print('The key value generated by B is: ', b_secret)









'''simple docstring'''


import inspect
from typing import Callable, List, Optional, Set, Tuple, Union

import torch
from packaging import version
from safetensors.torch import storage_ptr, storage_size
from torch import nn

from .utils import logging


lowerCAmelCase__      				=			[nn.LayerNorm]

lowerCAmelCase__      				=			logging.get_logger(__name__)

lowerCAmelCase__      				=			version.parse(version.parse(torch.__version__).base_version)

lowerCAmelCase__      				=			parsed_torch_version_base >= version.parse("2.0")
lowerCAmelCase__      				=			parsed_torch_version_base >= version.parse("1.12")
lowerCAmelCase__      				=			parsed_torch_version_base >= version.parse("1.11")
lowerCAmelCase__      				=			parsed_torch_version_base < version.parse("1.11")







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,self	)     ->     List[Any]:
	from torch import _softmax_backward_data

	if is_torch_less_than_1_11:
		return _softmax_backward_data(UpperCamelCase ,UpperCamelCase ,parent.dim ,self	)
	else:
		return _softmax_backward_data(UpperCamelCase ,UpperCamelCase ,parent.dim ,self.dtype	)







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase = 0	)     ->     nn.Linear:
	UpperCAmelCase_		:   Tuple													=       index.to(layer.weight.device	)
	UpperCAmelCase_		:   Tuple													=       layer.weight.index_select(UpperCamelCase ,UpperCamelCase	).clone().detach()
	if layer.bias is not None:
		if dim == 1:
			UpperCAmelCase_		:   List[Any]													=       layer.bias.clone().detach()
		else:
			UpperCAmelCase_		:   Tuple													=       layer.bias[index].clone().detach()
	UpperCAmelCase_		:   Optional[Any]													=       list(layer.weight.size()	)
	UpperCAmelCase_		:   int													=       len(UpperCamelCase	)
	UpperCAmelCase_		:   str													=       nn.Linear(new_size[1] ,new_size[0] ,bias=layer.bias is not None	).to(layer.weight.device	)
	UpperCAmelCase_		:   str													=       False
	new_layer.weight.copy_(W.contiguous()	)
	UpperCAmelCase_		:   Tuple													=       True
	if layer.bias is not None:
		UpperCAmelCase_		:   Union[str, Any]													=       False
		new_layer.bias.copy_(b.contiguous()	)
		UpperCAmelCase_		:   Any													=       True
	return new_layer



class        lowercase    (	nn.Module			):


							def __init__(      self     ,      _snake_case     ,      _snake_case)				->					int:
								super().__init__()
								UpperCAmelCase_		:   List[Any]													=       nf
								UpperCAmelCase_		:   List[Any]													=       nn.Parameter(torch.empty(_snake_case     ,      _snake_case))
								UpperCAmelCase_		:   List[Any]													=       nn.Parameter(torch.zeros(_snake_case))
								nn.init.normal_(self.weight     ,      std=0.02)





							def     _snake_case				(      self     ,      _snake_case)				->					Optional[int]:
								UpperCAmelCase_		:   Dict													=       x.size()[:-1] + (self.nf,)
								UpperCAmelCase_		:   Optional[Any]													=       torch.addmm(self.bias     ,      x.view(-1     ,      x.size(-1))     ,      self.weight)
								UpperCAmelCase_		:   List[str]													=       x.view(_snake_case)
								return x







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase = 1	)     ->     ConvaD:
	UpperCAmelCase_		:   List[str]													=       index.to(layer.weight.device	)
	UpperCAmelCase_		:   Optional[Any]													=       layer.weight.index_select(UpperCamelCase ,UpperCamelCase	).clone().detach()
	if dim == 0:
		UpperCAmelCase_		:   Tuple													=       layer.bias.clone().detach()
	else:
		UpperCAmelCase_		:   str													=       layer.bias[index].clone().detach()
	UpperCAmelCase_		:   str													=       list(layer.weight.size()	)
	UpperCAmelCase_		:   List[str]													=       len(UpperCamelCase	)
	UpperCAmelCase_		:   List[Any]													=       ConvaD(new_size[1] ,new_size[0]	).to(layer.weight.device	)
	UpperCAmelCase_		:   Tuple													=       False
	new_layer.weight.copy_(W.contiguous()	)
	UpperCAmelCase_		:   Optional[Any]													=       True
	UpperCAmelCase_		:   Any													=       False
	new_layer.bias.copy_(b.contiguous()	)
	UpperCAmelCase_		:   Union[str, Any]													=       True
	return new_layer







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase = None	)     ->     Union[nn.Linear, ConvaD]:
	if isinstance(UpperCamelCase ,nn.Linear	):
		return prune_linear_layer(UpperCamelCase ,UpperCamelCase ,dim=0 if dim is None else dim	)
	elif isinstance(UpperCamelCase ,UpperCamelCase	):
		return prune_convad_layer(UpperCamelCase ,UpperCamelCase ,dim=1 if dim is None else dim	)
	else:
		raise ValueError(f"""Can't prune layer of class {layer.__class__}"""	)







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,*UpperCamelCase	)     ->     torch.Tensor:
	assert len(UpperCamelCase	) > 0, f"""{input_tensors} has to be a tuple/list of tensors"""

	# inspect.signature exist since python 3.5 and is a python method -> no problem with backward compatibility
	UpperCAmelCase_		:   str													=       len(inspect.signature(UpperCamelCase	).parameters	)
	if num_args_in_forward_chunk_fn != len(UpperCamelCase	):
		raise ValueError(
		    f"""forward_chunk_fn expects {num_args_in_forward_chunk_fn} arguments, but only {len(UpperCamelCase	)} input """
		    'tensors are given'	)

	if chunk_size > 0:
		UpperCAmelCase_		:   Optional[int]													=       input_tensors[0].shape[chunk_dim]
		for input_tensor in input_tensors:
			if input_tensor.shape[chunk_dim] != tensor_shape:
				raise ValueError(
				    f"""All input tenors have to be of the same shape: {tensor_shape}, """
				    f"""found shape {input_tensor.shape[chunk_dim]}"""	)

		if input_tensors[0].shape[chunk_dim] % chunk_size != 0:
			raise ValueError(
			    f"""The dimension to be chunked {input_tensors[0].shape[chunk_dim]} has to be a multiple of the chunk """
			    f"""size {chunk_size}"""	)

		UpperCAmelCase_		:   Any													=       input_tensors[0].shape[chunk_dim] // chunk_size

		# chunk input tensor into tuples
		UpperCAmelCase_		:   int													=       tuple(input_tensor.chunk(UpperCamelCase ,dim=UpperCamelCase	) for input_tensor in input_tensors	)
		# apply forward fn to every tuple
		UpperCAmelCase_		:   List[str]													=       tuple(forward_fn(*UpperCamelCase	) for input_tensors_chunk in zip(*UpperCamelCase	)	)
		# concatenate output at same dimension
		return torch.cat(UpperCamelCase ,dim=UpperCamelCase	)

	return forward_fn(*UpperCamelCase	)







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,UpperCamelCase	)     ->     Tuple[Set[int], torch.LongTensor]:
	UpperCAmelCase_		:   List[Any]													=       torch.ones(UpperCamelCase ,UpperCamelCase	)
	UpperCAmelCase_		:   Optional[int]													=       set(UpperCamelCase	) - already_pruned_heads  # Convert to set and remove already pruned heads
	for head in heads:
		# Compute how many pruned heads are before the head and move the index accordingly
		UpperCAmelCase_		:   Any													=       head - sum(1 if h < head else 0 for h in already_pruned_heads	)
		UpperCAmelCase_		:   List[Any]													=       0
	UpperCAmelCase_		:   str													=       mask.view(-1	).contiguous().eq(1	)
	UpperCAmelCase_		:   torch.LongTensor													=       torch.arange(len(UpperCamelCase	)	)[mask].long()
	return heads, index







def     SCREAMING_SNAKE_CASE(	*UpperCamelCase ,UpperCamelCase = None	)     ->     Tuple[torch.Tensor, ...]:
	return torch.meshgrid(*UpperCamelCase ,indexing=UpperCamelCase	)







def     SCREAMING_SNAKE_CASE(	UpperCamelCase	)     ->     Tuple[torch.device, int, int]:
	return tensor.device, storage_ptr(UpperCamelCase	), storage_size(UpperCamelCase	)






