


"""simple docstring"""


import os
from pickle import UnpicklingError
from typing import Dict, Tuple

import jax
import jax.numpy as jnp
import numpy as np
from flax.serialization import from_bytes
from flax.traverse_util import flatten_dict, unflatten_dict

import transformers

from .utils import logging


__snake_case    					=					logging.get_logger(__name__)


def    _lowerCamelCase   (     lowerCamelCase__	:							List[Any]       ,		lowerCamelCase__	:							Union[str, Any]       ,		lowerCamelCase__	:							Tuple       ,		lowerCamelCase__	:							Tuple=False  ):
 try:
  import torch  # noqa: F401
 except ImportError:
  logger.error(
      """Loading a PyTorch model in Flax, requires both PyTorch and Flax to be installed. Please see"""
      """ https://pytorch.org/ and https://flax.readthedocs.io/en/latest/installation.html for installation"""
      """ instructions."""  )
  raise

 if not is_sharded:
  lowercase__       :       List[Any]				=						os.path.abspath(lowerCamelCase__  )
  logger.info(f'''Loading PyTorch weights from {pt_path}'''  )

  lowercase__       :       Union[str, Any]				=						torch.load(lowerCamelCase__       ,		map_location="""cpu"""  )
  logger.info(f'''PyTorch checkpoint contains {sum(t.numel() for t in pt_state_dict.values()  ):,} parameters.'''  )

  lowercase__       :       List[str]				=						convert_pytorch_state_dict_to_flax(lowerCamelCase__       ,		lowerCamelCase__  )
 else:
  # model is sharded and pytorch_checkpoint_path already contains the list of .pt shard files
  lowercase__       :       Optional[Any]				=						convert_pytorch_sharded_state_dict_to_flax(lowerCamelCase__       ,		lowerCamelCase__  )
 return flax_state_dict


def    _lowerCamelCase   (     lowerCamelCase__	:							Tuple[str]       ,		lowerCamelCase__	:							np.ndarray       ,		lowerCamelCase__	:							Dict[str, jnp.ndarray]       ,		lowerCamelCase__	:							str       ,		):

 def is_key_or_prefix_key_in_dict(lowerCamelCase__	:							Tuple[str]  ) -> bool:
  return len(set(lowerCamelCase__  ) & {key, (model_prefix,) + key}  ) > 0

 # layer norm
 lowercase__       :       Union[str, Any]				=						pt_tuple_key[:-1] + ("""scale""",)
 if pt_tuple_key[-1] in ["weight", "gamma"] and is_key_or_prefix_key_in_dict(lowerCamelCase__  ):
  return renamed_pt_tuple_key, pt_tensor

 # batch norm layer mean
 lowercase__       :       List[Any]				=						pt_tuple_key[:-1] + ("""mean""",)
 if pt_tuple_key[-1] == "running_mean" and not is_key_or_prefix_key_in_dict(lowerCamelCase__  ):
  return renamed_pt_tuple_key, pt_tensor

 # batch norm layer var
 lowercase__       :       Optional[Any]				=						pt_tuple_key[:-1] + ("""var""",)
 if pt_tuple_key[-1] == "running_var" and not is_key_or_prefix_key_in_dict(lowerCamelCase__  ):
  return renamed_pt_tuple_key, pt_tensor

 # embedding
 lowercase__       :       Any				=						pt_tuple_key[:-1] + ("""embedding""",)
 if pt_tuple_key[-1] == "weight" and is_key_or_prefix_key_in_dict(lowerCamelCase__  ):
  return renamed_pt_tuple_key, pt_tensor

 # conv layer
 lowercase__       :       Any				=						pt_tuple_key[:-1] + ("""kernel""",)
 if pt_tuple_key[-1] == "weight" and pt_tensor.ndim == 4 and not is_key_or_prefix_key_in_dict(lowerCamelCase__  ):
  lowercase__       :       List[Any]				=						pt_tensor.transpose(2       ,		3       ,		1       ,		0  )
  return renamed_pt_tuple_key, pt_tensor

 # linear layer
 lowercase__       :       Any				=						pt_tuple_key[:-1] + ("""kernel""",)
 if pt_tuple_key[-1] == "weight" and not is_key_or_prefix_key_in_dict(lowerCamelCase__  ):
  lowercase__       :       Any				=						pt_tensor.T
  return renamed_pt_tuple_key, pt_tensor

 # old PyTorch layer norm weight
 lowercase__       :       Dict				=						pt_tuple_key[:-1] + ("""weight""",)
 if pt_tuple_key[-1] == "gamma":
  return renamed_pt_tuple_key, pt_tensor

 # old PyTorch layer norm bias
 lowercase__       :       int				=						pt_tuple_key[:-1] + ("""bias""",)
 if pt_tuple_key[-1] == "beta":
  return renamed_pt_tuple_key, pt_tensor

 # New `weight_norm` from https://github.com/huggingface/transformers/pull/24030
 lowercase__       :       Union[str, Any]				=						None
 if pt_tuple_key[-3::2] == ("parametrizations", "original0"):
  lowercase__       :       Optional[Any]				=						pt_tuple_key[-2] + """_g"""
 elif pt_tuple_key[-3::2] == ("parametrizations", "original1"):
  lowercase__       :       Tuple				=						pt_tuple_key[-2] + """_v"""
 if name is not None:
  lowercase__       :       Any				=						pt_tuple_key[:-3] + (name,)
  return renamed_pt_tuple_key, pt_tensor

 return pt_tuple_key, pt_tensor


def    _lowerCamelCase   (     lowerCamelCase__	:							List[str]       ,		lowerCamelCase__	:							List[Any]  ):
 # convert pytorch tensor to numpy
 lowercase__       :       str				=						{k: v.numpy() for k, v in pt_state_dict.items()}

 lowercase__       :       int				=						flax_model.base_model_prefix

 # use params dict if the model contains batch norm layers
 if "params" in flax_model.params:
  lowercase__       :       Dict				=						flax_model.params["""params"""]
 else:
  lowercase__       :       Dict				=						flax_model.params
 lowercase__       :       Optional[int]				=						flatten_dict(lowerCamelCase__  )

 # add batch_stats keys,values to dict
 if "batch_stats" in flax_model.params:
  lowercase__       :       Optional[Any]				=						flatten_dict(flax_model.params["""batch_stats"""]  )
  random_flax_state_dict.update(lowerCamelCase__  )

 lowercase__       :       Dict				=						{}

 lowercase__       :       str				=						(model_prefix not in flax_model_params) and (
     model_prefix in {k.split("""."""  )[0] for k in pt_state_dict.keys()}
 )
 lowercase__       :       List[Any]				=						(model_prefix in flax_model_params) and (
     model_prefix not in {k.split("""."""  )[0] for k in pt_state_dict.keys()}
 )

 # Need to change some parameters name to match Flax names
 for pt_key, pt_tensor in pt_state_dict.items():
  lowercase__       :       str				=						tuple(pt_key.split("""."""  )  )

  # remove base model prefix if necessary
  lowercase__       :       Dict				=						pt_tuple_key[0] == model_prefix
  if load_model_with_head_into_base_model and has_base_model_prefix:
   lowercase__       :       Tuple				=						pt_tuple_key[1:]

  # Correctly rename weight parameters
  lowercase__	,       lowercase__       :       List[str]				=						rename_key_and_reshape_tensor(
      lowerCamelCase__       ,		lowerCamelCase__       ,		lowerCamelCase__       ,		lowerCamelCase__  )

  # add model prefix if necessary
  lowercase__       :       Optional[int]				=						(model_prefix,) + flax_key in random_flax_state_dict
  if load_base_model_into_model_with_head and require_base_model_prefix:
   lowercase__       :       Optional[int]				=						(model_prefix,) + flax_key

  if flax_key in random_flax_state_dict:
   if flax_tensor.shape != random_flax_state_dict[flax_key].shape:
    raise ValueError(
        f'''PyTorch checkpoint seems to be incorrect. Weight {pt_key} was expected to be of shape '''
        f'''{random_flax_state_dict[flax_key].shape}, but is {flax_tensor.shape}.'''  )

        # add batch stats if the model contains batchnorm layers
  if "batch_stats" in flax_model.params:
   if "mean" in flax_key[-1] or "var" in flax_key[-1]:
    lowercase__       :       List[str]				=						jnp.asarray(lowerCamelCase__  )
    continue
   # remove num_batches_tracked key
   if "num_batches_tracked" in flax_key[-1]:
    flax_state_dict.pop(lowerCamelCase__       ,		lowerCamelCase__  )
    continue

   # also add unexpected weight so that warning is thrown
   lowercase__       :       List[Any]				=						jnp.asarray(lowerCamelCase__  )

  else:
   # also add unexpected weight so that warning is thrown
   lowercase__       :       str				=						jnp.asarray(lowerCamelCase__  )

 return unflatten_dict(lowerCamelCase__  )


def    _lowerCamelCase   (     lowerCamelCase__	:							List[Any]       ,		lowerCamelCase__	:							str  ):
 import torch

 # Load the index
 lowercase__       :       Any				=						{}
 for shard_file in shard_filenames:
  # load using msgpack utils
  lowercase__       :       Union[str, Any]				=						torch.load(lowerCamelCase__  )
  lowercase__       :       Tuple				=						{k: v.numpy() for k, v in pt_state_dict.items()}

  lowercase__       :       Optional[int]				=						flax_model.base_model_prefix

  # use params dict if the model contains batch norm layers and then add batch_stats keys,values to dict
  if "batch_stats" in flax_model.params:
   lowercase__       :       Optional[Any]				=						flax_model.params["""params"""]

   lowercase__       :       Union[str, Any]				=						flatten_dict(lowerCamelCase__  )
   random_flax_state_dict.update(flatten_dict(flax_model.params["""batch_stats"""]  )  )
  else:
   lowercase__       :       List[Any]				=						flax_model.params
   lowercase__       :       Optional[Any]				=						flatten_dict(lowerCamelCase__  )

  lowercase__       :       int				=						(model_prefix not in flax_model_params) and (
      model_prefix in {k.split("""."""  )[0] for k in pt_state_dict.keys()}
  )
  lowercase__       :       Tuple				=						(model_prefix in flax_model_params) and (
      model_prefix not in {k.split("""."""  )[0] for k in pt_state_dict.keys()}
  )
  # Need to change some parameters name to match Flax names
  for pt_key, pt_tensor in pt_state_dict.items():
   lowercase__       :       Any				=						tuple(pt_key.split("""."""  )  )

   # remove base model prefix if necessary
   lowercase__       :       Optional[Any]				=						pt_tuple_key[0] == model_prefix
   if load_model_with_head_into_base_model and has_base_model_prefix:
    lowercase__       :       int				=						pt_tuple_key[1:]

   # Correctly rename weight parameters
   lowercase__	,       lowercase__       :       List[Any]				=						rename_key_and_reshape_tensor(
       lowerCamelCase__       ,		lowerCamelCase__       ,		lowerCamelCase__       ,		lowerCamelCase__  )
   # add model prefix if necessary
   lowercase__       :       Union[str, Any]				=						(model_prefix,) + flax_key in random_flax_state_dict
   if load_base_model_into_model_with_head and require_base_model_prefix:
    lowercase__       :       Optional[int]				=						(model_prefix,) + flax_key

   if flax_key in random_flax_state_dict:
    if flax_tensor.shape != random_flax_state_dict[flax_key].shape:
     raise ValueError(
         f'''PyTorch checkpoint seems to be incorrect. Weight {pt_key} was expected to be of shape '''
         f'''{random_flax_state_dict[flax_key].shape}, but is {flax_tensor.shape}.'''  )

            # add batch stats if the model contains batchnorm layers
   if "batch_stats" in flax_model.params:
    if "mean" in flax_key[-1]:
     lowercase__       :       str				=						jnp.asarray(lowerCamelCase__  )
     continue
    if "var" in flax_key[-1]:
     lowercase__       :       Union[str, Any]				=						jnp.asarray(lowerCamelCase__  )
     continue
    # remove num_batches_tracked key
    if "num_batches_tracked" in flax_key[-1]:
     flax_state_dict.pop(lowerCamelCase__       ,		lowerCamelCase__  )
     continue

    # also add unexpected weight so that warning is thrown
    lowercase__       :       Dict				=						jnp.asarray(lowerCamelCase__  )

   else:
    # also add unexpected weight so that warning is thrown
    lowercase__       :       Optional[Any]				=						jnp.asarray(lowerCamelCase__  )
 return unflatten_dict(lowerCamelCase__  )


def    _lowerCamelCase   (     lowerCamelCase__	:							str       ,		lowerCamelCase__	:							int  ):
 lowercase__       :       Optional[Any]				=						os.path.abspath(lowerCamelCase__  )
 logger.info(f'''Loading Flax weights from {flax_checkpoint_path}'''  )

 # import correct flax class
 lowercase__       :       int				=						getattr(lowerCamelCase__       ,		"""Flax""" + model.__class__.__name__  )

 # load flax weight dict
 with open(lowerCamelCase__       ,		"""rb"""  ) as state_f:
  try:
   lowercase__       :       Tuple				=						from_bytes(lowerCamelCase__       ,		state_f.read()  )
  except UnpicklingError:
   raise EnvironmentError(f'''Unable to convert {flax_checkpoint_path} to Flax deserializable object. '''  )

 return load_flax_weights_in_pytorch_model(lowerCamelCase__       ,		lowerCamelCase__  )






def    _lowerCamelCase   (     lowerCamelCase__	:							Union[str, Any]       ,		lowerCamelCase__	:							Optional[Any]  ):

 try:
  import torch  # noqa: F401
 except ImportError:
  logger.error(
      """Loading a Flax weights in PyTorch, requires both PyTorch and Flax to be installed. Please see"""
      """ https://pytorch.org/ and https://flax.readthedocs.io/en/latest/installation.html for installation"""
      """ instructions."""  )
  raise

 # check if we have bf16 weights
 lowercase__       :       Optional[Any]				=						flatten_dict(jax.tree_util.tree_map(lambda lowerCamelCase__  : x.dtype == jnp.bfloataa       ,		lowerCamelCase__  )  ).values()
 if any(lowerCamelCase__  ):
  # convert all weights to fp32 if the are bf16 since torch.from_numpy can-not handle bf16
  # and bf16 is not fully supported in PT yet.
  logger.warning(
      """Found ``bfloat16`` weights in Flax model. Casting all ``bfloat16`` weights to ``float32`` """
      """before loading those in PyTorch model."""  )
  lowercase__       :       Tuple				=						jax.tree_util.tree_map(
      lambda lowerCamelCase__  : params.astype(np.floataa  ) if params.dtype == jnp.bfloataa else params       ,		lowerCamelCase__  )

 lowercase__       :       int				=						flatten_dict(lowerCamelCase__  )
 lowercase__       :       Optional[Any]				=						pt_model.state_dict()

 lowercase__       :       str				=						(pt_model.base_model_prefix in flax_state) and (
     pt_model.base_model_prefix not in {k.split("""."""  )[0] for k in pt_model_dict.keys()}
 )
 lowercase__       :       Union[str, Any]				=						(pt_model.base_model_prefix not in flax_state) and (
     pt_model.base_model_prefix in {k.split("""."""  )[0] for k in pt_model_dict.keys()}
 )

 # keep track of unexpected & missing keys
 lowercase__       :       Optional[Any]				=						[]
 lowercase__       :       List[str]				=						set(pt_model_dict.keys()  )

 for flax_key_tuple, flax_tensor in flax_state_dict.items():
  lowercase__       :       List[str]				=						flax_key_tuple[0] == pt_model.base_model_prefix
  lowercase__       :       Union[str, Any]				=						""".""".join((pt_model.base_model_prefix,) + flax_key_tuple  ) in pt_model_dict

  # adapt flax_key to prepare for loading from/to base model only
  if load_model_with_head_into_base_model and has_base_model_prefix:
   lowercase__       :       int				=						flax_key_tuple[1:]
  elif load_base_model_into_model_with_head and require_base_model_prefix:
   lowercase__       :       List[Any]				=						(pt_model.base_model_prefix,) + flax_key_tuple

  # rename flax weights to PyTorch format
  if flax_key_tuple[-1] == "kernel" and flax_tensor.ndim == 4 and ".".join(lowerCamelCase__  ) not in pt_model_dict:
   # conv layer
   lowercase__       :       Dict				=						flax_key_tuple[:-1] + ("""weight""",)
   lowercase__       :       int				=						jnp.transpose(lowerCamelCase__       ,		(3, 2, 0, 1)  )
  elif flax_key_tuple[-1] == "kernel" and ".".join(lowerCamelCase__  ) not in pt_model_dict:
   # linear layer
   lowercase__       :       List[Any]				=						flax_key_tuple[:-1] + ("""weight""",)
   lowercase__       :       Optional[int]				=						flax_tensor.T
  elif flax_key_tuple[-1] in ["scale", "embedding"]:
   lowercase__       :       int				=						flax_key_tuple[:-1] + ("""weight""",)

  # adding batch stats from flax batch norm to pt
  elif "mean" in flax_key_tuple[-1]:
   lowercase__       :       Optional[int]				=						flax_key_tuple[:-1] + ("""running_mean""",)
  elif "var" in flax_key_tuple[-1]:
   lowercase__       :       Union[str, Any]				=						flax_key_tuple[:-1] + ("""running_var""",)

  if "batch_stats" in flax_state:
   lowercase__       :       str				=						""".""".join(flax_key_tuple[1:]  )  # Remove the params/batch_stats header
  else:
   lowercase__       :       List[str]				=						""".""".join(lowerCamelCase__  )

  # We also need to look at `pt_model_dict` and see if there are keys requiring further transformation.
  lowercase__       :       Tuple				=						{}
  # New `weight_norm` from https://github.com/huggingface/transformers/pull/24030
  for key in pt_model_dict:
   lowercase__       :       Any				=						key.split("""."""  )
   lowercase__       :       Tuple				=						None
   if key_components[-3::2] == ["parametrizations", "original0"]:
    lowercase__       :       Any				=						key_components[-2] + """_g"""
   elif key_components[-3::2] == ["parametrizations", "original1"]:
    lowercase__       :       List[Any]				=						key_components[-2] + """_v"""
   if name is not None:
    lowercase__       :       Optional[Any]				=						key_components[:-3] + [name]
    lowercase__       :       Any				=						""".""".join(lowerCamelCase__  )
    lowercase__       :       str				=						key

  if flax_key in special_pt_names:
   lowercase__       :       int				=						special_pt_names[flax_key]

  if flax_key in pt_model_dict:
   if flax_tensor.shape != pt_model_dict[flax_key].shape:
    raise ValueError(
        f'''Flax checkpoint seems to be incorrect. Weight {flax_key_tuple} was expected '''
        f'''to be of shape {pt_model_dict[flax_key].shape}, but is {flax_tensor.shape}.'''  )
   else:
    # add weight to pytorch dict
    lowercase__       :       Dict				=						np.asarray(lowerCamelCase__  ) if not isinstance(lowerCamelCase__       ,		np.ndarray  ) else flax_tensor
    lowercase__       :       Optional[int]				=						torch.from_numpy(lowerCamelCase__  )
    # remove from missing keys
    missing_keys.remove(lowerCamelCase__  )
  else:
   # weight is not expected by PyTorch model
   unexpected_keys.append(lowerCamelCase__  )

 pt_model.load_state_dict(lowerCamelCase__  )

 # re-transform missing_keys to list
 lowercase__       :       str				=						list(lowerCamelCase__  )

 if len(lowerCamelCase__  ) > 0:
  logger.warning(
      """Some weights of the Flax model were not used when initializing the PyTorch model"""
      f''' {pt_model.__class__.__name__}: {unexpected_keys}\n- This IS expected if you are initializing'''
      f''' {pt_model.__class__.__name__} from a Flax model trained on another task or with another architecture'''
      """ (e.g. initializing a BertForSequenceClassification model from a FlaxBertForPreTraining model).\n- This"""
      f''' IS NOT expected if you are initializing {pt_model.__class__.__name__} from a Flax model that you expect'''
      """ to be exactly identical (e.g. initializing a BertForSequenceClassification model from a"""
      """ FlaxBertForSequenceClassification model)."""  )
 else:
  logger.warning(f'''All Flax model weights were used when initializing {pt_model.__class__.__name__}.\n'''  )
 if len(lowerCamelCase__  ) > 0:
  logger.warning(
      f'''Some weights of {pt_model.__class__.__name__} were not initialized from the Flax model and are newly'''
      f''' initialized: {missing_keys}\nYou should probably TRAIN this model on a down-stream task to be able to'''
      """ use it for predictions and inference."""  )
 else:
  logger.warning(
      f'''All the weights of {pt_model.__class__.__name__} were initialized from the Flax model.\n'''
      """If your task is similar to the task the model of the checkpoint was trained on, """
      f'''you can already use {pt_model.__class__.__name__} for predictions without further training.'''  )

 return pt_model



"""simple docstring"""


from decimal import Decimal, getcontext
from math import ceil, factorial


def    _lowerCamelCase   (     lowerCamelCase__	:							int  ):

 if not isinstance(lowerCamelCase__       ,		lowerCamelCase__  ):
  raise TypeError("""Undefined for non-integers"""  )
 elif precision < 1:
  raise ValueError("""Undefined for non-natural numbers"""  )

 lowercase__       :       List[str]				=						precision
 lowercase__       :       Optional[int]				=						ceil(precision / 14  )
 lowercase__       :       Union[str, Any]				=						42_68_80 * Decimal(1_00_05  ).sqrt()
 lowercase__       :       Optional[Any]				=						1
 lowercase__       :       Optional[Any]				=						13_59_14_09
 lowercase__       :       List[Any]				=						Decimal(lowerCamelCase__  )
 for k in range(1       ,		lowerCamelCase__  ):
  lowercase__       :       Optional[int]				=						factorial(6 * k  ) // (factorial(3 * k  ) * factorial(lowerCamelCase__  ) ** 3)
  linear_term += 5_45_14_01_34
  exponential_term *= -26_25_37_41_26_40_76_80_00
  partial_sum += Decimal(multinomial_term * linear_term  ) / exponential_term
 return str(constant_term / partial_sum  )[:-1]


if __name__ == "__main__":
   __snake_case    					=					50
   print(F"The first {n} digits of pi is: {pi(n)}")