
from math import factorial

class __snake_case		:
    def __init__(  self		,snake_case		,snake_case      ):



           '''simple docstring'''







           lowercase							:     List[str]       	=      real
           if isinstance(snake_case		,snake_case      ):
                  lowercase							:     Any       	=      [1] * rank
           else:
                  lowercase							:     Optional[Any]       	=      rank
    def __repr__(  self      ):



           '''simple docstring'''







           return (
               f"{self.real}+"
               f"{'+'.join(str(snake_case      )+'E'+str(n+1      )for n,dual in enumerate(self.duals      )      )}"
           )
    def       _SCREAMING_SNAKE_CASE       (  self      ):



           '''simple docstring'''







           lowercase							:     Dict       	=      self.duals.copy()
           while cur[-1] == 0:
                  cur.pop(-1      )
           return Dual(self.real		,snake_case      )
    def __add__(  self		,snake_case      ):



           '''simple docstring'''







           if not isinstance(snake_case		,snake_case      ):
                  return Dual(self.real + other		,self.duals      )
           lowercase							:     Optional[int]       	=      self.duals.copy()
           lowercase							:     Optional[Any]       	=      other.duals.copy()
           if len(snake_case      ) > len(snake_case      ):
                  o_dual.extend([1] * (len(snake_case      ) - len(snake_case      ))      )
           elif len(snake_case      ) < len(snake_case      ):
                  s_dual.extend([1] * (len(snake_case      ) - len(snake_case      ))      )
           lowercase							:     Dict       	=      []
           for i in range(len(snake_case      )      ):
                  new_duals.append(s_dual[i] + o_dual[i]      )
           return Dual(self.real + other.real		,snake_case      )

    _a		:						Union[str, Any]=				__add__
    def __sub__(  self		,snake_case      ):



           '''simple docstring'''







           return self + other * -1
    def __mul__(  self		,snake_case      ):



           '''simple docstring'''







           if not isinstance(snake_case		,snake_case      ):
                  lowercase							:     str       	=      []
                  for i in self.duals:
                         new_duals.append(i * other      )
                  return Dual(self.real * other		,snake_case      )
           lowercase							:     Union[str, Any]       	=      [0] * (len(self.duals      ) + len(other.duals      ) + 1)
           for i, item in enumerate(self.duals      ):
                  for j, jtem in enumerate(other.duals      ):
                         new_duals[i + j + 1] += item * jtem
           for k in range(len(self.duals      )      ):
                  new_duals[k] += self.duals[k] * other.real
           for index in range(len(other.duals      )      ):
                  new_duals[index] += other.duals[index] * self.real
           return Dual(self.real * other.real		,snake_case      )

    _a		:						int=				__mul__
    def __truediv__(  self		,snake_case      ):



           '''simple docstring'''







           if not isinstance(snake_case		,snake_case      ):
                  lowercase							:     Union[str, Any]       	=      []
                  for i in self.duals:
                         new_duals.append(i / other      )
                  return Dual(self.real / other		,snake_case      )
           raise ValueError
    def __floordiv__(  self		,snake_case      ):



           '''simple docstring'''







           if not isinstance(snake_case		,snake_case      ):
                  lowercase							:     List[Any]       	=      []
                  for i in self.duals:
                         new_duals.append(i // other      )
                  return Dual(self.real // other		,snake_case      )
           raise ValueError
    def __pow__(  self		,snake_case      ):



           '''simple docstring'''







           if n < 0 or isinstance(snake_case		,snake_case      ):
                  raise ValueError("""power must be a positive integer"""      )
           if n == 0:
                  return 1
           if n == 1:
                  return self
           lowercase							:     str       	=      self
           for _ in range(n - 1      ):
                  x *= self
           return x







def 						_snake_case(  SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) ->    Dict:
       if not callable(SCREAMING_SNAKE_CASE__				):
              raise ValueError("""differentiate() requires a function as input for func"""				)
       if not isinstance(SCREAMING_SNAKE_CASE__					,	(float, int)				):
              raise ValueError("""differentiate() requires a float as input for position"""				)
       if not isinstance(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				):
              raise ValueError("""differentiate() requires an int as input for order"""				)
       lowercase							:     List[Any]       	=      Dual(SCREAMING_SNAKE_CASE__					,	1				)
       lowercase							:     List[Any]       	=      func(SCREAMING_SNAKE_CASE__				)
       if order == 0:
              return result.real
       return result.duals[order - 1] * factorial(SCREAMING_SNAKE_CASE__				)


if __name__ == "__main__":
  import doctest

  doctest.testmod()







  def 						_snake_case(  SCREAMING_SNAKE_CASE__				) ->    Union[str, Any]:
         return y**2 * y**4




  print(differentiate(f, 9, 2))





'''simple docstring'''






# coding=utf-8
# Copyright 2020 The HuggingFace Inc. team.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

# this script dumps information about the environment

import os
import sys

import transformers


UpperCamelCase__:   Optional[int]								=			"3"

print("Python version:", sys.version)
print("transformers version:", transformers.__version__)

try:
						import torch

						print("Torch version:", torch.__version__)
						print("Cuda available:", torch.cuda.is_available())
						print("Cuda version:", torch.version.cuda)
						print("CuDNN version:", torch.backends.cudnn.version())
						print("Number of GPUs available:", torch.cuda.device_count())
						print("NCCL version:", torch.cuda.nccl.version())
except ImportError:
						print("Torch version:", None)

try:
						import deepspeed

						print("DeepSpeed version:", deepspeed.__version__)
except ImportError:
						print("DeepSpeed version:", None)

try:
						import tensorflow as tf

						print("TensorFlow version:", tf.__version__)
						print("TF GPUs available:", bool(tf.config.list_physical_devices("GPU")))
						print("Number of TF GPUs available:", len(tf.config.list_physical_devices("GPU")))
except ImportError:
						print("TensorFlow version:", None)





