





def     _lowerCAmelCase		(  _lowerCAmelCase     ):
			'''simple docstring'''


			A_     :				List[Any]			      =	current_set.copy()
			for row_index, row in enumerate(_lowerCAmelCase     ):
						A_     :				int			      =	row[0]
						for column_index, column in enumerate(_lowerCAmelCase     ):
									if magnitude == 0:
												A_     :				int			      =	column
												continue
									A_     :				int			      =	column / magnitude
    # Subtract to cancel term
			A_     :				Optional[Any]			      =	current_set[0]
			A_     :				int			      =	[first_row]
			A_     :				List[Any]			      =	current_set[1::]
			for row in current_set:
						A_     :				Optional[int]			      =	[]
						# If first term is 0, it is already in form we want, so we preserve it
						if row[0] == 0:
									final_set.append(_lowerCAmelCase     )
									continue
						for column_index in range(len(_lowerCAmelCase     )     ):
									temp_row.append(first_row[column_index] - row[column_index]     )
						final_set.append(_lowerCAmelCase     )
			# Create next recursion iteration set
			if len(final_set[0]     ) != 3:
						A_     :				Any			      =	final_set[0]
						A_     :				Union[str, Any]			      =	[]
						A_     :				Union[str, Any]			      =	[]
						for row in final_set[1::]:
									current_first_column.append(row[0]     )
									next_iteration.append(row[1::]     )
						A_     :				Union[str, Any]			      =	simplify(_lowerCAmelCase     )
						for i in range(len(_lowerCAmelCase     )     ):
									resultant[i].insert(0  ,current_first_column[i]     )
						resultant.insert(0  ,_lowerCAmelCase     )
						A_     :				Dict			      =	resultant
			return final_set



def     _lowerCAmelCase		(  _lowerCAmelCase     ):
			'''simple docstring'''


			if len(_lowerCAmelCase     ) == 0:
						raise IndexError("""solve_simultaneous() requires n lists of length n+1"""     )
			A_     :				int			      =	len(_lowerCAmelCase     ) + 1
			if any(len(_lowerCAmelCase     ) != _length for item in equations     ):
						raise IndexError("""solve_simultaneous() requires n lists of length n+1"""     )
			for row in equations:
						if any(not isinstance(_lowerCAmelCase  ,(int, float)     ) for column in row     ):
									raise ValueError("""solve_simultaneous() requires lists of integers"""     )
			if len(_lowerCAmelCase     ) == 1:
						return [equations[0][-1] / equations[0][0]]
			A_     :				Optional[Any]			      =	equations.copy()
			if any(0 in row for row in data_set     ):
						A_     :				Dict			      =	data_set.copy()
						A_     :				Optional[Any]			      =	[]
						for row_index, row in enumerate(_lowerCAmelCase     ):
									if 0 not in row:
												A_     :				Optional[int]			      =	data_set.pop(_lowerCAmelCase     )
												break
						if not full_row:
									raise ValueError("""solve_simultaneous() requires at least 1 full equation"""     )
						data_set.insert(0  ,_lowerCAmelCase     )
			A_     :				Optional[int]			      =	data_set.copy()
			A_     :				Union[str, Any]			      =	simplify(_lowerCAmelCase     )
			A_     :				List[Any]			      =	simplified[::-1]
			A_     :				list			      =	[]
			for row in simplified:
						A_     :				Optional[Any]			      =	row[-1]
						if not solutions:
									if row[-2] == 0:
												solutions.append(0     )
												continue
									solutions.append(current_solution / row[-2]     )
									continue
						A_     :				Dict			      =	row.copy()[: len(_lowerCAmelCase     ) - 1 :]
						while temp_row[0] == 0:
									temp_row.pop(0     )
						if len(_lowerCAmelCase     ) == 0:
									solutions.append(0     )
									continue
						A_     :				List[str]			      =	temp_row[1::]
						A_     :				Any			      =	temp_row[::-1]
						for column_index, column in enumerate(_lowerCAmelCase     ):
									current_solution -= column * solutions[column_index]
						solutions.append(_lowerCAmelCase     )
			A_     :				int			      =	[]
			for item in solutions:
						final.append(float(round(_lowerCAmelCase  ,5     )     )     )
			return final[::-1]


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						_lowerCAmelCase 				=     [
						    [2, 1, 1, 1, 1, 4],
						    [1, 2, 1, 1, 1, 5],
						    [1, 1, 2, 1, 1, 6],
						    [1, 1, 1, 2, 1, 7],
						    [1, 1, 1, 1, 2, 8],
						]
						print(solve_simultaneous(eq))
						print(solve_simultaneous([[4, 2]]))













# 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


_lowerCAmelCase 				=     """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)






