


"""simple docstring"""






from __future__ import annotations

from collections.abc import Callable

_lowerCAmelCase							:    Union[str, Any]					   =	list[list[float | int]]







def        lowerCamelCase_(		_lowerCamelCase			,		_lowerCamelCase       )    ->     Matrix:
   '''simple docstring'''





   _lowerCamelCase   :				int							=     len(_lowerCamelCase       )
   _lowerCamelCase   :				Matrix							=     [[0 for _ in range(size + 1       )] for _ in range(_lowerCamelCase       )]
   _lowerCamelCase   :				int
   _lowerCamelCase   :				int
   _lowerCamelCase   :				int
   _lowerCamelCase   :				int
   _lowerCamelCase   :				int
   _lowerCamelCase   :				float

   for row in range(_lowerCamelCase       ):
      for col in range(_lowerCamelCase       ):
         _lowerCamelCase   :				List[str]							=     matrix[row][col]

      _lowerCamelCase   :				List[str]							=     vector[row][0]

   _lowerCamelCase   :				int							=     0
   _lowerCamelCase   :				List[Any]							=     0
   while row < size and col < size:
      # pivoting
      _lowerCamelCase   :				Tuple							=     max((abs(augmented[rowa][col]       ), rowa) for rowa in range(_lowerCamelCase			,		_lowerCamelCase       )       )[
          1
      ]
      if augmented[pivot_row][col] == 0:
         col += 1
         continue
      else:
         _lowerCamelCase,					_lowerCamelCase   :				Any							=     augmented[pivot_row], augmented[row]

      for rowa in range(row + 1			,		_lowerCamelCase       ):
         _lowerCamelCase   :				Any							=     augmented[rowa][col] / augmented[row][col]
         _lowerCamelCase   :				Any							=     0
         for cola in range(col + 1			,		size + 1       ):
            augmented[rowa][cola] -= augmented[row][cola] * ratio

      row += 1
      col += 1

   # back substitution
   for col in range(1			,		_lowerCamelCase       ):
      for row in range(_lowerCamelCase       ):
         _lowerCamelCase   :				List[str]							=     augmented[row][col] / augmented[col][col]
         for cola in range(_lowerCamelCase			,		size + 1       ):
            augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
   return [
       [round(augmented[row][size] / augmented[row][row]			,		10       )] for row in range(_lowerCamelCase       )
   ]







def        lowerCamelCase_(		_lowerCamelCase       )    ->     Callable[[int], int]:
   '''simple docstring'''





   _lowerCamelCase   :				int							=     len(_lowerCamelCase       )
   _lowerCamelCase   :				Matrix							=     [[0 for _ in range(_lowerCamelCase       )] for _ in range(_lowerCamelCase       )]
   _lowerCamelCase   :				Matrix							=     [[0] for _ in range(_lowerCamelCase       )]
   _lowerCamelCase   :				Matrix
   _lowerCamelCase   :				int
   _lowerCamelCase   :				int
   _lowerCamelCase   :				int

   for x_val, y_val in enumerate(_lowerCamelCase       ):
      for col in range(_lowerCamelCase       ):
         _lowerCamelCase   :				List[str]							=     (x_val + 1) ** (size - col - 1)
      _lowerCamelCase   :				Optional[Any]							=     y_val

   _lowerCamelCase   :				str							=     solve(_lowerCamelCase			,		_lowerCamelCase       )

   def interpolated_func(_lowerCamelCase       ) -> int:
      return sum(
          round(coeffs[x_val][0]       ) * (var ** (size - x_val - 1))
          for x_val in range(_lowerCamelCase       )       )

   return interpolated_func







def        lowerCamelCase_(		_lowerCamelCase       )    ->     int:
   '''simple docstring'''





   return (
       1
       - variable
       + variable**2
       - variable**3
       + variable**4
       - variable**5
       + variable**6
       - variable**7
       + variable**8
       - variable**9
       + variable**10
   )







def        lowerCamelCase_(		_lowerCamelCase = question_function			,		_lowerCamelCase = 10       )    ->     int:
   '''simple docstring'''





   _lowerCamelCase   :				list[int]							=     [func(_lowerCamelCase       ) for x_val in range(1			,		order + 1       )]

   _lowerCamelCase   :				list[Callable[[int], int]]							=     [
       interpolate(data_points[:max_coeff]       ) for max_coeff in range(1			,		order + 1       )
   ]

   _lowerCamelCase   :				int							=     0
   _lowerCamelCase   :				Callable[[int], int]
   _lowerCamelCase   :				int

   for poly in polynomials:
      _lowerCamelCase   :				Tuple							=     1
      while func(_lowerCamelCase       ) == poly(_lowerCamelCase       ):
         x_val += 1

      ret += poly(_lowerCamelCase       )

   return ret


if __name__ == "__main__":
  print(f'''{solution() = }''')





import math

import tensorflow as tf
from packaging import version




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						str										=tf.convert_to_tensor(lowerCamelCase )
				__magic_name__						:						List[str]										=0.5 * (1.0 + tf.math.erf(x / tf.cast(tf.sqrt(2.0 )						,  x.dtype ) ))

				return x * cdf




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						str										=tf.convert_to_tensor(lowerCamelCase )
				__magic_name__						:						Optional[Any]										=tf.cast(math.pi						,  x.dtype )
				__magic_name__						:						int										=tf.cast(0.0_4_4_7_1_5						,  x.dtype )
				__magic_name__						:						Tuple										=0.5 * (1.0 + tf.tanh(tf.sqrt(2.0 / pi ) * (x + coeff * tf.pow(lowerCamelCase						,  3 )) ))

				return x * cdf




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						Any										=tf.convert_to_tensor(lowerCamelCase )

				return x * tf.tanh(tf.math.softplus(lowerCamelCase ) )




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						Optional[Any]										=tf.convert_to_tensor(lowerCamelCase )
				__magic_name__						:						Union[str, Any]										=tf.cast(0.0_4_4_7_1_5						,  x.dtype )
				__magic_name__						:						Tuple										=tf.cast(0.7_9_7_8_8_4_5_6_0_8						,  x.dtype )

				return 0.5 * x * (1.0 + tf.tanh(x * coeffa * (1.0 + coeffa * x * x) ))




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						List[str]										=tf.convert_to_tensor(lowerCamelCase )
				__magic_name__						:						Dict										=tf.cast(1.7_0_2						,  x.dtype )
				return x * tf.math.sigmoid(coeff * x )




def 		lowerCAmelCase_ (						lowerCamelCase ):
				return tf.clip_by_value(_gelu(lowerCamelCase )						,  -10						,  10 )




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase=-1 ):
				__magic_name__					,			__magic_name__						:						List[Any]										=tf.split(lowerCamelCase						,  2						,  axis=lowerCamelCase )
				return a * tf.math.sigmoid(lowerCamelCase )


if version.parse(tf.version.VERSION) >= version.parse("2.4"):




							def 		lowerCAmelCase_ (						lowerCamelCase ):
											return tf.keras.activations.gelu(lowerCamelCase						,  approximate=lowerCamelCase )

							UpperCAmelCase_		:					List[str]          =  tf.keras.activations.gelu



							UpperCAmelCase_		:					Dict          =  approximate_gelu_wrap
else:
							UpperCAmelCase_		:					Dict          =  _gelu
							UpperCAmelCase_		:					str          =  _gelu_new


UpperCAmelCase_		:					Any          =  {
    "gelu": gelu,
    "gelu_10": gelu_aa,
    "gelu_fast": gelu_fast,
    "gelu_new": gelu_new,
    "glu": glu,
    "mish": mish,
    "quick_gelu": quick_gelu,
    "relu": tf.keras.activations.relu,
    "sigmoid": tf.keras.activations.sigmoid,
    "silu": tf.keras.activations.swish,
    "swish": tf.keras.activations.swish,
    "tanh": tf.keras.activations.tanh,
}




def 		lowerCAmelCase_ (						lowerCamelCase ):
				if activation_string in ACTaFN:
								return ACTaFN[activation_string]
				else:
								raise KeyError(F"function {activation_string} not found in ACT2FN mapping {list(ACTaFN.keys() )}" )




