



import math

import tensorflow as tf
from packaging import version






def  UpperCAmelCase__    (    lowercase__   ) ->      Any:
						__lowercase					=				tf.convert_to_tensor(lowercase__   )
						__lowercase					=				0.5 * (1.0 + tf.math.erf(x / tf.cast(tf.sqrt(2.0   )						,       x.dtype   )   ))

						return x * cdf






def  UpperCAmelCase__    (    lowercase__   ) ->      List[Any]:
						__lowercase					=				tf.convert_to_tensor(lowercase__   )
						__lowercase					=				tf.cast(math.pi						,       x.dtype   )
						__lowercase					=				tf.cast(0.044715						,       x.dtype   )
						__lowercase					=				0.5 * (1.0 + tf.tanh(tf.sqrt(2.0 / pi   ) * (x + coeff * tf.pow(lowercase__						,       3   ))   ))

						return x * cdf






def  UpperCAmelCase__    (    lowercase__   ) ->      List[Any]:
						__lowercase					=				tf.convert_to_tensor(lowercase__   )

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






def  UpperCAmelCase__    (    lowercase__   ) ->      Union[str, Any]:
						__lowercase					=				tf.convert_to_tensor(lowercase__   )
						__lowercase					=				tf.cast(0.044715						,       x.dtype   )
						__lowercase					=				tf.cast(0.7978845608						,       x.dtype   )

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






def  UpperCAmelCase__    (    lowercase__   ) ->      List[Any]:
						__lowercase					=				tf.convert_to_tensor(lowercase__   )
						__lowercase					=				tf.cast(1.702						,       x.dtype   )
						return x * tf.math.sigmoid(coeff * x   )






def  UpperCAmelCase__    (    lowercase__   ) ->      List[Any]:
						return tf.clip_by_value(_gelu(lowercase__   )						,       -10						,       10   )






def  UpperCAmelCase__    (    lowercase__						,       lowercase__=-1   ) ->      Tuple:
						__lowercase	,			__lowercase					=				tf.split(lowercase__						,       2						,       axis=lowercase__   )
						return a * tf.math.sigmoid(lowercase__   )


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






			def  UpperCAmelCase__    (    lowercase__   ) ->      str:
									return tf.keras.activations.gelu(lowercase__						,       approximate=lowercase__   )

			UpperCamelCase__ =						tf.keras.activations.gelu







			UpperCamelCase__ =						approximate_gelu_wrap
else:
			UpperCamelCase__ =						_gelu
			UpperCamelCase__ =						_gelu_new


UpperCamelCase__ =						{
    "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  UpperCAmelCase__    (    lowercase__   ) ->      List[str]:
						if activation_string in ACTaFN:
												return ACTaFN[activation_string]
						else:
												raise KeyError(F"function {activation_string} not found in ACT2FN mapping {list(ACTaFN.keys()   )}"   )










from __future__ import annotations

from collections.abc import Callable

UpperCamelCase__ =						list[list[float | int]]






def  UpperCAmelCase__    (    lowercase__						,       lowercase__   ) ->      Matrix:
						__lowercase					=				len(lowercase__   )
						__lowercase					=				[[0 for _ in range(size + 1   )] for _ in range(lowercase__   )]
						__lowercase					=				42
						__lowercase					=				42
						__lowercase					=				42
						__lowercase					=				42
						__lowercase					=				42
						__lowercase					=				42

						for row in range(lowercase__   ):
												for col in range(lowercase__   ):
																		__lowercase					=				matrix[row][col]

												__lowercase					=				vector[row][0]

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

												for rowa in range(row + 1						,       lowercase__   ):
																		__lowercase					=				augmented[rowa][col] / augmented[row][col]
																		__lowercase					=				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						,       lowercase__   ):
												for row in range(lowercase__   ):
																		__lowercase					=				augmented[row][col] / augmented[col][col]
																		for cola in range(lowercase__						,       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(lowercase__   )
						]






def  UpperCAmelCase__    (    lowercase__   ) ->      Callable[[int], int]:
						__lowercase					=				len(lowercase__   )
						__lowercase					=				[[0 for _ in range(lowercase__   )] for _ in range(lowercase__   )]
						__lowercase					=				[[0] for _ in range(lowercase__   )]
						__lowercase					=				42
						__lowercase					=				42
						__lowercase					=				42
						__lowercase					=				42

						for x_val, y_val in enumerate(lowercase__   ):
												for col in range(lowercase__   ):
																		__lowercase					=				(x_val + 1) ** (size - col - 1)
												__lowercase					=				y_val

						__lowercase					=				solve(lowercase__						,       lowercase__   )

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

						return interpolated_func






def  UpperCAmelCase__    (    lowercase__   ) ->      int:
						return (
						    1
						    - variable
						    + variable**2
						    - variable**3
						    + variable**4
						    - variable**5
						    + variable**6
						    - variable**7
						    + variable**8
						    - variable**9
						    + variable**10
						)






def  UpperCAmelCase__    (    lowercase__ = question_function						,       lowercase__ = 10   ) ->      int:
						__lowercase					=				[func(lowercase__   ) for x_val in range(1						,       order + 1   )]

						__lowercase					=				[
						    interpolate(data_points[:max_coeff]   ) for max_coeff in range(1						,       order + 1   )
						]

						__lowercase					=				0
						__lowercase					=				42
						__lowercase					=				42

						for poly in polynomials:
												__lowercase					=				1
												while func(lowercase__   ) == poly(lowercase__   ):
																		x_val += 1

												ret += poly(lowercase__   )

						return ret


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





