
import numpy as np
import torch
from imwatermark import WatermarkEncoder


# Copied from https://github.com/Stability-AI/generative-models/blob/613af104c6b85184091d42d374fef420eddb356d/scripts/demo/streamlit_helpers.py#L66
_snake_case      = 0b101100111110110010010000011110111011000110011110
# bin(x)[2:] gives bits of x as str, use int to convert them to 0/1
_snake_case      = [int(bit) for bit in bin(WATERMARK_MESSAGE)[2:]]
class       _lowerCAmelCase  :

 """simple docstring"""

 def __init__(						self			:			Optional[int]   ):






      """simple docstring"""



      UpperCamelCase						    =					WATERMARK_BITS
      UpperCamelCase						    =					WatermarkEncoder()

      self.encoder.set_watermark('bits'					, self.watermark   )






 def      __lowerCAmelCase  (						self			:			int					, SCREAMING_SNAKE_CASE__			:			torch.FloatTensor   ):






      """simple docstring"""



      if images.shape[-1] < 2_56:
           return images

      UpperCamelCase						    =					(2_55 * (images / 2 + 0.5)).cpu().permute(0					, 2					, 3					, 1   ).float().numpy()

      UpperCamelCase						    =					[self.encoder.encode(SCREAMING_SNAKE_CASE__					, 'dwtDct'   ) for image in images]

      UpperCamelCase						    =					torch.from_numpy(np.array(SCREAMING_SNAKE_CASE__   )   ).permute(0					, 3					, 1					, 2   )

      UpperCamelCase						    =					torch.clamp(2 * (images / 2_55 - 0.5)					, min=-1.0					, max=1.0   )
      return images




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

def  __lowerCamelCase					( _lowercase			)       ->      str:

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

     UpperCamelCase						    =					precision
     UpperCamelCase						    =					ceil(precision / 14			)
     UpperCamelCase						    =					426880 * Decimal(10005			).sqrt()
     UpperCamelCase						    =					1
     UpperCamelCase						    =					13591409
     UpperCamelCase						    =					Decimal(_lowercase			)
     for k in range(1						,     _lowercase			):
          UpperCamelCase						    =					factorial(6 * k			) // (factorial(3 * k			) * factorial(_lowercase			) ** 3)
          linear_term += 545140134
          exponential_term *= -262537412640768000
          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)}")


