






import numpy as np
def       a__						(  A		,				A="utf-8"		,				A="surrogatepass"					):
   lowercase__						:	Optional[Any]         = bin(int.from_bytes(text.encode(__a		,				__a					)		,				"""big"""					)					)[2:]
   return bits.zfill(8 * ((len(__a					) + 7) // 8)					)
def       a__						(  A		,				A="utf-8"		,				A="surrogatepass"					):
   lowercase__						:	Any         = int(__a		,				2					)
   return n.to_bytes((n.bit_length() + 7) // 8		,				"""big"""					).decode(__a		,				__a					) or "\0"
def       a__						(  A		,				A					):





   if size_par + len(__a					) <= 2**size_par - (len(__a					) - 1):
      raise ValueError("""size of parity don\'t match with size of data"""					)

   lowercase__						:	int         = []
   lowercase__						:	int         = []
   lowercase__						:	int         = [bin(__a					)[2:] for x in range(1		,				size_par + len(__a					) + 1					)]

   # sorted information data for the size of the output data
   lowercase__						:	int         = []
   # data position template + parity
   lowercase__						:	List[Any]         = []
   # parity bit counter
   lowercase__						:	Tuple         = 0
   # counter position of data bits
   lowercase__						:	List[str]         = 0

   for x in range(1		,				size_par + len(__a					) + 1					):
      # Performs a template of bit positions - who should be given,
      # and who should be parity
      if qtd_bp < size_par:
         if (np.log(__a					) / np.log(2					)).is_integer():
            data_out_gab.append("""P"""					)
            lowercase__						:	Dict         = qtd_bp + 1
         else:
            data_out_gab.append("""D"""					)
      else:
         data_out_gab.append("""D"""					)

      # Sorts the data to the new output size
      if data_out_gab[-1] == "D":
         data_ord.append(data[cont_data]					)
         cont_data += 1
      else:
         data_ord.append(__a					)

    # Calculates parity
   lowercase__						:	List[Any]         = 0  # parity bit counter
   for bp in range(1		,				size_par + 1					):
      # Bit counter one for a given parity
      lowercase__						:	Tuple         = 0
      # counter to control the loop reading
      lowercase__						:	List[str]         = 0
      for x in data_ord:
         if x is not None:
            try:
               lowercase__						:	Any         = (bin_pos[cont_loop])[-1 * (bp)]
            except IndexError:
               lowercase__						:	int         = '''0'''
            if aux == "1" and x == "1":
               cont_bo += 1
         cont_loop += 1
      parity.append(cont_bo % 2					)

      qtd_bp += 1

   # Mount the message
   lowercase__						:	Any         = 0  # parity bit counter
   for x in range(0		,				size_par + len(__a					)					):
      if data_ord[x] is None:
         data_out.append(str(parity[cont_bp]					)					)
         cont_bp += 1
      else:
         data_out.append(data_ord[x]					)

   return data_out






def       a__						(  A		,				A					):
   lowercase__						:	Union[str, Any]         = []
   # Parity bit counter
   lowercase__						:	Optional[int]         = 0
   # Counter p data bit reading
   lowercase__						:	List[str]         = 0
   # list of parity received
   lowercase__						:	str         = []
   lowercase__						:	List[Any]         = []

   for x in range(1		,				len(__a					) + 1					):
      # Performs a template of bit positions - who should be given,
      #  and who should be parity
      if qtd_bp < size_par and (np.log(__a					) / np.log(2					)).is_integer():
         data_out_gab.append("""P"""					)
         lowercase__						:	List[str]         = qtd_bp + 1
      else:
         data_out_gab.append("""D"""					)

      # Sorts the data to the new output size
      if data_out_gab[-1] == "D":
         data_output.append(data[cont_data]					)
      else:
         parity_received.append(data[cont_data]					)
      cont_data += 1

   # -----------calculates the parity with the data
   lowercase__						:	Optional[Any]         = []
   lowercase__						:	Union[str, Any]         = []
   lowercase__						:	Optional[int]         = [bin(__a					)[2:] for x in range(1		,				size_par + len(__a					) + 1					)]

   #  sorted information data for the size of the output data
   lowercase__						:	Union[str, Any]         = []
   # Data position feedback + parity
   lowercase__						:	str         = []
   # Parity bit counter
   lowercase__						:	List[str]         = 0
   # Counter p data bit reading
   lowercase__						:	Any         = 0

   for x in range(1		,				size_par + len(__a					) + 1					):
      # Performs a template position of bits - who should be given,
      # and who should be parity
      if qtd_bp < size_par and (np.log(__a					) / np.log(2					)).is_integer():
         data_out_gab.append("""P"""					)
         lowercase__						:	Any         = qtd_bp + 1
      else:
         data_out_gab.append("""D"""					)

      # Sorts the data to the new output size
      if data_out_gab[-1] == "D":
         data_ord.append(data_output[cont_data]					)
         cont_data += 1
      else:
         data_ord.append(__a					)

    # Calculates parity
   lowercase__						:	Tuple         = 0  # parity bit counter
   for bp in range(1		,				size_par + 1					):
      # Bit counter one for a certain parity
      lowercase__						:	List[Any]         = 0
      # Counter to control loop reading
      lowercase__						:	Any         = 0
      for x in data_ord:
         if x is not None:
            try:
               lowercase__						:	Optional[int]         = (bin_pos[cont_loop])[-1 * (bp)]
            except IndexError:
               lowercase__						:	Optional[int]         = '''0'''
            if aux == "1" and x == "1":
               cont_bo += 1
         cont_loop += 1
      parity.append(str(cont_bo % 2					)					)

      qtd_bp += 1

   # Mount the message
   lowercase__						:	List[str]         = 0  # Parity bit counter
   for x in range(0		,				size_par + len(__a					)					):
      if data_ord[x] is None:
         data_out.append(str(parity[cont_bp]					)					)
         cont_bp += 1
      else:
         data_out.append(data_ord[x]					)

   lowercase__						:	Tuple         = parity_received == parity
   return data_output, ack










from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve
def       a__						(  A		,				A		,				A					):
   lowercase__						:	Dict         = np.stack((horizontal_flow, vertical_flow)		,				2					)

   # Create a grid of all pixel coordinates and subtract the flow to get the
   # target pixels coordinates
   lowercase__						:	Tuple         = np.stack(
       np.meshgrid(np.arange(0		,				image.shape[1]					)		,				np.arange(0		,				image.shape[0]					)					)		,				2					)
   lowercase__						:	Union[str, Any]         = np.round(grid - flow					).astype(np.intaa					)

   # Find the locations outside of the original image
   lowercase__						:	Optional[Any]         = (grid < 0) | (grid >= np.array([image.shape[1], image.shape[0]]					))
   lowercase__						:	int         = 0

   lowercase__						:	Tuple         = image[grid[:, :, 1], grid[:, :, 0]]

   # Set pixels at invalid locations to 0
   lowercase__						:	str         = 0

   return warped
def       a__						(  A		,				A		,				A		,				A = None		,				):
   if alpha is None:
      lowercase__						:	Tuple         = 0.1

   # Initialize flow
   lowercase__						:	Optional[int]         = np.zeros_like(A					)
   lowercase__						:	Tuple         = np.zeros_like(A					)

   # Prepare kernels for the calculation of the derivatives and the average velocity
   lowercase__						:	Tuple         = np.array([[-1, 1], [-1, 1]]					) * 0.2_5
   lowercase__						:	int         = np.array([[-1, -1], [1, 1]]					) * 0.2_5
   lowercase__						:	Optional[int]         = np.array([[1, 1], [1, 1]]					) * 0.2_5
   lowercase__						:	Optional[Any]         = np.array(
       [[1 / 12, 1 / 6, 1 / 12], [1 / 6, 0, 1 / 6], [1 / 12, 1 / 6, 1 / 12]]					)

   # Iteratively refine the flow
   for _ in range(A					):
      lowercase__						:	Optional[int]         = warp(A		,				A		,				A					)
      lowercase__						:	Union[str, Any]         = convolve(A		,				A					) + convolve(A		,				A					)
      lowercase__						:	Union[str, Any]         = convolve(A		,				A					) + convolve(A		,				A					)
      lowercase__						:	str         = convolve(A		,				A					) + convolve(A		,				-kernel_t					)

      lowercase__						:	str         = convolve(A		,				A					)
      lowercase__						:	Tuple         = convolve(A		,				A					)

      # This updates the flow as proposed in the paper (Step 12)
      lowercase__						:	List[Any]         = (
          derivative_x * avg_horizontal_velocity
          + derivative_y * avg_vertical_velocity
          + derivative_t
      )
      lowercase__						:	Union[str, Any]         = update / (alpha**2 + derivative_x**2 + derivative_y**2)

      lowercase__						:	Optional[int]         = avg_horizontal_velocity - derivative_x * update
      lowercase__						:	int         = avg_vertical_velocity - derivative_y * update

   return horizontal_flow, vertical_flow


if __name__ == "__main__":
 import doctest

 doctest.testmod()


