





import numpy as np




def 			lowerCAmelCase_			(				UpperCamelCase_       ,		UpperCamelCase_="utf-8"       ,		UpperCamelCase_="surrogatepass"	)  ->		int:
       UpperCamelCase_ 							=	bin(int.from_bytes(text.encode(UpperCamelCase_       ,		UpperCamelCase_	)       ,		"big"	)	)[2:]
       return bits.zfill(8 * ((len(UpperCamelCase_	) + 7) // 8)	)




def 			lowerCAmelCase_			(				UpperCamelCase_       ,		UpperCamelCase_="utf-8"       ,		UpperCamelCase_="surrogatepass"	)  ->		Union[str, Any]:
       UpperCamelCase_ 							=	int(UpperCamelCase_       ,		2	)
       return n.to_bytes((n.bit_length() + 7) // 8       ,		"big"	).decode(UpperCamelCase_       ,		UpperCamelCase_	) or "\0"




def 			lowerCAmelCase_			(				UpperCamelCase_       ,		UpperCamelCase_	)  ->		Union[str, Any]:







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

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

       # sorted information data for the size of the output data
       UpperCamelCase_ 							=	[]
       # data position template + parity
       UpperCamelCase_ 							=	[]
       # parity bit counter
       UpperCamelCase_ 							=	0
       # counter position of data bits
       UpperCamelCase_ 							=	0

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

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

              qtd_bp += 1

       # Mount the message
       UpperCamelCase_ 							=	0  # parity bit counter
       for x in range(0       ,		size_par + len(UpperCamelCase_	)	):
              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 			lowerCAmelCase_			(				UpperCamelCase_       ,		UpperCamelCase_	)  ->		int:
       UpperCamelCase_ 							=	[]
       # Parity bit counter
       UpperCamelCase_ 							=	0
       # Counter p data bit reading
       UpperCamelCase_ 							=	0
       # list of parity received
       UpperCamelCase_ 							=	[]
       UpperCamelCase_ 							=	[]

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

       #  sorted information data for the size of the output data
       UpperCamelCase_ 							=	[]
       # Data position feedback + parity
       UpperCamelCase_ 							=	[]
       # Parity bit counter
       UpperCamelCase_ 							=	0
       # Counter p data bit reading
       UpperCamelCase_ 							=	0

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

              # Calculates parity
       UpperCamelCase_ 							=	0  # parity bit counter
       for bp in range(1       ,		size_par + 1	):
              # Bit counter one for a certain parity
              UpperCamelCase_ 							=	0
              # Counter to control loop reading
              UpperCamelCase_ 							=	0
              for x in data_ord:
                     if x is not None:
                            try:
                                   UpperCamelCase_ 							=	(bin_pos[cont_loop])[-1 * (bp)]
                            except IndexError:
                                   UpperCamelCase_ 							=	"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
       UpperCamelCase_ 							=	0  # Parity bit counter
       for x in range(0       ,		size_par + len(UpperCamelCase_	)	):
              if data_ord[x] is None:
                     data_out.append(str(parity[cont_bp]	)	)
                     cont_bp += 1
              else:
                     data_out.append(data_ord[x]	)

       UpperCamelCase_ 							=	parity_received == parity
       return data_output, ack









"""simple docstring"""




import math






def 							lowerCAmelCase			(   UpperCamelCase_:				int       )							->				list:







  '''simple docstring'''







  if n <= 0:
    raise ValueError("Only positive integers have prime factors"       )
  _a					      =						[]
  while n % 2 == 0:
    pf.append(2       )
    _a					      =						int(n / 2       )
  for i in range(3  ,			int(math.sqrt(UpperCamelCase_       )       ) + 1  ,			2       ):
    while n % i == 0:
      pf.append(UpperCamelCase_       )
      _a					      =						int(n / i       )
  if n > 2:
    pf.append(UpperCamelCase_       )
  return pf






def 							lowerCAmelCase			(   UpperCamelCase_:				int       )							->				int:







  '''simple docstring'''







  if n <= 0:
    raise ValueError("Only positive numbers are accepted"       )
  _a					      =						1
  _a					      =						1
  while n % 2 == 0:
    temp += 1
    _a					      =						int(n / 2       )
  div *= temp
  for i in range(3  ,			int(math.sqrt(UpperCamelCase_       )       ) + 1  ,			2       ):
    _a					      =						1
    while n % i == 0:
      temp += 1
      _a					      =						int(n / i       )
    div *= temp
  if n > 1:
    div *= 2
  return div






def 							lowerCAmelCase			(   UpperCamelCase_:				int       )							->				int:







  '''simple docstring'''







  if n <= 0:
    raise ValueError("Only positive numbers are accepted"       )
  _a					      =						1
  _a					      =						1
  while n % 2 == 0:
    temp += 1
    _a					      =						int(n / 2       )
  if temp > 1:
    s *= (2**temp - 1) / (2 - 1)
  for i in range(3  ,			int(math.sqrt(UpperCamelCase_       )       ) + 1  ,			2       ):
    _a					      =						1
    while n % i == 0:
      temp += 1
      _a					      =						int(n / i       )
    if temp > 1:
      s *= (i**temp - 1) / (i - 1)
  return int(UpperCamelCase_       )






def 							lowerCAmelCase			(   UpperCamelCase_:				int       )							->				int:







  '''simple docstring'''







  _a					      =						n
  for x in set(prime_factors(UpperCamelCase_       )       ):
    s *= (x - 1) / x
  return int(UpperCamelCase_       )


if __name__ == "__main__":
     import doctest

     doctest.testmod()


