



from binascii import hexlify
from hashlib import shaaaa
from os import urandom

# RFC 3526 - More Modular Exponential (MODP) Diffie-Hellman groups for
# Internet Key Exchange (IKE) https://tools.ietf.org/html/rfc3526

__UpperCAmelCase			  =			{
    # 1536-bit
    5: {
        '''prime''': int(
            '''FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1'''
            + '''29024E088A67CC74020BBEA63B139B22514A08798E3404DD'''
            + '''EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245'''
            + '''E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED'''
            + '''EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D'''
            + '''C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F'''
            + '''83655D23DCA3AD961C62F356208552BB9ED529077096966D'''
            + '''670C354E4ABC9804F1746C08CA237327FFFFFFFFFFFFFFFF''',
            base=16,
        ),
        '''generator''': 2,
    },
    # 2048-bit
    14: {
        '''prime''': int(
            '''FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1'''
            + '''29024E088A67CC74020BBEA63B139B22514A08798E3404DD'''
            + '''EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245'''
            + '''E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED'''
            + '''EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D'''
            + '''C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F'''
            + '''83655D23DCA3AD961C62F356208552BB9ED529077096966D'''
            + '''670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B'''
            + '''E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9'''
            + '''DE2BCBF6955817183995497CEA956AE515D2261898FA0510'''
            + '''15728E5A8AACAA68FFFFFFFFFFFFFFFF''',
            base=16,
        ),
        '''generator''': 2,
    },
    # 3072-bit
    15: {
        '''prime''': int(
            '''FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1'''
            + '''29024E088A67CC74020BBEA63B139B22514A08798E3404DD'''
            + '''EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245'''
            + '''E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED'''
            + '''EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D'''
            + '''C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F'''
            + '''83655D23DCA3AD961C62F356208552BB9ED529077096966D'''
            + '''670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B'''
            + '''E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9'''
            + '''DE2BCBF6955817183995497CEA956AE515D2261898FA0510'''
            + '''15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64'''
            + '''ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7'''
            + '''ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B'''
            + '''F12FFA06D98A0864D87602733EC86A64521F2B18177B200C'''
            + '''BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31'''
            + '''43DB5BFCE0FD108E4B82D120A93AD2CAFFFFFFFFFFFFFFFF''',
            base=16,
        ),
        '''generator''': 2,
    },
    # 4096-bit
    16: {
        '''prime''': int(
            '''FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1'''
            + '''29024E088A67CC74020BBEA63B139B22514A08798E3404DD'''
            + '''EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245'''
            + '''E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED'''
            + '''EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D'''
            + '''C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F'''
            + '''83655D23DCA3AD961C62F356208552BB9ED529077096966D'''
            + '''670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B'''
            + '''E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9'''
            + '''DE2BCBF6955817183995497CEA956AE515D2261898FA0510'''
            + '''15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64'''
            + '''ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7'''
            + '''ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B'''
            + '''F12FFA06D98A0864D87602733EC86A64521F2B18177B200C'''
            + '''BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31'''
            + '''43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7'''
            + '''88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA'''
            + '''2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6'''
            + '''287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED'''
            + '''1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9'''
            + '''93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934063199'''
            + '''FFFFFFFFFFFFFFFF''',
            base=16,
        ),
        '''generator''': 2,
    },
    # 6144-bit
    17: {
        '''prime''': int(
            '''FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E08'''
            + '''8A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B'''
            + '''302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9'''
            + '''A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE6'''
            + '''49286651ECE45B3DC2007CB8A163BF0598DA48361C55D39A69163FA8'''
            + '''FD24CF5F83655D23DCA3AD961C62F356208552BB9ED529077096966D'''
            + '''670C354E4ABC9804F1746C08CA18217C32905E462E36CE3BE39E772C'''
            + '''180E86039B2783A2EC07A28FB5C55DF06F4C52C9DE2BCBF695581718'''
            + '''3995497CEA956AE515D2261898FA051015728E5A8AAAC42DAD33170D'''
            + '''04507A33A85521ABDF1CBA64ECFB850458DBEF0A8AEA71575D060C7D'''
            + '''B3970F85A6E1E4C7ABF5AE8CDB0933D71E8C94E04A25619DCEE3D226'''
            + '''1AD2EE6BF12FFA06D98A0864D87602733EC86A64521F2B18177B200C'''
            + '''BBE117577A615D6C770988C0BAD946E208E24FA074E5AB3143DB5BFC'''
            + '''E0FD108E4B82D120A92108011A723C12A787E6D788719A10BDBA5B26'''
            + '''99C327186AF4E23C1A946834B6150BDA2583E9CA2AD44CE8DBBBC2DB'''
            + '''04DE8EF92E8EFC141FBECAA6287C59474E6BC05D99B2964FA090C3A2'''
            + '''233BA186515BE7ED1F612970CEE2D7AFB81BDD762170481CD0069127'''
            + '''D5B05AA993B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492'''
            + '''36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BDF8FF9406'''
            + '''AD9E530EE5DB382F413001AEB06A53ED9027D831179727B0865A8918'''
            + '''DA3EDBEBCF9B14ED44CE6CBACED4BB1BDB7F1447E6CC254B33205151'''
            + '''2BD7AF426FB8F401378CD2BF5983CA01C64B92ECF032EA15D1721D03'''
            + '''F482D7CE6E74FEF6D55E702F46980C82B5A84031900B1C9E59E7C97F'''
            + '''BEC7E8F323A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA'''
            + '''CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE32806A1D58B'''
            + '''B7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55CDA56C9EC2EF29632'''
            + '''387FE8D76E3C0468043E8F663F4860EE12BF2D5B0B7474D6E694F91E'''
            + '''6DCC4024FFFFFFFFFFFFFFFF''',
            base=16,
        ),
        '''generator''': 2,
    },
    # 8192-bit
    18: {
        '''prime''': int(
            '''FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1'''
            + '''29024E088A67CC74020BBEA63B139B22514A08798E3404DD'''
            + '''EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245'''
            + '''E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED'''
            + '''EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D'''
            + '''C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F'''
            + '''83655D23DCA3AD961C62F356208552BB9ED529077096966D'''
            + '''670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B'''
            + '''E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9'''
            + '''DE2BCBF6955817183995497CEA956AE515D2261898FA0510'''
            + '''15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64'''
            + '''ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7'''
            + '''ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B'''
            + '''F12FFA06D98A0864D87602733EC86A64521F2B18177B200C'''
            + '''BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31'''
            + '''43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7'''
            + '''88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA'''
            + '''2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6'''
            + '''287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED'''
            + '''1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9'''
            + '''93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492'''
            + '''36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BD'''
            + '''F8FF9406AD9E530EE5DB382F413001AEB06A53ED9027D831'''
            + '''179727B0865A8918DA3EDBEBCF9B14ED44CE6CBACED4BB1B'''
            + '''DB7F1447E6CC254B332051512BD7AF426FB8F401378CD2BF'''
            + '''5983CA01C64B92ECF032EA15D1721D03F482D7CE6E74FEF6'''
            + '''D55E702F46980C82B5A84031900B1C9E59E7C97FBEC7E8F3'''
            + '''23A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA'''
            + '''CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE328'''
            + '''06A1D58BB7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55C'''
            + '''DA56C9EC2EF29632387FE8D76E3C0468043E8F663F4860EE'''
            + '''12BF2D5B0B7474D6E694F91E6DBE115974A3926F12FEE5E4'''
            + '''38777CB6A932DF8CD8BEC4D073B931BA3BC832B68D9DD300'''
            + '''741FA7BF8AFC47ED2576F6936BA424663AAB639C5AE4F568'''
            + '''3423B4742BF1C978238F16CBE39D652DE3FDB8BEFC848AD9'''
            + '''22222E04A4037C0713EB57A81A23F0C73473FC646CEA306B'''
            + '''4BCBC8862F8385DDFA9D4B7FA2C087E879683303ED5BDD3A'''
            + '''062B3CF5B3A278A66D2A13F83F44F82DDF310EE074AB6A36'''
            + '''4597E899A0255DC164F31CC50846851DF9AB48195DED7EA1'''
            + '''B1D510BD7EE74D73FAF36BC31ECFA268359046F4EB879F92'''
            + '''4009438B481C6CD7889A002ED5EE382BC9190DA6FC026E47'''
            + '''9558E4475677E9AA9E3050E2765694DFC81F56E880B96E71'''
            + '''60C980DD98EDD3DFFFFFFFFFFFFFFFFF''',
            base=16,
        ),
        '''generator''': 2,
    },
}



class 							lowerCAmelCase_						:
       def __init__(     self,     SCREAMING_SNAKE_CASE_ = 14			)	->						None:
          if group not in primes:
             raise ValueError('Unsupported Group'			)
          UpperCamelCase       :    Tuple		      =      primes[group]['prime']
          UpperCamelCase       :    Optional[int]		      =      primes[group]['generator']

          UpperCamelCase       :    List[str]		      =      int(hexlify(urandom(32			)			),     base=16			)
       def    snake_case_			(     self			)	->						str:
          return hex(self.__private_key			)[2:]
       def    snake_case_			(     self			)	->						str:
          UpperCamelCase       :    Optional[Any]		      =      pow(self.generator,     self.__private_key,     self.prime			)
          return hex(SCREAMING_SNAKE_CASE_			)[2:]
       def    snake_case_			(     self,     SCREAMING_SNAKE_CASE_			)	->						bool:
          # check if the other public key is valid based on NIST SP800-56
          return (
              2 <= key <= self.prime - 2
              and pow(SCREAMING_SNAKE_CASE_,     (self.prime - 1) // 2,     self.prime			) == 1
          )
       def    snake_case_			(     self,     SCREAMING_SNAKE_CASE_			)	->						str:
          UpperCamelCase       :    List[str]		      =      int(SCREAMING_SNAKE_CASE_,     base=16			)
          if not self.is_valid_public_key(SCREAMING_SNAKE_CASE_			):
             raise ValueError('Invalid public key'			)
          UpperCamelCase       :    Optional[Any]		      =      pow(SCREAMING_SNAKE_CASE_,     self.__private_key,     self.prime			)
          return shaaaa(str(SCREAMING_SNAKE_CASE_			).encode()			).hexdigest()
       @staticmethod
       def    snake_case_			(     SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_			)	->						bool:
          # check if the other public key is valid based on NIST SP800-56
          return (
              2 <= remote_public_key_str <= prime - 2
              and pow(SCREAMING_SNAKE_CASE_,     (prime - 1) // 2,     SCREAMING_SNAKE_CASE_			) == 1
          )






       @staticmethod
       def    snake_case_			(     SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_ = 14			)	->						str:
          UpperCamelCase       :    Union[str, Any]		      =      int(SCREAMING_SNAKE_CASE_,     base=16			)
          UpperCamelCase       :    Union[str, Any]		      =      int(SCREAMING_SNAKE_CASE_,     base=16			)
          UpperCamelCase       :    int		      =      primes[group]['prime']
          if not DiffieHellman.is_valid_public_key_static(SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_			):
             raise ValueError('Invalid public key'			)
          UpperCamelCase       :    List[Any]		      =      pow(SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_			)
          return shaaaa(str(SCREAMING_SNAKE_CASE_			).encode()			).hexdigest()


if __name__ == "__main__":
    import doctest

    doctest.testmod()









'''simple docstring'''


import PIL.Image
import PIL.ImageOps
from packaging import version
from PIL import Image


if version.parse(version.parse(PIL.__version__).base_version) >= version.parse('9.1.0'):
				_snake_case : Tuple  				=						{
				    'linear': PIL.Image.Resampling.BILINEAR,
				    'bilinear': PIL.Image.Resampling.BILINEAR,
				    'bicubic': PIL.Image.Resampling.BICUBIC,
				    'lanczos': PIL.Image.Resampling.LANCZOS,
				    'nearest': PIL.Image.Resampling.NEAREST,
				}
else:
				_snake_case : Any  				=						{
				    'linear': PIL.Image.LINEAR,
				    'bilinear': PIL.Image.BILINEAR,
				    'bicubic': PIL.Image.BICUBIC,
				    'lanczos': PIL.Image.LANCZOS,
				    'nearest': PIL.Image.NEAREST,
				}
def 						snake_case_       (UpperCamelCase			:    Optional[int] ):





							'''simple docstring'''


							_a      	=							(images / 2 + 0.5).clamp(0					,		1 )
							_a      	=							images.cpu().permute(0					,		2					,		3					,		1 ).float().numpy()
							_a      	=							numpy_to_pil(UpperCamelCase )
							return images

def 						snake_case_       (UpperCamelCase			:    str ):





							'''simple docstring'''


							if images.ndim == 3:
														_a      	=							images[None, ...]
							_a      	=							(images * 255).round().astype('''uint8''' )
							if images.shape[-1] == 1:
														# special case for grayscale (single channel) images
														_a      	=							[Image.fromarray(image.squeeze()					,		mode='''L''' ) for image in images]
							else:
														_a      	=							[Image.fromarray(UpperCamelCase ) for image in images]

							return pil_images

