'''simple docstring'''

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__     :	Union[str, Any]				=			{
    # 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 				_lowercase	:
      '''simple docstring'''


      def __init__(				self					,lowerCamelCase_ = 14							)			->			None:



         '''simple docstring'''



         if group not in primes:
            raise ValueError('''Unsupported Group'''							)
         UpperCAmelCase__							:				Optional[int]   				=  primes[group]['''prime''']
         UpperCAmelCase__							:				List[str]   				=  primes[group]['''generator''']

         UpperCAmelCase__							:				str   				=  int(hexlify(urandom(32							)							)					,base=16							)




      def 		lowerCAmelCase__					(				self							)			->			str:



         '''simple docstring'''



         return hex(self.__private_key							)[2:]




      def 		lowerCAmelCase__					(				self							)			->			str:



         '''simple docstring'''



         UpperCAmelCase__							:				Tuple   				=  pow(self.generator					,self.__private_key					,self.prime							)
         return hex(lowerCamelCase_							)[2:]




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_							)			->			bool:



         '''simple docstring'''



         return (
             2 <= key <= self.prime - 2
             and pow(lowerCamelCase_					,(self.prime - 1) // 2					,self.prime							) == 1
         )




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_							)			->			str:



         '''simple docstring'''



         UpperCAmelCase__							:				Optional[Any]   				=  int(lowerCamelCase_					,base=16							)
         if not self.is_valid_public_key(lowerCamelCase_							):
            raise ValueError('''Invalid public key'''							)
         UpperCAmelCase__							:				List[Any]   				=  pow(lowerCamelCase_					,self.__private_key					,self.prime							)
         return shaaaa(str(lowerCamelCase_							).encode()							).hexdigest()




      @staticmethod
      def 		lowerCAmelCase__					(				lowerCamelCase_					,lowerCamelCase_							)			->			bool:



         '''simple docstring'''



         return (
             2 <= remote_public_key_str <= prime - 2
             and pow(lowerCamelCase_					,(prime - 1) // 2					,lowerCamelCase_							) == 1
         )




      @staticmethod
      def 		lowerCAmelCase__					(				lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_ = 14							)			->			str:



         '''simple docstring'''



         UpperCAmelCase__							:				List[Any]   				=  int(lowerCamelCase_					,base=16							)
         UpperCAmelCase__							:				Optional[int]   				=  int(lowerCamelCase_					,base=16							)
         UpperCAmelCase__							:				Optional[int]   				=  primes[group]['''prime''']
         if not DiffieHellman.is_valid_public_key_static(lowerCamelCase_					,lowerCamelCase_							):
            raise ValueError('''Invalid public key'''							)
         UpperCAmelCase__							:				Any   				=  pow(lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_							)
         return shaaaa(str(lowerCamelCase_							).encode()							).hexdigest()


if __name__ == "__main__":
  import doctest

  doctest.testmod()





'''simple docstring'''

import torch

from transformers import AutoModel


class 				_lowercase	(      torch.nn.Module   ):
      '''simple docstring'''


      def __init__(				self					,lowerCamelCase_="sayef/fsner-bert-base-uncased"							)			->			Dict:



         '''simple docstring'''



         super(lowerCamelCase_					,self							).__init__()

         UpperCAmelCase__							:				Union[str, Any]   				=  AutoModel.from_pretrained(lowerCamelCase_					,return_dict=lowerCamelCase_							)
         UpperCAmelCase__							:				str   				=  torch.nn.CosineSimilarity(3					,1e-08							)
         UpperCAmelCase__							:				int   				=  torch.nn.Softmax(dim=1							)




      def 		lowerCAmelCase__					(				self					,**lowerCamelCase_							)			->			Optional[Any]:



         '''simple docstring'''



         return self.bert(**lowerCamelCase_							).last_hidden_state




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_							)			->			str:



         '''simple docstring'''



         return token_embeddings.sum(2					,keepdim=lowerCamelCase_							)




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_=1							)			->			int:



         '''simple docstring'''



         return self.softmax(T * self.cos(lowerCamelCase_					,lowerCamelCase_							)							)




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_					,lowerCamelCase_							)			->			Tuple:



         '''simple docstring'''



         UpperCAmelCase__							:				List[Any]   				=  W_supports['''sizes'''].tolist()
         UpperCAmelCase__							:				Union[str, Any]   				=  W_supports['''start_token_id'''].item()
         UpperCAmelCase__							:				int   				=  W_supports['''end_token_id'''].item()

         del W_supports["sizes"]
         del W_supports["start_token_id"]
         del W_supports["end_token_id"]

         UpperCAmelCase__							:				Any   				=  self.BERT(**lowerCamelCase_							)
         UpperCAmelCase__							:				Any   				=  self.BERT(**lowerCamelCase_							)

         UpperCAmelCase__							:				Any   				=  None
         UpperCAmelCase__							:				Tuple   				=  None

         UpperCAmelCase__							:				Dict   				=  W_supports['''input_ids'''] == start_token_id
         UpperCAmelCase__							:				Any   				=  W_supports['''input_ids'''] == end_token_id

         for i, size in enumerate(lowerCamelCase_							):
            if i == 0:
               UpperCAmelCase__							:				int   				=  0
            else:
               UpperCAmelCase__							:				str   				=  support_sizes[i - 1]

            UpperCAmelCase__							:				Dict   				=  S[s : s + size][start_token_masks[s : s + size]]
            UpperCAmelCase__							:				Union[str, Any]   				=  S[s : s + size][end_token_masks[s : s + size]]

            UpperCAmelCase__							:				int   				=  torch.matmul(q[i]					,s_start.T							).sum(1							).softmax(0							)
            UpperCAmelCase__							:				int   				=  torch.matmul(q[i]					,s_end.T							).sum(1							).softmax(0							)

            if p_starts is not None:
               UpperCAmelCase__							:				str   				=  torch.vstack((p_starts, p_start)							)
               UpperCAmelCase__							:				Optional[int]   				=  torch.vstack((p_ends, p_end)							)
            else:
               UpperCAmelCase__							:				Union[str, Any]   				=  p_start
               UpperCAmelCase__							:				int   				=  p_end

         return p_starts, p_ends




