






"""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

SCREAMING_SNAKE_CASE						:						Optional[int]					   =       {
    # 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       snake_case_       :



	"""simple docstring"""

	def __init__(      self  ,					__a = 14						):


					"""simple docstring"""

					if group not in primes:
									raise ValueError('Unsupported Group'						)
					A__							 =       primes[group]['prime']
					A__							 =       primes[group]['generator']

					A__							 =       int(hexlify(urandom(32						)						)  ,					base=16						)


	def       _UpperCAmelCase						(      self						):


					"""simple docstring"""

					return hex(self.__private_key						)[2:]


	def       _UpperCAmelCase						(      self						):


					"""simple docstring"""

					A__							 =       pow(self.generator  ,					self.__private_key  ,					self.prime						)
					return hex(__a						)[2:]


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

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


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					A__							 =       int(__a  ,					base=16						)
					if not self.is_valid_public_key(__a						):
									raise ValueError('Invalid public key'						)
					A__							 =       pow(__a  ,					self.__private_key  ,					self.prime						)
					return shaaaa(str(__a						).encode()						).hexdigest()


	@staticmethod
	def       _UpperCAmelCase						(      __a  ,					__a						):


					"""simple docstring"""

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






	@staticmethod
	def       _UpperCAmelCase						(      __a  ,					__a  ,					__a = 14						):


					"""simple docstring"""

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


if __name__ == "__main__":
					import doctest

					doctest.testmod()










"""simple docstring"""






class       snake_case_       :



	"""simple docstring"""

	def __init__(      self  ,					__a  ,					__a						):


					"""simple docstring"""

					A__							 =       name
					A__							 =       val


	def __str__(      self						):


					"""simple docstring"""

					return f'''{self.__class__.__name__}({self.name}, {self.val})'''






	def __lt__(      self  ,					__a						):


					"""simple docstring"""

					return self.val < other.val





class       snake_case_       :



	"""simple docstring"""

	def __init__(      self  ,					__a						):


					"""simple docstring"""

					A__							 =       {}
					A__							 =       {}
					A__							 =       self.build_heap(__a						)


	def __getitem__(      self  ,					__a						):


					"""simple docstring"""

					return self.get_value(__a						)


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					return (idx - 1) // 2


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					return idx * 2 + 1


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					return idx * 2 + 2


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					return self.heap_dict[key]


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					A__							 =       len(__a						) - 1
					A__							 =       self.get_parent_idx(__a						)

					for idx, i in enumerate(__a						):
									A__							 =       idx
									A__							 =       i.val

					for i in range(__a  ,					-1  ,					-1						):
									self.sift_down(__a  ,					__a						)
					return array


	def       _UpperCAmelCase						(      self  ,					__a  ,					__a						):


					"""simple docstring"""

					while True:
									A__							 =       self.get_left_child_idx(__a						)  # noqa: E741
									A__							 =       self.get_right_child_idx(__a						)

									A__							 =       idx
									if l < len(__a						) and array[l] < array[idx]:
													A__							 =       l
									if r < len(__a						) and array[r] < array[smallest]:
													A__							 =       r

									if smallest != idx:
													A__ ,			A__							 =       array[smallest], array[idx]
													(
													    (
													    A__
													) ,			(
													    A__
													) ,			
													)							 =       (
													    self.idx_of_element[array[smallest]],
													    self.idx_of_element[array[idx]],
													)
													A__							 =       smallest
									else:
													break


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					A__							 =       self.get_parent_idx(__a						)
					while p >= 0 and self.heap[p] > self.heap[idx]:
									A__ ,			A__							 =       self.heap[idx], self.heap[p]
									A__ ,			A__							 =       (
									    self.idx_of_element[self.heap[idx]],
									    self.idx_of_element[self.heap[p]],
									)
									A__							 =       p
									A__							 =       self.get_parent_idx(__a						)


	def       _UpperCAmelCase						(      self						):


					"""simple docstring"""

					return self.heap[0]


	def       _UpperCAmelCase						(      self						):


					"""simple docstring"""

					A__ ,			A__							 =       self.heap[-1], self.heap[0]
					A__ ,			A__							 =       (
					    self.idx_of_element[self.heap[-1]],
					    self.idx_of_element[self.heap[0]],
					)

					A__							 =       self.heap.pop()
					del self.idx_of_element[x]
					self.sift_down(0  ,					self.heap						)
					return x


	def       _UpperCAmelCase						(      self  ,					__a						):


					"""simple docstring"""

					self.heap.append(__a						)
					A__							 =       len(self.heap						) - 1
					A__							 =       node.val
					self.sift_up(len(self.heap						) - 1						)


	def       _UpperCAmelCase						(      self						):


					"""simple docstring"""

					return len(self.heap						) == 0






	def       _UpperCAmelCase						(      self  ,					__a  ,					__a						):


					"""simple docstring"""

					assert (
					    self.heap[self.idx_of_element[node]].val > new_value
					), "newValue must be less that current value"
					A__							 =       new_value
					A__							 =       new_value
					self.sift_up(self.idx_of_element[node]						)





SCREAMING_SNAKE_CASE						:						List[str]					   =       Node('''R''', -1)
SCREAMING_SNAKE_CASE						:						Tuple					   =       Node('''B''', 6)
SCREAMING_SNAKE_CASE						:						List[Any]					   =       Node('''A''', 3)
SCREAMING_SNAKE_CASE						:						int					   =       Node('''X''', 1)
SCREAMING_SNAKE_CASE						:						Union[str, Any]					   =       Node('''E''', 4)

# Use one of these two ways to generate Min-Heap

# Generating Min-Heap from array
SCREAMING_SNAKE_CASE						:						str					   =       MinHeap([r, b, a, x, e])

# Generating Min-Heap by Insert method
# myMinHeap.insert(a)
# myMinHeap.insert(b)
# myMinHeap.insert(x)
# myMinHeap.insert(r)
# myMinHeap.insert(e)

# Before
print('''Min Heap - before decrease key''')
for i in my_min_heap.heap:
					print(i)

print('''Min Heap - After decrease key of node [B -> -17]''')
my_min_heap.decrease_key(b, -17)

# After
for i in my_min_heap.heap:
					print(i)

if __name__ == "__main__":
					import doctest

					doctest.testmod()


