'''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	: List[str]    		=  {
    # 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__		:


						def __init__( self			:       Optional[Any]					,	UpperCamelCase__			:       int = 14		):





												'''simple docstring'''





												if group not in primes:
																		raise ValueError('''Unsupported Group'''		)
												SCREAMING_SNAKE_CASE							:					Any           =							primes[group]["prime"]
												SCREAMING_SNAKE_CASE							:					str           =							primes[group]["generator"]

												SCREAMING_SNAKE_CASE							:					List[str]           =							int(hexlify(urandom(32		)		)					,	base=16		)


						def  __A ( self			:       str		):





												'''simple docstring'''





												return hex(self.__private_key		)[2:]


						def  __A ( self			:       int		):





												'''simple docstring'''





												SCREAMING_SNAKE_CASE							:					Dict           =							pow(self.generator					,	self.__private_key					,	self.prime		)
												return hex(__lowerCamelCase		)[2:]


						def  __A ( self			:       Dict					,	UpperCamelCase__			:       int		):





												'''simple docstring'''





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


						def  __A ( self			:       Any					,	UpperCamelCase__			:       str		):





												'''simple docstring'''





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


						@staticmethod
						def  __A ( UpperCamelCase__			:       int					,	UpperCamelCase__			:       int		):





												'''simple docstring'''





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



						@staticmethod
						def  __A ( UpperCamelCase__			:       str					,	UpperCamelCase__			:       str					,	UpperCamelCase__			:       int = 14		):





												'''simple docstring'''





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


if __name__ == "__main__":
					import doctest

					doctest.testmod()






from __future__ import annotations

import math
from collections import Counter
from string import ascii_lowercase
def    A			(					_lowercase		):
						SCREAMING_SNAKE_CASE       ,						SCREAMING_SNAKE_CASE							:					Union[str, Any]           =							analyze_text(_lowercase		)
						SCREAMING_SNAKE_CASE							:					Any           =							list(''' ''' + ascii_lowercase		)
						# what is our total sum of probabilities.
						SCREAMING_SNAKE_CASE							:					Tuple           =							sum(single_char_strings.values()		)

						# one length string
						SCREAMING_SNAKE_CASE							:					Tuple           =							0
						# for each alpha we go in our dict and if it is in it we calculate entropy
						for ch in my_alphas:
												if ch in single_char_strings:
																		SCREAMING_SNAKE_CASE							:					Tuple           =							single_char_strings[ch]
																		SCREAMING_SNAKE_CASE							:					List[str]           =							my_str / all_sum
																		my_fir_sum += prob * math.loga(_lowercase		)  # entropy formula.

    # print entropy
						print(f"""{round(-1 * my_fir_sum		):.1f}"""		)

						# two len string
						SCREAMING_SNAKE_CASE							:					Optional[Any]           =							sum(two_char_strings.values()		)
						SCREAMING_SNAKE_CASE							:					List[str]           =							0
						# for each alpha (two in size) calculate entropy.
						for cha in my_alphas:
												for cha in my_alphas:
																		SCREAMING_SNAKE_CASE							:					Union[str, Any]           =							cha + cha
																		if sequence in two_char_strings:
																								SCREAMING_SNAKE_CASE							:					Any           =							two_char_strings[sequence]
																								SCREAMING_SNAKE_CASE							:					Dict           =							int(_lowercase		) / all_sum
																								my_sec_sum += prob * math.loga(_lowercase		)

    # print second entropy
						print(f"""{round(-1 * my_sec_sum		):.1f}"""		)

						# print the difference between them
						print(f"""{round((-1 * my_sec_sum) - (-1 * my_fir_sum)		):.1f}"""		)
def    A			(					_lowercase		):
						SCREAMING_SNAKE_CASE							:					Tuple           =							Counter()  # type: ignore
						SCREAMING_SNAKE_CASE							:					Any           =							Counter()  # type: ignore
						single_char_strings[text[-1]] += 1

						# first case when we have space at start.
						two_char_strings[" " + text[0]] += 1
						for i in range(0	,						len(_lowercase		) - 1		):
												single_char_strings[text[i]] += 1
												two_char_strings[text[i : i + 2]] += 1
						return single_char_strings, two_char_strings
def    A			(					):
						import doctest

						doctest.testmod()
						# text = (
						#     "Had repulsive dashwoods suspicion sincerity but advantage now him. Remark "
						#     "easily garret nor nay. Civil those mrs enjoy shy fat merry. You greatest "
						#     "jointure saw horrible. He private he on be imagine suppose. Fertile "
						#     "beloved evident through no service elderly is. Blind there if every no so "
						#     "at. Own neglected you preferred way sincerity delivered his attempted. To "
						#     "of message cottage windows do besides against uncivil.  Delightful "
						#     "unreserved impossible few estimating men favourable see entreaties. She "
						#     "propriety immediate was improving. He or entrance humoured likewise "
						#     "moderate. Much nor game son say feel. Fat make met can must form into "
						#     "gate. Me we offending prevailed discovery. "
						# )

						# calculate_prob(text)


if __name__ == "__main__":
					main()





