

"""simple docstring"""

_UpperCamelCase		     =    {}



def       SCREAMING_SNAKE_CASE							( lowercase__					,					lowercase__					,					lowercase__   )			->						int:

 # if we are absent twice, or late 3 consecutive days,
 # no further prize strings are possible
 if late == 3 or absent == 2:
  return 0

 # if we have no days left, and have not failed any other rules,
 # we have a prize string
 if days == 0:
  return 1

 # No easy solution, so now we need to do the recursive calculation

 # First, check if the combination is already in the cache, and
 # if yes, return the stored value from there since we already
 # know the number of possible prize strings from this point on
 lowerCAmelCase__   :				List[Any] 			=				(days, absent, late)
 if key in cache:
  return cache[key]

 # now we calculate the three possible ways that can unfold from
 # this point on, depending on our attendance today

 # 1) if we are late (but not absent), the "absent" counter stays as
 # it is, but the "late" counter increases by one
 lowerCAmelCase__   :				int 			=				_calculate(days - 1					,					lowercase__					,					late + 1   )

 # 2) if we are absent, the "absent" counter increases by 1, and the
 # "late" counter resets to 0
 lowerCAmelCase__   :				Optional[int] 			=				_calculate(days - 1					,					absent + 1					,					0   )

 # 3) if we are on time, this resets the "late" counter and keeps the
 # absent counter
 lowerCAmelCase__   :				Any 			=				_calculate(days - 1					,					lowercase__					,					0   )

 lowerCAmelCase__   :				int 			=				state_late + state_absent + state_ontime

 lowerCAmelCase__   :				str 			=				prizestrings
 return prizestrings



def       SCREAMING_SNAKE_CASE							( lowercase__ = 3_0   )			->						int:
 return _calculate(lowercase__					,					absent=0					,					late=0   )


if __name__ == "__main__":
    print(solution())









"""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		     =    {
    # 1536-bit
    5: {
        """prime""": int(
            """FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"""
            + """29024E088A67CC74020BBEA63B139B22514A08798E3404DD"""
            + """EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"""
            + """E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"""
            + """EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"""
            + """C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"""
            + """83655D23DCA3AD961C62F356208552BB9ED529077096966D"""
            + """670C354E4ABC9804F1746C08CA237327FFFFFFFFFFFFFFFF""",
            base=1_6,
        ),
        """generator""": 2,
    },
    # 2048-bit
    1_4: {
        """prime""": int(
            """FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"""
            + """29024E088A67CC74020BBEA63B139B22514A08798E3404DD"""
            + """EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"""
            + """E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"""
            + """EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"""
            + """C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"""
            + """83655D23DCA3AD961C62F356208552BB9ED529077096966D"""
            + """670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"""
            + """E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"""
            + """DE2BCBF6955817183995497CEA956AE515D2261898FA0510"""
            + """15728E5A8AACAA68FFFFFFFFFFFFFFFF""",
            base=1_6,
        ),
        """generator""": 2,
    },
    # 3072-bit
    1_5: {
        """prime""": int(
            """FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1"""
            + """29024E088A67CC74020BBEA63B139B22514A08798E3404DD"""
            + """EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"""
            + """E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED"""
            + """EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D"""
            + """C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F"""
            + """83655D23DCA3AD961C62F356208552BB9ED529077096966D"""
            + """670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B"""
            + """E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9"""
            + """DE2BCBF6955817183995497CEA956AE515D2261898FA0510"""
            + """15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64"""
            + """ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7"""
            + """ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B"""
            + """F12FFA06D98A0864D87602733EC86A64521F2B18177B200C"""
            + """BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31"""
            + """43DB5BFCE0FD108E4B82D120A93AD2CAFFFFFFFFFFFFFFFF""",
            base=1_6,
        ),
        """generator""": 2,
    },
    # 4096-bit
    1_6: {
        """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=1_6,
        ),
        """generator""": 2,
    },
    # 6144-bit
    1_7: {
        """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=1_6,
        ),
        """generator""": 2,
    },
    # 8192-bit
    1_8: {
        """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=1_6,
        ),
        """generator""": 2,
    },
}






class 			__a					:





       """simple docstring"""


       def __init__(   self			,					snake_case = 14   ):





        """simple docstring"""

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

        lowerCAmelCase__   :				Any 			=				int(hexlify(urandom(32   )   )			,					base=16   )






       def 			SCREAMING_SNAKE_CASE_	(   self   ):





        """simple docstring"""

        return hex(self.__private_key   )[2:]






       def 			SCREAMING_SNAKE_CASE_	(   self   ):





        """simple docstring"""

        lowerCAmelCase__   :				Optional[int] 			=				pow(self.generator			,					self.__private_key			,					self.prime   )
        return hex(snake_case   )[2:]






       def 			SCREAMING_SNAKE_CASE_	(   self			,					snake_case   ):





        """simple docstring"""

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






       def 			SCREAMING_SNAKE_CASE_	(   self			,					snake_case   ):





        """simple docstring"""

        lowerCAmelCase__   :				int 			=				int(snake_case			,					base=16   )
        if not self.is_valid_public_key(snake_case   ):
         raise ValueError("Invalid public key"   )
        lowerCAmelCase__   :				Tuple 			=				pow(snake_case			,					self.__private_key			,					self.prime   )
        return shaaaa(str(snake_case   ).encode()   ).hexdigest()






       @staticmethod
       def 			SCREAMING_SNAKE_CASE_	(   snake_case			,					snake_case   ):





        """simple docstring"""

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






       @staticmethod
       def 			SCREAMING_SNAKE_CASE_	(   snake_case			,					snake_case			,					snake_case = 14   ):





        """simple docstring"""

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


if __name__ == "__main__":
    import doctest

    doctest.testmod()






