


'''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

lowerCamelCase__					=   {
    # 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     :   str		,     lowerCamelCase__     :   int = 14       )      ->None:



					'''simple docstring'''







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

					_UpperCAmelCase						:				Optional[int]	    =					int(hexlify(urandom(32       )       )		,     base=16       )




			def 							lowerCAmelCase__			(						self     :   Union[str, Any]       )      ->str:



					'''simple docstring'''







					return hex(self.__private_key       )[2:]




			def 							lowerCAmelCase__			(						self     :   Optional[int]       )      ->str:



					'''simple docstring'''







					_UpperCAmelCase						:				List[Any]	    =					pow(self.generator		,     self.__private_key		,     self.prime       )
					return hex(lowerCamelCase__       )[2:]




			def 							lowerCAmelCase__			(						self     :   Tuple		,     lowerCamelCase__     :   int       )      ->bool:



					'''simple docstring'''







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




			def 							lowerCAmelCase__			(						self     :   Any		,     lowerCamelCase__     :   str       )      ->str:



					'''simple docstring'''







					_UpperCAmelCase						:				Optional[int]	    =					int(lowerCamelCase__		,     base=16       )
					if not self.is_valid_public_key(lowerCamelCase__       ):
							raise ValueError("Invalid public key"       )
					_UpperCAmelCase						:				int	    =					pow(lowerCamelCase__		,     self.__private_key		,     self.prime       )
					return shaaaa(str(lowerCamelCase__       ).encode()       ).hexdigest()




			@staticmethod
			def 							lowerCAmelCase__			(						lowerCamelCase__     :   int		,     lowerCamelCase__     :   int       )      ->bool:



					'''simple docstring'''







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






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



					'''simple docstring'''







					_UpperCAmelCase						:				str	    =					int(lowerCamelCase__		,     base=16       )
					_UpperCAmelCase						:				Dict	    =					int(lowerCamelCase__		,     base=16       )
					_UpperCAmelCase						:				str	    =					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'''


#
# This a `torch.distributed` diagnostics script that checks that all GPUs in the cluster (one or
# many nodes) can talk to each other via nccl and allocate gpu memory.
#
# To run first adjust the number of processes and nodes:
#
# python -m torch.distributed.run --nproc_per_node 2 --nnodes 1 torch-distributed-gpu-test.py
#
# You may need to add --master_addr $MASTER_ADDR --master_port $MASTER_PORT if using a custom addr:port
#
# You can also use the rdzv API: --rdzv_endpoint $MASTER_ADDR:$MASTER_PORT --rdzv_backend c10d
#
# use torch.distributed.launch instead of torch.distributed.run for torch < 1.9
#
# If you get a hanging in `barrier` calls you have some network issues, you may try to debug this with:
#
# NCCL_DEBUG=INFO python -m torch.distributed.run --nproc_per_node 2 --nnodes 1 torch-distributed-gpu-test.py
#
# which should tell you what's going on behind the scenes.
#
#
# This script can be run via `srun` in the SLURM environment as well. Here is a SLURM script that
# runs on 2 nodes of 4 gpus per node:
#
# #SBATCH --job-name=test-nodes        # name
# #SBATCH --nodes=2                    # nodes
# #SBATCH --ntasks-per-node=1          # crucial - only 1 task per dist per node!
# #SBATCH --cpus-per-task=10           # number of cores per tasks
# #SBATCH --gres=gpu:4                 # number of gpus
# #SBATCH --time 0:05:00               # maximum execution time (HH:MM:SS)
# #SBATCH --output=%x-%j.out           # output file name
#
# GPUS_PER_NODE=4
# MASTER_ADDR=$(scontrol show hostnames $SLURM_JOB_NODELIST | head -n 1)
# MASTER_PORT=6000
#
# srun --jobid $SLURM_JOBID bash -c 'python -m torch.distributed.run \
# --nproc_per_node $GPUS_PER_NODE --nnodes $SLURM_NNODES --node_rank $SLURM_PROCID \
# --master_addr $MASTER_ADDR --master_port $MASTER_PORT \
# torch-distributed-gpu-test.py'
#

import fcntl
import os
import socket

import torch
import torch.distributed as dist






def        __lowerCAmelCase       (*__lowerCAmelCase      ):
		with open(__lowerCAmelCase					,       "r"      ) as fh:
				fcntl.flock(__lowerCAmelCase					,       fcntl.LOCK_EX      )
				try:
						print(*__lowerCAmelCase      )
				finally:
						fcntl.flock(__lowerCAmelCase					,       fcntl.LOCK_UN      )


lowerCamelCase__					=   int(os.environ['LOCAL_RANK'])
torch.cuda.set_device(local_rank)
lowerCamelCase__					=   torch.device('cuda', local_rank)
lowerCamelCase__					=   socket.gethostname()

lowerCamelCase__					=   F'''[{hostname}-{local_rank}]'''

try:
						# test distributed
						dist.init_process_group('nccl')
						dist.all_reduce(torch.ones(1).to(device), op=dist.ReduceOp.SUM)
						dist.barrier()

						# test cuda is available and can allocate memory
						torch.cuda.is_available()
						torch.ones(1).cuda(local_rank)

						# global rank
						lowerCamelCase__					=   dist.get_rank()
						lowerCamelCase__					=   dist.get_world_size()

						printflock(F'''{gpu} is OK (global rank: {rank}/{world_size})''')

						dist.barrier()
						if rank == 0:
												printflock(F'''pt={torch.__version__}, cuda={torch.version.cuda}, nccl={torch.cuda.nccl.version()}''')

except Exception:
						printflock(F'''{gpu} is broken''')
						raise



