


'''simple docstring'''







def 				lowerCAmelCase__	(    lowerCamelCase					:      str       ):
       _A					:     Union[str, Any]     = 0

       # if input_string is "aba" than new_input_string become "a|b|a"
       _A					:     Optional[Any]     = ''
       _A					:     Dict     = ''

       # append each character + "|" in new_string for range(0, length-1)
       for i in input_string[: len(lowerCamelCase       ) - 1]:
              new_input_string += i + "|"
       # append last character
       new_input_string += input_string[-1]

       # we will store the starting and ending of previous furthest ending palindromic
       # substring
       _A  ,			_A					:     Dict     = 0, 0

       # length[i] shows the length of palindromic substring with center i
       _A					:     Any     = [1 for i in range(len(lowerCamelCase       )       )]

       # for each character in new_string find corresponding palindromic string
       _A					:     Optional[int]     = 0
       for j in range(len(lowerCamelCase       )       ):
              _A					:     Optional[Any]     = 1 if j > r else min(length[l + r - j] // 2  ,r - j + 1       )
              while (
                  j - k >= 0
                  and j + k < len(lowerCamelCase       )
                  and new_input_string[k + j] == new_input_string[j - k]
              ):
                     k += 1

              _A					:     Any     = 2 * k - 1

              # does this string is ending after the previously explored end (that is r) ?
              # if yes the update the new r to the last index of this
              if j + k - 1 > r:
                     _A					:     Dict     = j - k + 1  # noqa: E741
                     _A					:     List[str]     = j + k - 1

              # update max_length and start position
              if max_length < length[j]:
                     _A					:     Union[str, Any]     = length[j]
                     _A					:     Dict     = j

    # create that string
       _A					:     int     = new_input_string[start - max_length // 2 : start + max_length // 2 + 1]
       for i in s:
              if i != "|":
                     output_string += i

       return output_string


if __name__ == "__main__":
   import doctest

   doctest.testmod()










'''simple docstring'''







import operator as op


A				:					List[str]    						=			'''scaler.pt'''
A				:					Optional[int]    						=			'''pytorch_model'''
A				:					Union[str, Any]    						=			'''random_states'''
A				:					List[Any]    						=			'''optimizer'''
A				:					Optional[Any]    						=			'''scheduler'''
A				:					Optional[int]    						=			'''pytorch_model.bin'''
A				:					List[str]    						=			'''pytorch_model.bin.index.json'''
A				:					List[Any]    						=			'''model.safetensors'''
A				:					int    						=			'''model.safetensors.index.json'''
A				:					List[str]    						=			'''1.10.2'''
A				:					str    						=			'''py38'''
A				:					int    						=			'''4.17.0'''
A				:					Tuple    						=			['''ml.p3.16xlarge''', '''ml.p3dn.24xlarge''', '''ml.p4dn.24xlarge''']
A				:					Union[str, Any]    						=			['''FULL_SHARD''', '''SHARD_GRAD_OP''', '''NO_SHARD''', '''HYBRID_SHARD''', '''HYBRID_SHARD_ZERO2''']
A				:					Optional[Any]    						=			['''TRANSFORMER_BASED_WRAP''', '''SIZE_BASED_WRAP''', '''NO_WRAP''']
A				:					Dict    						=			['''BACKWARD_PRE''', '''BACKWARD_POST''', '''NO_PREFETCH''']
A				:					Any    						=			['''FULL_STATE_DICT''', '''LOCAL_STATE_DICT''', '''SHARDED_STATE_DICT''']
A				:					Tuple    						=			'''2.0.1'''
A				:					List[str]    						=			['''pdsh''', '''standard''', '''openmpi''', '''mvapich''']
A				:					Union[str, Any]    						=			['''default''', '''reduce-overhead''', '''max-autotune''']

A				:					List[Any]    						=			{'''>''': op.gt, '''>=''': op.ge, '''==''': op.eq, '''!=''': op.ne, '''<=''': op.le, '''<''': op.lt}

# These are the args for `torch.distributed.launch` for pytorch < 1.9
A				:					Tuple    						=			[
    '''nnodes''',
    '''nproc_per_node''',
    '''rdzv_backend''',
    '''rdzv_endpoint''',
    '''rdzv_id''',
    '''rdzv_conf''',
    '''standalone''',
    '''max_restarts''',
    '''monitor_interval''',
    '''start_method''',
    '''role''',
    '''module''',
    '''m''',
    '''no_python''',
    '''run_path''',
    '''log_dir''',
    '''r''',
    '''redirects''',
    '''t''',
    '''tee''',
    '''node_rank''',
    '''master_addr''',
    '''master_port''',
]

A				:					List[str]    						=			['''DEEPSPEED''', '''MULTI_GPU''', '''FSDP''', '''MEGATRON_LM''']
A				:					Any    						=			['''DEEPSPEED''', '''MULTI_XPU''', '''FSDP''']






