code: 
  
  
  
  
  
  import collections
  
  from .utils import ExplicitEnum, is_torch_available, logging
  
  
  if is_torch_available():
  				import torch
  
  
  __lowerCAmelCase     =			logging.get_logger(__name__)
  
  
  
  
  class   _UpperCAmelCase	:
  
  
  
  
  					def __init__(						self    ,      __lowerCAmelCase    ,      __lowerCAmelCase=21    ,      __lowerCAmelCase=[]    ,      __lowerCAmelCase=None       )						->  List[Any]:
  							UpperCamelCase__         =	model
  							UpperCamelCase__         =	trace_batch_nums
  							UpperCamelCase__         =	abort_after_batch_num
  
  							# keep a LIFO buffer of frames to dump as soon as inf/nan is encountered to give context to the problem emergence
  							UpperCamelCase__         =	collections.deque([]    ,      __lowerCAmelCase       )
  							UpperCamelCase__         =	[]
  							UpperCamelCase__         =	0
  							UpperCamelCase__         =	0
  							UpperCamelCase__         =	False
  							UpperCamelCase__         =	"""                 """
  
  							self.analyse_model()
  
  							self.register_forward_hook()
  
  
  
  
  					def 	snake_case_		(						self    ,      __lowerCAmelCase=None       )						->  Tuple:
  							if frame is not None:
  									self.expand_frame(__lowerCAmelCase       )
  							self.frames.append("""\n""".join(self.frame       )       )
  							UpperCamelCase__         =	[]  # start a new frame
  
  
  
  
  					def 	snake_case_		(						self    ,      __lowerCAmelCase       )						->  Tuple:
  							self.frame.append(__lowerCAmelCase       )
  
  
  
  
  					def 	snake_case_		(						self       )						->  Union[str, Any]:
  							print("""\n""".join(self.frames       )       )
  							UpperCamelCase__         =	[]
  
  
  
  
  					def 	snake_case_		(						self       )						->  Tuple:
  							UpperCamelCase__         =	[]
  
  
  
  
  					def 	snake_case_		(						self       )						->  str:
  							print(F"""\nDetected inf/nan during batch_number={self.batch_number}"""       )
  							print(F"""Last {len(self.frames       )} forward frames:"""       )
  							print(F"""{'abs min':8} {'abs max':8} metadata"""       )
  							print("""\n""".join(self.frames       )       )
  							print("""\n\n"""       )
  							UpperCamelCase__         =	[]
  
  
  
  
  					def 	snake_case_		(						self       )						->  int:
  							# extract the fully qualified module names, to be able to report at run time. e.g.:
  							# encoder.block.2.layer.0.SelfAttention.o
  							#
  							# for shared weights only the first shared module name will be registered
  							UpperCamelCase__         =	{m: name for name, m in self.model.named_modules()}
  							# self.longest_module_name = max(len(v) for v in self.module_names.values())
  
  
  
  
  					def 	snake_case_		(						self    ,      __lowerCAmelCase    ,      __lowerCAmelCase       )						->  List[Any]:
  							if torch.is_tensor(__lowerCAmelCase       ):
  									self.expand_frame(get_abs_min_max(__lowerCAmelCase    ,      __lowerCAmelCase       )       )
  									if detect_overflow(__lowerCAmelCase    ,      __lowerCAmelCase       ):
  											UpperCamelCase__         =	True
  							elif var is None:
  									self.expand_frame(F"""{'None':>17} {ctx}"""       )
  							else:
  									self.expand_frame(F"""{'not a tensor':>17} {ctx}"""       )
  
  
  
  
  					def 	snake_case_		(						self       )						->  Optional[Any]:
  							self.expand_frame(F"""\n\n{self.prefix} *** Starting batch number={self.batch_number} ***"""       )
  							self.expand_frame(F"""{'abs min':8} {'abs max':8} metadata"""       )
  
  
  
  
  					def 	snake_case_		(						self       )						->  Optional[Any]:
  							self.expand_frame(F"""{self.prefix} *** Finished batch number={self.batch_number-1} ***\n\n"""       )
  
  
  
  
  					def 	snake_case_		(						self    ,      __lowerCAmelCase    ,      __lowerCAmelCase    ,      __lowerCAmelCase       )						->  List[Any]:
  							self.expand_frame(F"""{self.prefix} {self.module_names[module]} {module.__class__.__name__}"""       )
  
  							# params
  							for name, p in module.named_parameters(recurse=__lowerCAmelCase       ):
  									self.analyse_variable(__lowerCAmelCase    ,      __lowerCAmelCase       )
  
  							# inputs
  							if isinstance(__lowerCAmelCase    ,      __lowerCAmelCase       ):
  									for i, x in enumerate(__lowerCAmelCase       ):
  											self.analyse_variable(__lowerCAmelCase    ,      F"""input[{i}]"""       )
  							else:
  									self.analyse_variable(__lowerCAmelCase    ,      """input"""       )
  
  							# outputs
  							if isinstance(__lowerCAmelCase    ,      __lowerCAmelCase       ):
  									for i, x in enumerate(__lowerCAmelCase       ):
  											# possibly a tuple of tuples
  											if isinstance(__lowerCAmelCase    ,      __lowerCAmelCase       ):
  													for j, y in enumerate(__lowerCAmelCase       ):
  															self.analyse_variable(__lowerCAmelCase    ,      F"""output[{i}][{j}]"""       )
  											else:
  													self.analyse_variable(__lowerCAmelCase    ,      F"""output[{i}]"""       )
  							else:
  									self.analyse_variable(__lowerCAmelCase    ,      """output"""       )
  
  							self.save_frame()
  
  
  
  
  					def 	snake_case_		(						self       )						->  Tuple:
  							self.model.apply(self._register_forward_hook       )
  
  
  
  
  					def 	snake_case_		(						self    ,      __lowerCAmelCase       )						->  Tuple:
  							module.register_forward_hook(self.forward_hook       )
  
  
  
  
  					def 	snake_case_		(						self    ,      __lowerCAmelCase    ,      __lowerCAmelCase    ,      __lowerCAmelCase       )						->  Optional[Any]:
  							# - input is a tuple of packed inputs (could be non-Tensors)
  							# - output could be a Tensor or a tuple of Tensors and non-Tensors
  
  							UpperCamelCase__         =	False
  
  							UpperCamelCase__         =	True if self.batch_number in self.trace_batch_nums else False
  							if trace_mode:
  									self.reset_saved_frames()
  
  							if self.total_calls == 0:
  									self.batch_start_frame()
  							self.total_calls += 1
  
  							# count batch numbers - the very first forward hook of the batch will be called when the
  							# batch completes - i.e. it gets called very last - we know this batch has finished
  							if module == self.model:
  									self.batch_number += 1
  									UpperCamelCase__         =	True
  
  							self.create_frame(__lowerCAmelCase    ,      __lowerCAmelCase    ,      __lowerCAmelCase       )
  
  							# if last_frame_of_batch:
  							#     self.batch_end_frame()
  
  							if trace_mode:
  									self.trace_frames()
  
  							if last_frame_of_batch:
  									self.batch_start_frame()
  
  							if self.detected_overflow and not trace_mode:
  									self.dump_saved_frames()
  
  									# now we can abort, as it's pointless to continue running
  									raise ValueError(
  									    """DebugUnderflowOverflow: inf/nan detected, aborting as there is no point running further. """
  									    """Please scroll up above this traceback to see the activation values prior to this event."""       )
  
  							# abort after certain batch if requested to do so
  							if self.abort_after_batch_num is not None and self.batch_number > self.abort_after_batch_num:
  									raise ValueError(
  									    F"""DebugUnderflowOverflow: aborting after {self.batch_number} batches due to"""
  									    F""" `abort_after_batch_num={self.abort_after_batch_num}` arg"""       )
  
  
  
  def     a						(      _lowercase   :     List[Any] ,						_lowercase   :     List[Any]       )     ->Union[str, Any]:
  		UpperCamelCase__         =	var.abs()
  		return F"""{abs_var.min():8.2e} {abs_var.max():8.2e} {ctx}"""
  
  def     a						(      _lowercase   :     Any ,						_lowercase   :     Any       )     ->Optional[int]:
  		UpperCamelCase__         =	False
  		if torch.isnan(_lowercase       ).any().item():
  				UpperCamelCase__         =	True
  				print(F"""{ctx} has nans"""       )
  		if torch.isinf(_lowercase       ).any().item():
  				UpperCamelCase__         =	True
  				print(F"""{ctx} has infs"""       )
  
  		# if needed to monitor large elements can enable the following
  		if 0:  # and detected:
  				UpperCamelCase__         =	var[torch.ge(var.abs() ,						1_0_0       )]
  				if naaa.numel() > 0:
  						print(F"""{ctx}:  n100={naaa.numel()}"""       )
  				UpperCamelCase__         =	var[torch.ge(var.abs() ,						1_0_0_0       )]
  				if naaaa.numel() > 0:
  						print(F"""{ctx}: n1000={naaaa.numel()}"""       )
  				UpperCamelCase__         =	var[torch.ge(var.abs() ,						1_0_0_0_0       )]
  				if naaaaa.numel() > 0:
  						print(F"""{ctx}: n10000={naaaaa.numel()}"""       )
  
  		if 0:
  				print(F"""min={var.min():9.2e} max={var.max():9.2e}"""       )
  
  		if 0:
  				print(F"""min={var.min():9.2e} max={var.max():9.2e} var={var.var():9.2e} mean={var.mean():9.2e} ({ctx})"""       )
  
  		return detected
  
  
  
  
  class   _UpperCAmelCase	(   _lowercase					):
  					__A          =   "underflow_overflow"
  					__A          =   "tpu_metrics_debug"
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  def     a						(      _lowercase   :     int ,						_lowercase   :     int       )     ->int:
  		UpperCamelCase__         =	1.0
  		for i in range(1 ,						r + 1       ):
  				ret *= (n + 1 - i) / i
  		return round(_lowercase       )
  
  def     a						(      _lowercase   :     int       )     ->int:
  		return choose(8 + n ,						_lowercase       ) + choose(9 + n ,						_lowercase       ) - 1_0
  
  def     a						(      _lowercase   :     int       )     ->int:
  		return sum(non_bouncy_exact(_lowercase       ) for i in range(1 ,						n + 1       )       )
  
  def     a						(      _lowercase   :     int = 1_0_0       )     ->int:
  		return non_bouncy_upto(_lowercase       )
  
  
  if __name__ == "__main__":
  				print(f"""{solution() = }""")
  
  
  
  
  
  