




"""simple docstring"""


import torch
from torch import nn






class  lowercase(					nn.Module			):







 '''simple docstring'''





 def __init__(    self:		Any,				a_:		List[str],				a_:		Union[str, Any],				a_:		int,				a_:		int,				a_:		List[Any]=1,				a_:		Union[str, Any]=False		):




   '''simple docstring'''



   super().__init__()

   _snake_case							:		int								=  n_token
   _snake_case							:		Tuple								=  d_embed
   _snake_case							:		List[str]								=  d_proj

   _snake_case							:		Optional[int]								=  cutoffs + [n_token]
   _snake_case							:		Any								=  [0] + self.cutoffs
   _snake_case							:		Tuple								=  div_val

   _snake_case							:		Optional[int]								=  self.cutoffs[0]
   _snake_case							:		Union[str, Any]								=  len(self.cutoffs		) - 1
   _snake_case							:		Union[str, Any]								=  self.shortlist_size + self.n_clusters

   if self.n_clusters > 0:
     _snake_case							:		List[Any]								=  nn.Parameter(torch.zeros(self.n_clusters,				self.d_embed		)		)
     _snake_case							:		Tuple								=  nn.Parameter(torch.zeros(self.n_clusters		)		)

   _snake_case							:		Any								=  nn.ModuleList()
   _snake_case							:		Optional[Any]								=  nn.ParameterList()

   if div_val == 1:
     for i in range(len(self.cutoffs		)		):
       if d_proj != d_embed:
         self.out_projs.append(nn.Parameter(torch.FloatTensor(a_,				a_		)		)		)
       else:
         self.out_projs.append(a_		)

     self.out_layers.append(nn.Linear(a_,				a_		)		)
   else:
     for i in range(len(self.cutoffs		)		):
       _snake_case		, _snake_case							:		List[Any]								=  self.cutoff_ends[i], self.cutoff_ends[i + 1]
       _snake_case							:		Union[str, Any]								=  d_embed // (div_val**i)

       self.out_projs.append(nn.Parameter(torch.FloatTensor(a_,				a_		)		)		)

       self.out_layers.append(nn.Linear(a_,				r_idx - l_idx		)		)

   _snake_case							:		Optional[int]								=  keep_order


 def 			UpperCamelCase_       (    self:		str,				a_:		Union[str, Any],				a_:		Dict,				a_:		int,				a_:		Tuple		):




   '''simple docstring'''



   if proj is None:
     _snake_case							:		List[Any]								=  nn.functional.linear(a_,				a_,				bias=a_		)
   else:
     # if CUDA_MAJOR <= 9 and CUDA_MINOR <= 1:
     _snake_case							:		List[Any]								=  nn.functional.linear(a_,				proj.t().contiguous()		)
     _snake_case							:		Tuple								=  nn.functional.linear(a_,				a_,				bias=a_		)
     # else:
     #     logit = torch.einsum('bd,de,ev->bv', (hidden, proj, weight.t()))
     #     if bias is not None:
     #         logit = logit + bias

   return logit


 def 			UpperCamelCase_       (    self:		Dict,				a_:		Dict,				a_:		str=None,				a_:		Union[str, Any]=False		):




   '''simple docstring'''



   if labels is not None:
     # Shift so that tokens < n predict n
     _snake_case							:		int								=  hidden[..., :-1, :].contiguous()
     _snake_case							:		List[Any]								=  labels[..., 1:].contiguous()
     _snake_case							:		str								=  hidden.view(-1,				hidden.size(-1		)		)
     _snake_case							:		Dict								=  labels.view(-1		)
     if hidden.size(0		) != labels.size(0		):
       raise RuntimeError("""Input and labels should have the same size in the batch dimension."""		)
   else:
     _snake_case							:		int								=  hidden.view(-1,				hidden.size(-1		)		)

   if self.n_clusters == 0:
     _snake_case							:		Tuple								=  self._compute_logit(a_,				self.out_layers[0].weight,				self.out_layers[0].bias,				self.out_projs[0]		)
     if labels is not None:
       _snake_case							:		Dict								=  labels != -100
       _snake_case							:		str								=  torch.zeros_like(a_,				dtype=hidden.dtype,				device=hidden.device		)
       _snake_case							:		str								=  (
           -nn.functional.log_softmax(a_,				dim=-1		)[mask].gather(1,				labels[mask].unsqueeze(1		)		).squeeze(1		)
       )
     else:
       _snake_case							:		Optional[int]								=  nn.functional.log_softmax(a_,				dim=-1		)
   else:
     # construct weights and biases
     _snake_case		, _snake_case							:		Optional[int]								=  [], []
     for i in range(len(self.cutoffs		)		):
       if self.div_val == 1:
         _snake_case		, _snake_case							:		Optional[int]								=  self.cutoff_ends[i], self.cutoff_ends[i + 1]
         _snake_case							:		List[Any]								=  self.out_layers[0].weight[l_idx:r_idx]
         _snake_case							:		Tuple								=  self.out_layers[0].bias[l_idx:r_idx]
       else:
         _snake_case							:		Optional[int]								=  self.out_layers[i].weight
         _snake_case							:		int								=  self.out_layers[i].bias

       if i == 0:
         _snake_case							:		List[str]								=  torch.cat([weight_i, self.cluster_weight],				dim=0		)
         _snake_case							:		int								=  torch.cat([bias_i, self.cluster_bias],				dim=0		)

       weights.append(a_		)
       biases.append(a_		)

     _snake_case		, _snake_case		, _snake_case							:		Any								=  weights[0], biases[0], self.out_projs[0]

     _snake_case							:		List[str]								=  self._compute_logit(a_,				a_,				a_,				a_		)
     _snake_case							:		Union[str, Any]								=  nn.functional.log_softmax(a_,				dim=1		)

     if labels is None:
       _snake_case							:		Tuple								=  hidden.new_empty((head_logit.size(0		), self.n_token)		)
     else:
       _snake_case							:		Dict								=  torch.zeros_like(a_,				dtype=hidden.dtype,				device=hidden.device		)

     _snake_case							:		Union[str, Any]								=  0
     _snake_case							:		Optional[Any]								=  [0] + self.cutoffs
     for i in range(len(a_		) - 1		):
       _snake_case		, _snake_case							:		Dict								=  cutoff_values[i], cutoff_values[i + 1]

       if labels is not None:
         _snake_case							:		Dict								=  (labels >= l_idx) & (labels < r_idx)
         _snake_case							:		int								=  mask_i.nonzero().squeeze()

         if indices_i.numel() == 0:
           continue

         _snake_case							:		List[str]								=  labels.index_select(0,				a_		) - l_idx
         _snake_case							:		List[str]								=  head_logprob.index_select(0,				a_		)
         _snake_case							:		List[str]								=  hidden.index_select(0,				a_		)
       else:
         _snake_case							:		List[str]								=  hidden

       if i == 0:
         if labels is not None:
           _snake_case							:		Dict								=  head_logprob_i.gather(1,				target_i[:, None]		).squeeze(1		)
         else:
           _snake_case							:		Optional[Any]								=  head_logprob[:, : self.cutoffs[0]]
       else:
         _snake_case		, _snake_case		, _snake_case							:		Dict								=  weights[i], biases[i], self.out_projs[i]

         _snake_case							:		int								=  self._compute_logit(a_,				a_,				a_,				a_		)
         _snake_case							:		int								=  nn.functional.log_softmax(a_,				dim=1		)
         _snake_case							:		Dict								=  self.cutoffs[0] + i - 1  # No probability for the head cluster
         if labels is not None:
           _snake_case							:		Dict								=  head_logprob_i[:, cluster_prob_idx] + tail_logprob_i.gather(
               1,				target_i[:, None]		).squeeze(1		)
         else:
           _snake_case							:		Optional[Any]								=  head_logprob[:, cluster_prob_idx, None] + tail_logprob_i
           _snake_case							:		Any								=  logprob_i

       if labels is not None:
         if (hasattr(self,				"""keep_order"""		) and self.keep_order) or keep_order:
           out.index_copy_(0,				a_,				-logprob_i		)
         else:
           out[offset : offset + logprob_i.size(0		)].copy_(-logprob_i		)
         offset += logprob_i.size(0		)

   return out


 def 			UpperCamelCase_       (    self:		Union[str, Any],				a_:		Optional[int]		):




   '''simple docstring'''



   if self.n_clusters == 0:
     _snake_case							:		Optional[int]								=  self._compute_logit(a_,				self.out_layers[0].weight,				self.out_layers[0].bias,				self.out_projs[0]		)
     return nn.functional.log_softmax(a_,				dim=-1		)
   else:
     # construct weights and biases
     _snake_case		, _snake_case							:		List[Any]								=  [], []
     for i in range(len(self.cutoffs		)		):
       if self.div_val == 1:
         _snake_case		, _snake_case							:		Optional[Any]								=  self.cutoff_ends[i], self.cutoff_ends[i + 1]
         _snake_case							:		Optional[int]								=  self.out_layers[0].weight[l_idx:r_idx]
         _snake_case							:		str								=  self.out_layers[0].bias[l_idx:r_idx]
       else:
         _snake_case							:		List[Any]								=  self.out_layers[i].weight
         _snake_case							:		Union[str, Any]								=  self.out_layers[i].bias

       if i == 0:
         _snake_case							:		int								=  torch.cat([weight_i, self.cluster_weight],				dim=0		)
         _snake_case							:		Dict								=  torch.cat([bias_i, self.cluster_bias],				dim=0		)

       weights.append(a_		)
       biases.append(a_		)

     _snake_case		, _snake_case		, _snake_case							:		int								=  weights[0], biases[0], self.out_projs[0]
     _snake_case							:		List[Any]								=  self._compute_logit(a_,				a_,				a_,				a_		)

     _snake_case							:		List[Any]								=  hidden.new_empty((head_logit.size(0		), self.n_token)		)
     _snake_case							:		int								=  nn.functional.log_softmax(a_,				dim=1		)

     _snake_case							:		List[Any]								=  [0] + self.cutoffs
     for i in range(len(a_		) - 1		):
       _snake_case		, _snake_case							:		List[str]								=  cutoff_values[i], cutoff_values[i + 1]

       if i == 0:
         _snake_case							:		List[str]								=  head_logprob[:, : self.cutoffs[0]]
       else:
         _snake_case		, _snake_case		, _snake_case							:		List[Any]								=  weights[i], biases[i], self.out_projs[i]

         _snake_case							:		Optional[int]								=  self._compute_logit(a_,				a_,				a_,				a_		)
         _snake_case							:		Any								=  nn.functional.log_softmax(a_,				dim=1		)

         _snake_case							:		Dict								=  head_logprob[:, -i] + tail_logprob_i
         _snake_case							:		Any								=  logprob_i

     return out








"""simple docstring"""


def  UpperCAmelCase__	(snake_case__							: int   ):
  """simple docstring"""

  _snake_case							:		Optional[Any]								=  (1 + 24 * n) ** 0.5
  return ((1 + root) / 6) % 1 == 0


def  UpperCAmelCase__	(snake_case__							: int = 50_00   ):
  """simple docstring"""

  _snake_case							:		List[str]								=  [(i * (3 * i - 1)) // 2 for i in range(1		,       snake_case__   )]
  for i, pentagonal_i in enumerate(snake_case__   ):
    for j in range(snake_case__		,       len(snake_case__   )   ):
      _snake_case							:		Dict								=  pentagonal_nums[j]
      _snake_case							:		Optional[Any]								=  pentagonal_i + pentagonal_j
      _snake_case							:		List[str]								=  pentagonal_j - pentagonal_i
      if is_pentagonal(snake_case__   ) and is_pentagonal(snake_case__   ):
        return b

  return -1


if __name__ == "__main__":
     print(F'''{solution() = }''')


