


"""simple docstring"""




import torch
from torch import nn
class 					__lowerCAmelCase					(   nn.Module       ):


		'''simple docstring'''



		def __init__(  self							, _a							, _a							, _a							, _a							, _a=1							, _a=False      ):
				super().__init__()

				__a           =			n_token
				__a           =			d_embed
				__a           =			d_proj

				__a           =			cutoffs + [n_token]
				__a           =			[0] + self.cutoffs
				__a           =			div_val

				__a           =			self.cutoffs[0]
				__a           =			len(self.cutoffs      ) - 1
				__a           =			self.shortlist_size + self.n_clusters

				if self.n_clusters > 0:
						__a           =			nn.Parameter(torch.zeros(self.n_clusters							, self.d_embed      )      )
						__a           =			nn.Parameter(torch.zeros(self.n_clusters      )      )

				__a           =			nn.ModuleList()
				__a           =			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      )      ):
								__a      ,     __a           =			self.cutoff_ends[i], self.cutoff_ends[i + 1]
								__a           =			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      )      )

				__a           =			keep_order

		def 			__UpperCAmelCase       (  self							, _a							, _a							, _a							, _a      ):
				if proj is None:
						__a           =			nn.functional.linear(_a							, _a							, bias=_a      )
				else:
						# if CUDA_MAJOR <= 9 and CUDA_MINOR <= 1:
						__a           =			nn.functional.linear(_a							, proj.t().contiguous()      )
						__a           =			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							, _a							, _a=None							, _a=False      ):

				if labels is not None:
						# Shift so that tokens < n predict n
						__a           =			hidden[..., :-1, :].contiguous()
						__a           =			labels[..., 1:].contiguous()
						__a           =			hidden.view(-1							, hidden.size(-1      )      )
						__a           =			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:
						__a           =			hidden.view(-1							, hidden.size(-1      )      )

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

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

								weights.append(_a      )
								biases.append(_a      )

						__a      ,     __a      ,     __a           =			weights[0], biases[0], self.out_projs[0]

						__a           =			self._compute_logit(_a							, _a							, _a							, _a      )
						__a           =			nn.functional.log_softmax(_a							, dim=1      )

						if labels is None:
								__a           =			hidden.new_empty((head_logit.size(0      ), self.n_token)      )
						else:
								__a           =			torch.zeros_like(_a							, dtype=hidden.dtype							, device=hidden.device      )

						__a           =			0
						__a           =			[0] + self.cutoffs
						for i in range(len(_a      ) - 1      ):
								__a      ,     __a           =			cutoff_values[i], cutoff_values[i + 1]

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

										if indices_i.numel() == 0:
												continue

										__a           =			labels.index_select(0							, _a      ) - l_idx
										__a           =			head_logprob.index_select(0							, _a      )
										__a           =			hidden.index_select(0							, _a      )
								else:
										__a           =			hidden

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

										__a           =			self._compute_logit(_a							, _a							, _a							, _a      )
										__a           =			nn.functional.log_softmax(_a							, dim=1      )
										__a           =			self.cutoffs[0] + i - 1  # No probability for the head cluster
										if labels is not None:
												__a           =			head_logprob_i[:, cluster_prob_idx] + tail_logprob_i.gather(
												    1							, target_i[:, None]      ).squeeze(1      )
										else:
												__a           =			head_logprob[:, cluster_prob_idx, None] + tail_logprob_i
												__a           =			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							, _a      ):
				if self.n_clusters == 0:
						__a           =			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
						__a      ,     __a           =			[], []
						for i in range(len(self.cutoffs      )      ):
								if self.div_val == 1:
										__a      ,     __a           =			self.cutoff_ends[i], self.cutoff_ends[i + 1]
										__a           =			self.out_layers[0].weight[l_idx:r_idx]
										__a           =			self.out_layers[0].bias[l_idx:r_idx]
								else:
										__a           =			self.out_layers[i].weight
										__a           =			self.out_layers[i].bias

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

								weights.append(_a      )
								biases.append(_a      )

						__a      ,     __a      ,     __a           =			weights[0], biases[0], self.out_projs[0]
						__a           =			self._compute_logit(_a							, _a							, _a							, _a      )

						__a           =			hidden.new_empty((head_logit.size(0      ), self.n_token)      )
						__a           =			nn.functional.log_softmax(_a							, dim=1      )

						__a           =			[0] + self.cutoffs
						for i in range(len(_a      ) - 1      ):
								__a      ,     __a           =			cutoff_values[i], cutoff_values[i + 1]

								if i == 0:
										__a           =			head_logprob[:, : self.cutoffs[0]]
								else:
										__a      ,     __a      ,     __a           =			weights[i], biases[i], self.out_projs[i]

										__a           =			self._compute_logit(_a							, _a							, _a							, _a      )
										__a           =			nn.functional.log_softmax(_a							, dim=1      )

										__a           =			head_logprob[:, -i] + tail_logprob_i
										__a           =			logprob_i

						return out










"""simple docstring"""




import math

def        lowercase							(		lowerCAmelCase__ :     list    ,					lowerCAmelCase__ :     int			) ->      int:
		__a           =			len(lowerCAmelCase__			)
		__a           =			int(math.floor(math.sqrt(lowerCAmelCase__			)			)			)
		__a           =			0
		while arr[min(lowerCAmelCase__    ,					lowerCAmelCase__			) - 1] < x:
				__a           =			step
				step += int(math.floor(math.sqrt(lowerCAmelCase__			)			)			)
				if prev >= n:
						return -1

		while arr[prev] < x:
				__a           =			prev + 1
				if prev == min(lowerCAmelCase__    ,					lowerCAmelCase__			):
						return -1
		if arr[prev] == x:
				return prev
		return -1


if __name__ == "__main__":
				lowercase_			     =  input("Enter numbers separated by a comma:\n").strip()
				lowercase_			     =  [int(item) for item in user_input.split(",")]
				lowercase_			     =  int(input("Enter the number to be searched:\n"))
				lowercase_			     =  jump_search(arr, x)
				if res == -1:
								print("Number not found!")
				else:
								print(F'''Number {x} is at index {res}''')






