





from typing import Optional, Tuple, Union

import torch
from einops import rearrange, reduce

from diffusers import DDIMScheduler, DDPMScheduler, DiffusionPipeline, ImagePipelineOutput, UNetaDConditionModel
from diffusers.schedulers.scheduling_ddim import DDIMSchedulerOutput
from diffusers.schedulers.scheduling_ddpm import DDPMSchedulerOutput


__lowerCamelCase :  List[Any]										=  8



def 	A_       (  _lowerCAmelCase							,     _lowerCAmelCase=BITS  )		->				Optional[Any]:
 UpperCamelCase			:      Any 			=     x.device

 UpperCamelCase			:      List[str] 			=     (x * 255).int().clamp(0							,     255  )

 UpperCamelCase			:      int 			=     2 ** torch.arange(bits - 1							,     -1							,     -1							,     device=_lowerCAmelCase  )
 UpperCamelCase			:      Union[str, Any] 			=     rearrange(_lowerCAmelCase							,     "d -> d 1 1"  )
 UpperCamelCase			:      Any 			=     rearrange(_lowerCAmelCase							,     "b c h w -> b c 1 h w"  )

 UpperCamelCase			:      Any 			=     ((x & mask) != 0).float()
 UpperCamelCase			:      Union[str, Any] 			=     rearrange(_lowerCAmelCase							,     "b c d h w -> b (c d) h w"  )
 UpperCamelCase			:      Optional[int] 			=     bits * 2 - 1
 return bits



def 	A_       (  _lowerCAmelCase							,     _lowerCAmelCase=BITS  )		->				int:
 UpperCamelCase			:      Dict 			=     x.device

 UpperCamelCase			:      str 			=     (x > 0).int()
 UpperCamelCase			:      Optional[Any] 			=     2 ** torch.arange(bits - 1							,     -1							,     -1							,     device=_lowerCAmelCase							,     dtype=torch.intaa  )

 UpperCamelCase			:      Union[str, Any] 			=     rearrange(_lowerCAmelCase							,     "d -> d 1 1"  )
 UpperCamelCase			:      Tuple 			=     rearrange(_lowerCAmelCase							,     "b (c d) h w -> b c d h w"							,     d=8  )
 UpperCamelCase			:      List[Any] 			=     reduce(x * mask							,     "b c d h w -> b c h w"							,     "sum"  )
 return (dec / 255).clamp(0.0							,     1.0  )



def 	A_       (  self							,     _lowerCAmelCase							,     _lowerCAmelCase							,     _lowerCAmelCase							,     _lowerCAmelCase = 0.0							,     _lowerCAmelCase = True							,     _lowerCAmelCase=None							,     _lowerCAmelCase = True							,     )		->				Union[DDIMSchedulerOutput, Tuple]:
 if self.num_inference_steps is None:
  raise ValueError(
      "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"  )

 # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
 # Ideally, read DDIM paper in-detail understanding

 # Notation (<variable name> -> <name in paper>
 # - pred_noise_t -> e_theta(x_t, t)
 # - pred_original_sample -> f_theta(x_t, t) or x_0
 # - std_dev_t -> sigma_t
 # - eta -> η
 # - pred_sample_direction -> "direction pointing to x_t"
 # - pred_prev_sample -> "x_t-1"

 # 1. get previous step value (=t-1)
 UpperCamelCase			:      List[Any] 			=     timestep - self.config.num_train_timesteps // self.num_inference_steps

 # 2. compute alphas, betas
 UpperCamelCase			:      List[str] 			=     self.alphas_cumprod[timestep]
 UpperCamelCase			:      str 			=     self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod

 UpperCamelCase			:      Optional[Any] 			=     1 - alpha_prod_t

 # 3. compute predicted original sample from predicted noise also called
 # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
 UpperCamelCase			:      Any 			=     (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5

 # 4. Clip "predicted x_0"
 UpperCamelCase			:      List[str] 			=     self.bit_scale
 if self.config.clip_sample:
  UpperCamelCase			:      Any 			=     torch.clamp(_lowerCAmelCase							,     -scale							,     _lowerCAmelCase  )

 # 5. compute variance: "sigma_t(η)" -> see formula (16)
 # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
 UpperCamelCase			:      int 			=     self._get_variance(_lowerCAmelCase							,     _lowerCAmelCase  )
 UpperCamelCase			:      Union[str, Any] 			=     eta * variance ** 0.5

 if use_clipped_model_output:
  # the model_output is always re-derived from the clipped x_0 in Glide
  UpperCamelCase			:      Tuple 			=     (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5

 # 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
 UpperCamelCase			:      Union[str, Any] 			=     (1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

 # 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
 UpperCamelCase			:      Tuple 			=     alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

 if eta > 0:
  # randn_like does not support generator https://github.com/pytorch/pytorch/issues/27072
  UpperCamelCase			:      Any 			=     model_output.device if torch.is_tensor(_lowerCAmelCase  ) else "cpu"
  UpperCamelCase			:      Optional[Any] 			=     torch.randn(model_output.shape							,     dtype=model_output.dtype							,     generator=_lowerCAmelCase  ).to(_lowerCAmelCase  )
  UpperCamelCase			:      List[str] 			=     self._get_variance(_lowerCAmelCase							,     _lowerCAmelCase  ) ** 0.5 * eta * noise

  UpperCamelCase			:      str 			=     prev_sample + variance

 if not return_dict:
  return (prev_sample,)

 return DDIMSchedulerOutput(prev_sample=_lowerCAmelCase							,     pred_original_sample=_lowerCAmelCase  )



def 	A_       (  self							,     _lowerCAmelCase							,     _lowerCAmelCase							,     _lowerCAmelCase							,     _lowerCAmelCase="epsilon"							,     _lowerCAmelCase=None							,     _lowerCAmelCase = True							,     )		->				Union[DDPMSchedulerOutput, Tuple]:
 UpperCamelCase			:      Tuple 			=     timestep

 if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:
  UpperCamelCase			,					UpperCamelCase			:      List[Any] 			=     torch.split(_lowerCAmelCase							,     sample.shape[1]							,     dim=1  )
 else:
  UpperCamelCase			:      Any 			=     None

 # 1. compute alphas, betas
 UpperCamelCase			:      Union[str, Any] 			=     self.alphas_cumprod[t]
 UpperCamelCase			:      Optional[Any] 			=     self.alphas_cumprod[t - 1] if t > 0 else self.one
 UpperCamelCase			:      List[Any] 			=     1 - alpha_prod_t
 UpperCamelCase			:      Any 			=     1 - alpha_prod_t_prev

 # 2. compute predicted original sample from predicted noise also called
 # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
 if prediction_type == "epsilon":
  UpperCamelCase			:      Any 			=     (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
 elif prediction_type == "sample":
  UpperCamelCase			:      Optional[Any] 			=     model_output
 else:
  raise ValueError(F"""Unsupported prediction_type {prediction_type}."""  )

 # 3. Clip "predicted x_0"
 UpperCamelCase			:      Any 			=     self.bit_scale
 if self.config.clip_sample:
  UpperCamelCase			:      int 			=     torch.clamp(_lowerCAmelCase							,     -scale							,     _lowerCAmelCase  )

 # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
 # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
 UpperCamelCase			:      Any 			=     (alpha_prod_t_prev ** 0.5 * self.betas[t]) / beta_prod_t
 UpperCamelCase			:      List[Any] 			=     self.alphas[t] ** 0.5 * beta_prod_t_prev / beta_prod_t

 # 5. Compute predicted previous sample µ_t
 # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
 UpperCamelCase			:      List[str] 			=     pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

 # 6. Add noise
 UpperCamelCase			:      Optional[Any] 			=     0
 if t > 0:
  UpperCamelCase			:      Any 			=     torch.randn(
      model_output.size()							,     dtype=model_output.dtype							,     layout=model_output.layout							,     generator=_lowerCAmelCase  ).to(model_output.device  )
  UpperCamelCase			:      str 			=     (self._get_variance(_lowerCAmelCase							,     predicted_variance=_lowerCAmelCase  ) ** 0.5) * noise

 UpperCamelCase			:      str 			=     pred_prev_sample + variance

 if not return_dict:
  return (pred_prev_sample,)

 return DDPMSchedulerOutput(prev_sample=_lowerCAmelCase							,     pred_original_sample=_lowerCAmelCase  )



class       A__     ( __snake_case    ):





      def __init__(				self ,							A_ ,							A_ ,							A_ = 1.0 ,							):
       '''simple docstring'''




       super().__init__()
       UpperCamelCase			:      Optional[int] 			=     bit_scale
       UpperCamelCase			:      int 			=     (
           ddim_bit_scheduler_step if isinstance(A_ ,							A_     ) else ddpm_bit_scheduler_step
       )

       self.register_modules(unet=A_ ,							scheduler=A_     )





      @torch.no_grad()
      def __call__(				self ,							A_ = 256 ,							A_ = 256 ,							A_ = 50 ,							A_ = None ,							A_ = 1 ,							A_ = "pil" ,							A_ = True ,							**A_ ,							):
       '''simple docstring'''




       UpperCamelCase			:      str 			=     torch.randn(
           (batch_size, self.unet.config.in_channels, height, width) ,							generator=A_ ,							)
       UpperCamelCase			:      str 			=     decimal_to_bits(A_     ) * self.bit_scale
       UpperCamelCase			:      List[str] 			=     latents.to(self.device     )

       self.scheduler.set_timesteps(A_     )

       for t in self.progress_bar(self.scheduler.timesteps     ):
        # predict the noise residual
        UpperCamelCase			:      int 			=     self.unet(A_ ,							A_     ).sample

        # compute the previous noisy sample x_t -> x_t-1
        UpperCamelCase			:      Tuple 			=     self.scheduler.step(A_ ,							A_ ,							A_     ).prev_sample

       UpperCamelCase			:      Any 			=     bits_to_decimal(A_     )

       if output_type == "pil":
        UpperCamelCase			:      Any 			=     self.numpy_to_pil(A_     )

       if not return_dict:
        return (image,)

       return ImagePipelineOutput(images=A_     )







from __future__ import annotations

from random import random
from typing import Generic, TypeVar

__lowerCamelCase :  Dict										=  TypeVar("""KT""")
__lowerCamelCase :  Dict										=  TypeVar("""VT""")



class       A__     ( Generic[KT, VT]    ):





      def __init__(				self ,							A_ = "root" ,							A_ = None     ):
       '''simple docstring'''




       UpperCamelCase			:      int 			=     key
       UpperCamelCase			:      List[Any] 			=     value
       UpperCamelCase			:      list[Node[KT, VT]] 			=     []





      def __repr__(				self     ):
       '''simple docstring'''




       return F"""Node({self.key}: {self.value})"""





      @property
      def  __UpperCamelCase(				self     ):
       '''simple docstring'''




       return len(self.forward     )



class       A__     ( Generic[KT, VT]    ):





      def __init__(				self ,							A_ = 0.5 ,							A_ = 16     ):
       '''simple docstring'''




       UpperCamelCase			:      Node[KT, VT] 			=     Node[KT, VT]()
       UpperCamelCase			:      List[Any] 			=     0
       UpperCamelCase			:      Union[str, Any] 			=     p
       UpperCamelCase			:      List[str] 			=     max_level





      def __str__(				self     ):
       '''simple docstring'''




       UpperCamelCase			:      int 			=     list(self     )

       if len(A_     ) == 0:
        return F"""SkipList(level={self.level})"""

       UpperCamelCase			:      str 			=     max((len(str(A_     )     ) for item in items) ,							default=4     )
       UpperCamelCase			:      Dict 			=     max(A_ ,							4     ) + 4

       UpperCamelCase			:      str 			=     self.head
       UpperCamelCase			:      List[Any] 			=     []

       UpperCamelCase			:      int 			=     node.forward.copy()
       lines.append(F"""[{node.key}]""".ljust(A_ ,							"-"     ) + "* " * len(A_     )     )
       lines.append(" " * label_size + "| " * len(A_     )     )

       while len(node.forward     ) != 0:
        UpperCamelCase			:      Union[str, Any] 			=     node.forward[0]

        lines.append(
            F"""[{node.key}]""".ljust(A_ ,							"-"     )
            + " ".join(str(n.key     ) if n.key == node.key else "|" for n in forwards     )     )
        lines.append(" " * label_size + "| " * len(A_     )     )
        UpperCamelCase			:      Tuple 			=     node.forward

       lines.append("None".ljust(A_     ) + "* " * len(A_     )     )
       return F"""SkipList(level={self.level})\n""" + "\n".join(A_     )





      def __iter__(				self     ):
       '''simple docstring'''




       UpperCamelCase			:      Union[str, Any] 			=     self.head

       while len(node.forward     ) != 0:
        yield node.forward[0].key
        UpperCamelCase			:      Union[str, Any] 			=     node.forward[0]





      def  __UpperCamelCase(				self     ):
       '''simple docstring'''




       UpperCamelCase			:      Tuple 			=     1
       while random() < self.p and level < self.max_level:
        level += 1

       return level





      def  __UpperCamelCase(				self ,							A_     ):
       '''simple docstring'''




       UpperCamelCase			:      List[str] 			=     []

       UpperCamelCase			:      List[Any] 			=     self.head

       for i in reversed(range(self.level     )     ):
        # i < node.level - When node level is lesser than `i` decrement `i`.
        # node.forward[i].key < key - Jumping to node with key value higher
        #                             or equal to searched key would result
        #                             in skipping searched key.
        while i < node.level and node.forward[i].key < key:
         UpperCamelCase			:      str 			=     node.forward[i]
        # Each leftmost node (relative to searched node) will potentially have to
        # be updated.
        update_vector.append(A_     )

       update_vector.reverse()  # Note that we were inserting values in reverse order.

       # len(node.forward) != 0 - If current node doesn't contain any further
       #                          references then searched key is not present.
       # node.forward[0].key == key - Next node key should be equal to search key
       #                              if key is present.
       if len(node.forward     ) != 0 and node.forward[0].key == key:
        return node.forward[0], update_vector
       else:
        return None, update_vector





      def  __UpperCamelCase(				self ,							A_     ):
       '''simple docstring'''




       UpperCamelCase			,					UpperCamelCase			:      str 			=     self._locate_node(A_     )

       if node is not None:
        for i, update_node in enumerate(A_     ):
         # Remove or replace all references to removed node.
         if update_node.level > i and update_node.forward[i].key == key:
          if node.level > i:
           UpperCamelCase			:      Tuple 			=     node.forward[i]
          else:
           UpperCamelCase			:      List[Any] 			=     update_node.forward[:i]





      def  __UpperCamelCase(				self ,							A_ ,							A_     ):
       '''simple docstring'''




       UpperCamelCase			,					UpperCamelCase			:      Optional[int] 			=     self._locate_node(A_     )
       if node is not None:
        UpperCamelCase			:      Union[str, Any] 			=     value
       else:
        UpperCamelCase			:      Dict 			=     self.random_level()

        if level > self.level:
         # After level increase we have to add additional nodes to head.
         for _ in range(self.level - 1 ,							A_     ):
          update_vector.append(self.head     )
         UpperCamelCase			:      Optional[int] 			=     level

        UpperCamelCase			:      Dict 			=     Node(A_ ,							A_     )

        for i, update_node in enumerate(update_vector[:level]     ):
         # Change references to pass through new node.
         if update_node.level > i:
          new_node.forward.append(update_node.forward[i]     )

         if update_node.level < i + 1:
          update_node.forward.append(A_     )
         else:
          UpperCamelCase			:      List[Any] 			=     new_node





      def  __UpperCamelCase(				self ,							A_     ):
       '''simple docstring'''




       UpperCamelCase			,					UpperCamelCase			:      Union[str, Any] 			=     self._locate_node(A_     )

       if node is not None:
        return node.value

       return None



def 	A_       (  )		->				List[Any]:
 UpperCamelCase			:      int 			=     SkipList()
 skip_list.insert("Key1"							,     3  )
 skip_list.insert("Key2"							,     12  )
 skip_list.insert("Key3"							,     41  )
 skip_list.insert("Key4"							,     -19  )

 UpperCamelCase			:      Optional[int] 			=     skip_list.head
 UpperCamelCase			:      List[str] 			=     {}
 while node.level != 0:
  UpperCamelCase			:      str 			=     node.forward[0]
  UpperCamelCase			:      Optional[int] 			=     node.value

 assert len(_lowerCAmelCase  ) == 4
 assert all_values["Key1"] == 3
 assert all_values["Key2"] == 12
 assert all_values["Key3"] == 41
 assert all_values["Key4"] == -19



def 	A_       (  )		->				List[Any]:
 UpperCamelCase			:      Optional[int] 			=     SkipList()
 skip_list.insert("Key1"							,     10  )
 skip_list.insert("Key1"							,     12  )

 skip_list.insert("Key5"							,     7  )
 skip_list.insert("Key7"							,     10  )
 skip_list.insert("Key10"							,     5  )

 skip_list.insert("Key7"							,     7  )
 skip_list.insert("Key5"							,     5  )
 skip_list.insert("Key10"							,     10  )

 UpperCamelCase			:      Dict 			=     skip_list.head
 UpperCamelCase			:      Tuple 			=     {}
 while node.level != 0:
  UpperCamelCase			:      List[str] 			=     node.forward[0]
  UpperCamelCase			:      Dict 			=     node.value

 if len(_lowerCAmelCase  ) != 4:
  print()
 assert len(_lowerCAmelCase  ) == 4
 assert all_values["Key1"] == 12
 assert all_values["Key7"] == 7
 assert all_values["Key5"] == 5
 assert all_values["Key10"] == 10



def 	A_       (  )		->				List[Any]:
 UpperCamelCase			:      List[Any] 			=     SkipList()
 assert skip_list.find("Some key"  ) is None



def 	A_       (  )		->				Tuple:
 UpperCamelCase			:      Optional[int] 			=     SkipList()

 skip_list.insert("Key2"							,     20  )
 assert skip_list.find("Key2"  ) == 20

 skip_list.insert("Some Key"							,     10  )
 skip_list.insert("Key2"							,     8  )
 skip_list.insert("V"							,     13  )

 assert skip_list.find("Y"  ) is None
 assert skip_list.find("Key2"  ) == 8
 assert skip_list.find("Some Key"  ) == 10
 assert skip_list.find("V"  ) == 13



def 	A_       (  )		->				Dict:
 UpperCamelCase			:      Optional[int] 			=     SkipList()
 skip_list.delete("Some key"  )

 assert len(skip_list.head.forward  ) == 0



def 	A_       (  )		->				Dict:
 UpperCamelCase			:      List[Any] 			=     SkipList()

 skip_list.insert("Key1"							,     12  )
 skip_list.insert("V"							,     13  )
 skip_list.insert("X"							,     14  )
 skip_list.insert("Key2"							,     15  )

 skip_list.delete("V"  )
 skip_list.delete("Key2"  )

 assert skip_list.find("V"  ) is None
 assert skip_list.find("Key2"  ) is None



def 	A_       (  )		->				List[str]:
 UpperCamelCase			:      int 			=     SkipList()

 skip_list.insert("Key1"							,     12  )
 skip_list.insert("V"							,     13  )
 skip_list.insert("X"							,     14  )
 skip_list.insert("Key2"							,     15  )

 skip_list.delete("V"  )
 assert skip_list.find("V"  ) is None
 assert skip_list.find("X"  ) == 14
 assert skip_list.find("Key1"  ) == 12
 assert skip_list.find("Key2"  ) == 15

 skip_list.delete("X"  )
 assert skip_list.find("V"  ) is None
 assert skip_list.find("X"  ) is None
 assert skip_list.find("Key1"  ) == 12
 assert skip_list.find("Key2"  ) == 15

 skip_list.delete("Key1"  )
 assert skip_list.find("V"  ) is None
 assert skip_list.find("X"  ) is None
 assert skip_list.find("Key1"  ) is None
 assert skip_list.find("Key2"  ) == 15

 skip_list.delete("Key2"  )
 assert skip_list.find("V"  ) is None
 assert skip_list.find("X"  ) is None
 assert skip_list.find("Key1"  ) is None
 assert skip_list.find("Key2"  ) is None



def 	A_       (  )		->				List[Any]:
 UpperCamelCase			:      List[Any] 			=     SkipList()

 skip_list.insert("Key1"							,     12  )
 skip_list.insert("V"							,     13  )
 skip_list.insert("X"							,     142  )
 skip_list.insert("Key2"							,     15  )

 skip_list.delete("X"  )

 def traverse_keys(_lowerCAmelCase  ):
  yield node.key
  for forward_node in node.forward:
   yield from traverse_keys(_lowerCAmelCase  )

 assert len(set(traverse_keys(skip_list.head  )  )  ) == 4



def 	A_       (  )		->				Union[str, Any]:
 def is_sorted(_lowerCAmelCase  ):
  return all(next_item >= item for item, next_item in zip(_lowerCAmelCase							,     lst[1:]  )  )

 UpperCamelCase			:      int 			=     SkipList()
 for i in range(10  ):
  skip_list.insert(_lowerCAmelCase							,     _lowerCAmelCase  )
 assert is_sorted(list(_lowerCAmelCase  )  )
 skip_list.delete(5  )
 skip_list.delete(8  )
 skip_list.delete(2  )
 assert is_sorted(list(_lowerCAmelCase  )  )
 skip_list.insert(-12							,     -12  )
 skip_list.insert(77							,     77  )
 assert is_sorted(list(_lowerCAmelCase  )  )



def 	A_       (  )		->				Tuple:
 for _ in range(100  ):
  # Repeat test 100 times due to the probabilistic nature of skip list
  # random values == random bugs
  test_insert()
  test_insert_overrides_existing_value()

  test_searching_empty_list_returns_none()
  test_search()

  test_deleting_item_from_empty_list_do_nothing()
  test_deleted_items_are_not_founded_by_find_method()
  test_delete_removes_only_given_key()
  test_delete_doesnt_leave_dead_nodes()

  test_iter_always_yields_sorted_values()



def 	A_       (  )		->				List[str]:
 UpperCamelCase			:      Optional[int] 			=     SkipList()
 skip_list.insert(2							,     "2"  )
 skip_list.insert(4							,     "4"  )
 skip_list.insert(6							,     "4"  )
 skip_list.insert(4							,     "5"  )
 skip_list.insert(8							,     "4"  )
 skip_list.insert(9							,     "4"  )

 skip_list.delete(4  )

 print(_lowerCAmelCase  )


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    main()
