





"""simple docstring"""
from collections import deque
from math import floor
from random import random
from time import time






class 					_SCREAMING_SNAKE_CASE:




       def __init__(						self							)			->      Dict:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Tuple						=  {}




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__=1							)			->      List[str]:





             """simple docstring"""






             if self.graph.get(SCREAMING_SNAKE_CASE__							):
                   if self.graph[u].count([w, v]							) == 0:
                         self.graph[u].append([w, v]							)
             else:
                   __SCREAMING_SNAKE_CASE   :int						=  [[w, v]]
             if not self.graph.get(SCREAMING_SNAKE_CASE__							):
                   __SCREAMING_SNAKE_CASE   :Dict						=  []




       def     _UpperCamelCase     (						self							)			->      str:





             """simple docstring"""






             return list(self.graph							)




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__							)			->      int:





             """simple docstring"""






             if self.graph.get(SCREAMING_SNAKE_CASE__							):
                   for _ in self.graph[u]:
                         if _[1] == v:
                               self.graph[u].remove(SCREAMING_SNAKE_CASE__							)




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__=-2		,SCREAMING_SNAKE_CASE__=-1							)			->      str:





             """simple docstring"""






             if s == d:
                   return []
             __SCREAMING_SNAKE_CASE   :List[str]						=  []
             __SCREAMING_SNAKE_CASE   :Any						=  []
             if s == -2:
                   __SCREAMING_SNAKE_CASE   :Any						=  list(self.graph							)[0]
             stack.append(SCREAMING_SNAKE_CASE__							)
             visited.append(SCREAMING_SNAKE_CASE__							)
             __SCREAMING_SNAKE_CASE   :Dict						=  s

             while True:
                   # check if there is any non isolated nodes
                   if len(self.graph[s]							) != 0:
                         __SCREAMING_SNAKE_CASE   :List[str]						=  s
                         for node in self.graph[s]:
                               if visited.count(node[1]							) < 1:
                                     if node[1] == d:
                                           visited.append(SCREAMING_SNAKE_CASE__							)
                                           return visited
                                     else:
                                           stack.append(node[1]							)
                                           visited.append(node[1]							)
                                           __SCREAMING_SNAKE_CASE   :List[Any]						=  node[1]
                                           break

            # check if all the children are visited
                   if s == ss:
                         stack.pop()
                         if len(SCREAMING_SNAKE_CASE__							) != 0:
                               __SCREAMING_SNAKE_CASE   :str						=  stack[len(SCREAMING_SNAKE_CASE__							) - 1]
                   else:
                         __SCREAMING_SNAKE_CASE   :Any						=  ss

                   # check if se have reached the starting point
                   if len(SCREAMING_SNAKE_CASE__							) == 0:
                         return visited




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__=-1							)			->      int:





             """simple docstring"""






             if c == -1:
                   __SCREAMING_SNAKE_CASE   :Any						=  floor(random() * 1_00_00							) + 10
             for i in range(SCREAMING_SNAKE_CASE__							):
                   # every vertex has max 100 edges
                   for _ in range(floor(random() * 1_02							) + 1							):
                         __SCREAMING_SNAKE_CASE   :List[str]						=  floor(random() * c							) + 1
                         if n != i:
                               self.add_pair(SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,1							)




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__=-2							)			->      Tuple:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Any						=  deque()
             __SCREAMING_SNAKE_CASE   :List[str]						=  []
             if s == -2:
                   __SCREAMING_SNAKE_CASE   :str						=  list(self.graph							)[0]
             d.append(SCREAMING_SNAKE_CASE__							)
             visited.append(SCREAMING_SNAKE_CASE__							)
             while d:
                   __SCREAMING_SNAKE_CASE   :Optional[int]						=  d.popleft()
                   if len(self.graph[s]							) != 0:
                         for node in self.graph[s]:
                               if visited.count(node[1]							) < 1:
                                     d.append(node[1]							)
                                     visited.append(node[1]							)
             return visited




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__							)			->      Optional[int]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Dict						=  0
             for x in self.graph:
                   for y in self.graph[x]:
                         if y[1] == u:
                               count += 1
             return count




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__							)			->      Optional[Any]:





             """simple docstring"""






             return len(self.graph[u]							)




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__=-2							)			->      Optional[int]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Optional[int]						=  []
             __SCREAMING_SNAKE_CASE   :str						=  []
             if s == -2:
                   __SCREAMING_SNAKE_CASE   :Tuple						=  list(self.graph							)[0]
             stack.append(SCREAMING_SNAKE_CASE__							)
             visited.append(SCREAMING_SNAKE_CASE__							)
             __SCREAMING_SNAKE_CASE   :Tuple						=  s
             __SCREAMING_SNAKE_CASE   :Union[str, Any]						=  []

             while True:
                   # check if there is any non isolated nodes
                   if len(self.graph[s]							) != 0:
                         __SCREAMING_SNAKE_CASE   :int						=  s
                         for node in self.graph[s]:
                               if visited.count(node[1]							) < 1:
                                     stack.append(node[1]							)
                                     visited.append(node[1]							)
                                     __SCREAMING_SNAKE_CASE   :Any						=  node[1]
                                     break

            # check if all the children are visited
                   if s == ss:
                         sorted_nodes.append(stack.pop()							)
                         if len(SCREAMING_SNAKE_CASE__							) != 0:
                               __SCREAMING_SNAKE_CASE   :Optional[int]						=  stack[len(SCREAMING_SNAKE_CASE__							) - 1]
                   else:
                         __SCREAMING_SNAKE_CASE   :List[str]						=  ss

                   # check if se have reached the starting point
                   if len(SCREAMING_SNAKE_CASE__							) == 0:
                         return sorted_nodes




       def     _UpperCamelCase     (						self							)			->      int:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Any						=  []
             __SCREAMING_SNAKE_CASE   :Dict						=  []
             __SCREAMING_SNAKE_CASE   :Optional[Any]						=  list(self.graph							)[0]
             stack.append(SCREAMING_SNAKE_CASE__							)
             visited.append(SCREAMING_SNAKE_CASE__							)
             __SCREAMING_SNAKE_CASE   :Any						=  -2
             __SCREAMING_SNAKE_CASE   :int						=  []
             __SCREAMING_SNAKE_CASE   :int						=  s
             __SCREAMING_SNAKE_CASE   :str						=  False
             __SCREAMING_SNAKE_CASE   :int						=  set()

             while True:
                   # check if there is any non isolated nodes
                   if len(self.graph[s]							) != 0:
                         __SCREAMING_SNAKE_CASE   :List[str]						=  s
                         for node in self.graph[s]:
                               if (
                                   visited.count(node[1]							) > 0
                                   and node[1] != parent
                                   and indirect_parents.count(node[1]							) > 0
                                   and not on_the_way_back
                               ):
                                     __SCREAMING_SNAKE_CASE   :Dict						=  len(SCREAMING_SNAKE_CASE__							) - 1
                                     while len_stack >= 0:
                                           if stack[len_stack] == node[1]:
                                                 anticipating_nodes.add(node[1]							)
                                                 break
                                           else:
                                                 anticipating_nodes.add(stack[len_stack]							)
                                                 len_stack -= 1
                               if visited.count(node[1]							) < 1:
                                     stack.append(node[1]							)
                                     visited.append(node[1]							)
                                     __SCREAMING_SNAKE_CASE   :Any						=  node[1]
                                     break

            # check if all the children are visited
                   if s == ss:
                         stack.pop()
                         __SCREAMING_SNAKE_CASE   :Optional[int]						=  True
                         if len(SCREAMING_SNAKE_CASE__							) != 0:
                               __SCREAMING_SNAKE_CASE   :List[str]						=  stack[len(SCREAMING_SNAKE_CASE__							) - 1]
                   else:
                         __SCREAMING_SNAKE_CASE   :str						=  False
                         indirect_parents.append(SCREAMING_SNAKE_CASE__							)
                         __SCREAMING_SNAKE_CASE   :Tuple						=  s
                         __SCREAMING_SNAKE_CASE   :Any						=  ss

                   # check if se have reached the starting point
                   if len(SCREAMING_SNAKE_CASE__							) == 0:
                         return list(SCREAMING_SNAKE_CASE__							)




       def     _UpperCamelCase     (						self							)			->      Union[str, Any]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Optional[int]						=  []
             __SCREAMING_SNAKE_CASE   :Union[str, Any]						=  []
             __SCREAMING_SNAKE_CASE   :Tuple						=  list(self.graph							)[0]
             stack.append(SCREAMING_SNAKE_CASE__							)
             visited.append(SCREAMING_SNAKE_CASE__							)
             __SCREAMING_SNAKE_CASE   :Optional[Any]						=  -2
             __SCREAMING_SNAKE_CASE   :int						=  []
             __SCREAMING_SNAKE_CASE   :Dict						=  s
             __SCREAMING_SNAKE_CASE   :Optional[int]						=  False
             __SCREAMING_SNAKE_CASE   :int						=  set()

             while True:
                   # check if there is any non isolated nodes
                   if len(self.graph[s]							) != 0:
                         __SCREAMING_SNAKE_CASE   :str						=  s
                         for node in self.graph[s]:
                               if (
                                   visited.count(node[1]							) > 0
                                   and node[1] != parent
                                   and indirect_parents.count(node[1]							) > 0
                                   and not on_the_way_back
                               ):
                                     __SCREAMING_SNAKE_CASE   :Union[str, Any]						=  len(SCREAMING_SNAKE_CASE__							) - 1
                                     while len_stack_minus_one >= 0:
                                           if stack[len_stack_minus_one] == node[1]:
                                                 anticipating_nodes.add(node[1]							)
                                                 break
                                           else:
                                                 return True
                               if visited.count(node[1]							) < 1:
                                     stack.append(node[1]							)
                                     visited.append(node[1]							)
                                     __SCREAMING_SNAKE_CASE   :Dict						=  node[1]
                                     break

            # check if all the children are visited
                   if s == ss:
                         stack.pop()
                         __SCREAMING_SNAKE_CASE   :Any						=  True
                         if len(SCREAMING_SNAKE_CASE__							) != 0:
                               __SCREAMING_SNAKE_CASE   :List[str]						=  stack[len(SCREAMING_SNAKE_CASE__							) - 1]
                   else:
                         __SCREAMING_SNAKE_CASE   :Union[str, Any]						=  False
                         indirect_parents.append(SCREAMING_SNAKE_CASE__							)
                         __SCREAMING_SNAKE_CASE   :str						=  s
                         __SCREAMING_SNAKE_CASE   :Optional[int]						=  ss

                   # check if se have reached the starting point
                   if len(SCREAMING_SNAKE_CASE__							) == 0:
                         return False




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__=-2		,SCREAMING_SNAKE_CASE__=-1							)			->      List[str]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Dict						=  time()
             self.dfs(SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__							)
             __SCREAMING_SNAKE_CASE   :Union[str, Any]						=  time()
             return end - begin




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__=-2							)			->      Optional[Any]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Optional[int]						=  time()
             self.bfs(SCREAMING_SNAKE_CASE__							)
             __SCREAMING_SNAKE_CASE   :Dict						=  time()
             return end - begin






class 					_SCREAMING_SNAKE_CASE:




       def __init__(						self							)			->      Tuple:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Tuple						=  {}




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__=1							)			->      Union[str, Any]:





             """simple docstring"""






             if self.graph.get(SCREAMING_SNAKE_CASE__							):
                   # if there already is a edge
                   if self.graph[u].count([w, v]							) == 0:
                         self.graph[u].append([w, v]							)
             else:
                   # if u does not exist
                   __SCREAMING_SNAKE_CASE   :Dict						=  [[w, v]]
             # add the other way
             if self.graph.get(SCREAMING_SNAKE_CASE__							):
                   # if there already is a edge
                   if self.graph[v].count([w, u]							) == 0:
                         self.graph[v].append([w, u]							)
             else:
                   # if u does not exist
                   __SCREAMING_SNAKE_CASE   :Optional[int]						=  [[w, u]]




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__							)			->      Optional[int]:





             """simple docstring"""






             if self.graph.get(SCREAMING_SNAKE_CASE__							):
                   for _ in self.graph[u]:
                         if _[1] == v:
                               self.graph[u].remove(SCREAMING_SNAKE_CASE__							)
        # the other way round
             if self.graph.get(SCREAMING_SNAKE_CASE__							):
                   for _ in self.graph[v]:
                         if _[1] == u:
                               self.graph[v].remove(SCREAMING_SNAKE_CASE__							)




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__=-2		,SCREAMING_SNAKE_CASE__=-1							)			->      Tuple:





             """simple docstring"""






             if s == d:
                   return []
             __SCREAMING_SNAKE_CASE   :List[Any]						=  []
             __SCREAMING_SNAKE_CASE   :str						=  []
             if s == -2:
                   __SCREAMING_SNAKE_CASE   :str						=  list(self.graph							)[0]
             stack.append(SCREAMING_SNAKE_CASE__							)
             visited.append(SCREAMING_SNAKE_CASE__							)
             __SCREAMING_SNAKE_CASE   :Optional[int]						=  s

             while True:
                   # check if there is any non isolated nodes
                   if len(self.graph[s]							) != 0:
                         __SCREAMING_SNAKE_CASE   :int						=  s
                         for node in self.graph[s]:
                               if visited.count(node[1]							) < 1:
                                     if node[1] == d:
                                           visited.append(SCREAMING_SNAKE_CASE__							)
                                           return visited
                                     else:
                                           stack.append(node[1]							)
                                           visited.append(node[1]							)
                                           __SCREAMING_SNAKE_CASE   :Optional[int]						=  node[1]
                                           break

            # check if all the children are visited
                   if s == ss:
                         stack.pop()
                         if len(SCREAMING_SNAKE_CASE__							) != 0:
                               __SCREAMING_SNAKE_CASE   :List[Any]						=  stack[len(SCREAMING_SNAKE_CASE__							) - 1]
                   else:
                         __SCREAMING_SNAKE_CASE   :Union[str, Any]						=  ss

                   # check if se have reached the starting point
                   if len(SCREAMING_SNAKE_CASE__							) == 0:
                         return visited




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__=-1							)			->      Dict:





             """simple docstring"""






             if c == -1:
                   __SCREAMING_SNAKE_CASE   :Union[str, Any]						=  floor(random() * 1_00_00							) + 10
             for i in range(SCREAMING_SNAKE_CASE__							):
                   # every vertex has max 100 edges
                   for _ in range(floor(random() * 1_02							) + 1							):
                         __SCREAMING_SNAKE_CASE   :List[str]						=  floor(random() * c							) + 1
                         if n != i:
                               self.add_pair(SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,1							)




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__=-2							)			->      List[str]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :str						=  deque()
             __SCREAMING_SNAKE_CASE   :int						=  []
             if s == -2:
                   __SCREAMING_SNAKE_CASE   :Any						=  list(self.graph							)[0]
             d.append(SCREAMING_SNAKE_CASE__							)
             visited.append(SCREAMING_SNAKE_CASE__							)
             while d:
                   __SCREAMING_SNAKE_CASE   :Dict						=  d.popleft()
                   if len(self.graph[s]							) != 0:
                         for node in self.graph[s]:
                               if visited.count(node[1]							) < 1:
                                     d.append(node[1]							)
                                     visited.append(node[1]							)
             return visited




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__							)			->      Any:





             """simple docstring"""






             return len(self.graph[u]							)




       def     _UpperCamelCase     (						self							)			->      Union[str, Any]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :List[Any]						=  []
             __SCREAMING_SNAKE_CASE   :Optional[int]						=  []
             __SCREAMING_SNAKE_CASE   :Tuple						=  list(self.graph							)[0]
             stack.append(SCREAMING_SNAKE_CASE__							)
             visited.append(SCREAMING_SNAKE_CASE__							)
             __SCREAMING_SNAKE_CASE   :Union[str, Any]						=  -2
             __SCREAMING_SNAKE_CASE   :Optional[Any]						=  []
             __SCREAMING_SNAKE_CASE   :Dict						=  s
             __SCREAMING_SNAKE_CASE   :int						=  False
             __SCREAMING_SNAKE_CASE   :str						=  set()

             while True:
                   # check if there is any non isolated nodes
                   if len(self.graph[s]							) != 0:
                         __SCREAMING_SNAKE_CASE   :Optional[int]						=  s
                         for node in self.graph[s]:
                               if (
                                   visited.count(node[1]							) > 0
                                   and node[1] != parent
                                   and indirect_parents.count(node[1]							) > 0
                                   and not on_the_way_back
                               ):
                                     __SCREAMING_SNAKE_CASE   :str						=  len(SCREAMING_SNAKE_CASE__							) - 1
                                     while len_stack >= 0:
                                           if stack[len_stack] == node[1]:
                                                 anticipating_nodes.add(node[1]							)
                                                 break
                                           else:
                                                 anticipating_nodes.add(stack[len_stack]							)
                                                 len_stack -= 1
                               if visited.count(node[1]							) < 1:
                                     stack.append(node[1]							)
                                     visited.append(node[1]							)
                                     __SCREAMING_SNAKE_CASE   :Union[str, Any]						=  node[1]
                                     break

            # check if all the children are visited
                   if s == ss:
                         stack.pop()
                         __SCREAMING_SNAKE_CASE   :int						=  True
                         if len(SCREAMING_SNAKE_CASE__							) != 0:
                               __SCREAMING_SNAKE_CASE   :Any						=  stack[len(SCREAMING_SNAKE_CASE__							) - 1]
                   else:
                         __SCREAMING_SNAKE_CASE   :Union[str, Any]						=  False
                         indirect_parents.append(SCREAMING_SNAKE_CASE__							)
                         __SCREAMING_SNAKE_CASE   :int						=  s
                         __SCREAMING_SNAKE_CASE   :str						=  ss

                   # check if se have reached the starting point
                   if len(SCREAMING_SNAKE_CASE__							) == 0:
                         return list(SCREAMING_SNAKE_CASE__							)




       def     _UpperCamelCase     (						self							)			->      Optional[int]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :List[Any]						=  []
             __SCREAMING_SNAKE_CASE   :Dict						=  []
             __SCREAMING_SNAKE_CASE   :Tuple						=  list(self.graph							)[0]
             stack.append(SCREAMING_SNAKE_CASE__							)
             visited.append(SCREAMING_SNAKE_CASE__							)
             __SCREAMING_SNAKE_CASE   :Any						=  -2
             __SCREAMING_SNAKE_CASE   :List[str]						=  []
             __SCREAMING_SNAKE_CASE   :List[Any]						=  s
             __SCREAMING_SNAKE_CASE   :Tuple						=  False
             __SCREAMING_SNAKE_CASE   :Optional[int]						=  set()

             while True:
                   # check if there is any non isolated nodes
                   if len(self.graph[s]							) != 0:
                         __SCREAMING_SNAKE_CASE   :int						=  s
                         for node in self.graph[s]:
                               if (
                                   visited.count(node[1]							) > 0
                                   and node[1] != parent
                                   and indirect_parents.count(node[1]							) > 0
                                   and not on_the_way_back
                               ):
                                     __SCREAMING_SNAKE_CASE   :Optional[int]						=  len(SCREAMING_SNAKE_CASE__							) - 1
                                     while len_stack_minus_one >= 0:
                                           if stack[len_stack_minus_one] == node[1]:
                                                 anticipating_nodes.add(node[1]							)
                                                 break
                                           else:
                                                 return True
                               if visited.count(node[1]							) < 1:
                                     stack.append(node[1]							)
                                     visited.append(node[1]							)
                                     __SCREAMING_SNAKE_CASE   :Optional[int]						=  node[1]
                                     break

            # check if all the children are visited
                   if s == ss:
                         stack.pop()
                         __SCREAMING_SNAKE_CASE   :Dict						=  True
                         if len(SCREAMING_SNAKE_CASE__							) != 0:
                               __SCREAMING_SNAKE_CASE   :Union[str, Any]						=  stack[len(SCREAMING_SNAKE_CASE__							) - 1]
                   else:
                         __SCREAMING_SNAKE_CASE   :List[Any]						=  False
                         indirect_parents.append(SCREAMING_SNAKE_CASE__							)
                         __SCREAMING_SNAKE_CASE   :Optional[Any]						=  s
                         __SCREAMING_SNAKE_CASE   :Any						=  ss

                   # check if se have reached the starting point
                   if len(SCREAMING_SNAKE_CASE__							) == 0:
                         return False




       def     _UpperCamelCase     (						self							)			->      int:





             """simple docstring"""






             return list(self.graph							)




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__=-2		,SCREAMING_SNAKE_CASE__=-1							)			->      Optional[Any]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :int						=  time()
             self.dfs(SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__							)
             __SCREAMING_SNAKE_CASE   :Optional[int]						=  time()
             return end - begin




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__=-2							)			->      Dict:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Dict						=  time()
             self.bfs(SCREAMING_SNAKE_CASE__							)
             __SCREAMING_SNAKE_CASE   :Union[str, Any]						=  time()
             return end - begin






"""simple docstring"""
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin






@dataclass
class 					_SCREAMING_SNAKE_CASE(   A  ):
       SCREAMING_SNAKE_CASE_   :      torch.FloatTensor
       SCREAMING_SNAKE_CASE_   :      torch.FloatTensor
       SCREAMING_SNAKE_CASE_   :      Optional[torch.FloatTensor]							=  None






class 					_SCREAMING_SNAKE_CASE(   A    ,	A  ):
       SCREAMING_SNAKE_CASE_   :      Any							=  2




       @register_to_config
       def __init__(						self		,SCREAMING_SNAKE_CASE__ = 0.0_2		,SCREAMING_SNAKE_CASE__ = 1_00		,SCREAMING_SNAKE_CASE__ = 1.0_0_7		,SCREAMING_SNAKE_CASE__ = 80		,SCREAMING_SNAKE_CASE__ = 0.0_5		,SCREAMING_SNAKE_CASE__ = 50		,)			->      Union[str, Any]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Any						=  sigma_max

             # setable values
             __SCREAMING_SNAKE_CASE   :int						=  None
             __SCREAMING_SNAKE_CASE   :np.IntTensor						=  None
             __SCREAMING_SNAKE_CASE   :torch.FloatTensor						=  None  # sigma(t_i)




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__ = None							)			->      torch.FloatTensor:





             """simple docstring"""






             return sample




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__ = None							)			->      List[Any]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Optional[Any]						=  num_inference_steps
             __SCREAMING_SNAKE_CASE   :int						=  np.arange(0		,self.num_inference_steps							)[::-1].copy()
             __SCREAMING_SNAKE_CASE   :Optional[int]						=  torch.from_numpy(SCREAMING_SNAKE_CASE__							).to(SCREAMING_SNAKE_CASE__							)
             __SCREAMING_SNAKE_CASE   :Any						=  [
                 (
                     self.config.sigma_max**2
                     * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
                 )
                 for i in self.timesteps
             ]
             __SCREAMING_SNAKE_CASE   :List[str]						=  torch.tensor(SCREAMING_SNAKE_CASE__		,dtype=torch.floataa		,device=SCREAMING_SNAKE_CASE__							)




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__ = None							)			->      Tuple[torch.FloatTensor, float]:





             """simple docstring"""






             if self.config.s_min <= sigma <= self.config.s_max:
                   __SCREAMING_SNAKE_CASE   :List[str]						=  min(self.config.s_churn / self.num_inference_steps		,2**0.5 - 1							)
             else:
                   __SCREAMING_SNAKE_CASE   :Optional[Any]						=  0

             # sample eps ~ N(0, S_noise^2 * I)
             __SCREAMING_SNAKE_CASE   :Optional[int]						=  self.config.s_noise * randn_tensor(sample.shape		,generator=SCREAMING_SNAKE_CASE__							).to(sample.device							)
             __SCREAMING_SNAKE_CASE   :List[str]						=  sigma + gamma * sigma
             __SCREAMING_SNAKE_CASE   :str						=  sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

             return sample_hat, sigma_hat




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__ = True		,)			->      Union[KarrasVeOutput, Tuple]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :str						=  sample_hat + sigma_hat * model_output
             __SCREAMING_SNAKE_CASE   :Tuple						=  (sample_hat - pred_original_sample) / sigma_hat
             __SCREAMING_SNAKE_CASE   :List[Any]						=  sample_hat + (sigma_prev - sigma_hat) * derivative

             if not return_dict:
                   return (sample_prev, derivative)

             return KarrasVeOutput(
                 prev_sample=SCREAMING_SNAKE_CASE__		,derivative=SCREAMING_SNAKE_CASE__		,pred_original_sample=SCREAMING_SNAKE_CASE__							)




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__ = True		,)			->      Union[KarrasVeOutput, Tuple]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE   :Any						=  sample_prev + sigma_prev * model_output
             __SCREAMING_SNAKE_CASE   :List[Any]						=  (sample_prev - pred_original_sample) / sigma_prev
             __SCREAMING_SNAKE_CASE   :Dict						=  sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

             if not return_dict:
                   return (sample_prev, derivative)

             return KarrasVeOutput(
                 prev_sample=SCREAMING_SNAKE_CASE__		,derivative=SCREAMING_SNAKE_CASE__		,pred_original_sample=SCREAMING_SNAKE_CASE__							)




       def     _UpperCamelCase     (						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__							)			->      Union[str, Any]:





             """simple docstring"""






             raise NotImplementedError()