


'''simple docstring'''
lowerCAmelCase__  =     float('inf')







class 					_A						:



   '''simple docstring'''






   def __init__(	self	:					Any					, lowerCamelCase	:					Optional[int]						)->	Dict:
          snake_case__					:	str          =					[0] * n
          snake_case__					:	Union[str, Any]          =					[0] * n
          snake_case__					:	List[Any]          =					[0] * n
          snake_case__					:	int          =					[[] for _ in range(lowerCamelCase						)]




   def   __lowerCAmelCase						(	self	:					str					, lowerCamelCase	:					Optional[int]					, lowerCamelCase	:					str					, lowerCamelCase	:					Union[str, Any]					, lowerCamelCase	:					Tuple=0						)->	str:
          self.adj[a].append([b, len(self.adj[b]						), c, 0]						)
          self.adj[b].append([a, len(self.adj[a]						) - 1, rcap, 0]						)




   def   __lowerCAmelCase						(	self	:					List[str]					, lowerCamelCase	:					Tuple					, lowerCamelCase	:					Dict					, lowerCamelCase	:					Union[str, Any]						)->	Union[str, Any]:
          if vertex == sink or not flow:
                 return flow

          for i in range(self.ptr[vertex]					, len(self.adj[vertex]						)						):
                 snake_case__					:	Any          =					self.adj[vertex][i]
                 if self.lvl[e[0]] == self.lvl[vertex] + 1:
                        snake_case__					:	List[str]          =					self.depth_first_search(e[0]					, lowerCamelCase					, min(lowerCamelCase					, e[2] - e[3]						)						)
                        if p:
                               self.adj[vertex][i][3] += p
                               self.adj[e[0]][e[1]][3] -= p
                               return p
                 snake_case__					:	Dict          =					self.ptr[vertex] + 1
          return 0




   def   __lowerCAmelCase						(	self	:					List[str]					, lowerCamelCase	:					Any					, lowerCamelCase	:					int						)->	List[Any]:
          snake_case__       ,   snake_case__					:	Optional[int]          =					0, source
          for l in range(31						):  # noqa: E741  l = 30 maybe faster for random data
                 while True:
                        snake_case__       ,   snake_case__					:	Tuple          =					[0] * len(self.q						), [0] * len(self.q						)
                        snake_case__       ,   snake_case__       ,   snake_case__					:	List[Any]          =					0, 1, 1
                        while qi < qe and not self.lvl[sink]:
                               snake_case__					:	List[str]          =					self.q[qi]
                               qi += 1
                               for e in self.adj[v]:
                                      if not self.lvl[e[0]] and (e[2] - e[3]) >> (30 - l):
                                             snake_case__					:	Union[str, Any]          =					e[0]
                                             qe += 1
                                             snake_case__					:	List[str]          =					self.lvl[v] + 1

                        snake_case__					:	Tuple          =					self.depth_first_search(lowerCamelCase					, lowerCamelCase					, lowerCamelCase						)
                        while p:
                               flow += p
                               snake_case__					:	int          =					self.depth_first_search(lowerCamelCase					, lowerCamelCase					, lowerCamelCase						)

                        if not self.lvl[sink]:
                               break

          return flow
lowerCAmelCase__  =     Dinic(10)
lowerCAmelCase__  =     0
lowerCAmelCase__  =     9
for vertex in range(1, 5):
     graph.add_edge(source, vertex, 1)
for vertex in range(5, 9):
     graph.add_edge(vertex, sink, 1)
for vertex in range(1, 5):
     graph.add_edge(vertex, vertex + 4, 1)

# Now we can know that is the maximum flow(source -> sink)
print(graph.max_flow(source, sink))








'''simple docstring'''
from typing import Dict, Optional, Tuple

import torch



def 				lowerCAmelCase__	(       UpperCAmelCase     ):






       """simple docstring"""





       snake_case__					:	Optional[int]          =					boundaries[1] - boundaries[0]
       snake_case__					:	Optional[Any]          =					boundaries + step / 2
       snake_case__					:	str          =					torch.cat([bin_centers, (bin_centers[-1] + step).unsqueeze(-1     )]    ,       dim=0     )
       return bin_centers



def 				lowerCAmelCase__	(       UpperCAmelCase    ,       UpperCAmelCase    ,       ):






       """simple docstring"""





       snake_case__					:	str          =					_calculate_bin_centers(UpperCAmelCase     )
       return (
           torch.sum(aligned_distance_error_probs * bin_centers    ,       dim=-1     ),
           bin_centers[-1],
       )



def 				lowerCAmelCase__	(       UpperCAmelCase    ,       UpperCAmelCase = 31    ,       UpperCAmelCase = 64    ,       **UpperCAmelCase    ,       ):






       """simple docstring"""





       snake_case__					:	Dict          =					torch.linspace(0    ,       UpperCAmelCase    ,       steps=(no_bins - 1)    ,       device=logits.device     )

       snake_case__					:	str          =					torch.nn.functional.softmax(UpperCAmelCase    ,       dim=-1     )
       snake_case__       ,   snake_case__					:	List[str]          =					_calculate_expected_aligned_error(
           alignment_confidence_breaks=UpperCAmelCase    ,       aligned_distance_error_probs=UpperCAmelCase    ,       )

       return {
           "aligned_confidence_probs": aligned_confidence_probs,
           "predicted_aligned_error": predicted_aligned_error,
           "max_predicted_aligned_error": max_predicted_aligned_error,
       }






def 				lowerCAmelCase__	(       UpperCAmelCase    ,       UpperCAmelCase = None    ,       UpperCAmelCase = 31    ,       UpperCAmelCase = 64    ,       UpperCAmelCase = 1E-8    ,       **UpperCAmelCase    ,       ):






       """simple docstring"""





       if residue_weights is None:
              snake_case__					:	List[Any]          =					logits.new_ones(logits.shape[-2]     )

       snake_case__					:	Optional[Any]          =					torch.linspace(0    ,       UpperCAmelCase    ,       steps=(no_bins - 1)    ,       device=logits.device     )

       snake_case__					:	int          =					_calculate_bin_centers(UpperCAmelCase     )
       torch.sum(UpperCAmelCase     )
       snake_case__					:	Dict          =					logits.shape[-2]
       snake_case__					:	Optional[Any]          =					max(UpperCAmelCase    ,       19     )

       snake_case__					:	Optional[int]          =					1.2_4 * (clipped_n - 15) ** (1.0 / 3) - 1.8

       snake_case__					:	Tuple          =					torch.nn.functional.softmax(UpperCAmelCase    ,       dim=-1     )

       snake_case__					:	int          =					1.0 / (1 + (bin_centers**2) / (da**2))
       snake_case__					:	Optional[int]          =					torch.sum(probs * tm_per_bin    ,       dim=-1     )

       snake_case__					:	Optional[Any]          =					residue_weights / (eps + residue_weights.sum())
       snake_case__					:	Any          =					torch.sum(predicted_tm_term * normed_residue_mask    ,       dim=-1     )

       snake_case__					:	Dict          =					per_alignment * residue_weights

       snake_case__					:	List[str]          =					(weighted == torch.max(UpperCAmelCase     )).nonzero()[0]
       return per_alignment[tuple(UpperCAmelCase     )]




