



UpperCAmelCase__			:   Optional[Any]      			=    float('inf')





class 							lowerCAmelCase_		:







		def __init__(    self  :   List[str]       ,		UpperCAmelCase_  :   Dict					)       ->		List[Any]:


						'''simple docstring'''







						_UpperCAmelCase						:  List[Any]     					=	[0] * n
						_UpperCAmelCase						:  Optional[Any]     					=	[0] * n
						_UpperCAmelCase						:  Optional[int]     					=	[0] * n
						_UpperCAmelCase						:  Any     					=	[[] for _ in range(lowerCAmelCase__					)]







		def 					a_  (    self  :   List[Any]       ,		UpperCAmelCase_  :   Tuple       ,		UpperCAmelCase_  :   Dict       ,		UpperCAmelCase_  :   str       ,		UpperCAmelCase_  :   Optional[Any]=0					)       ->		Any:


						'''simple docstring'''







						self.adj[a].append([b, len(self.adj[b]					), c, 0]					)
						self.adj[b].append([a, len(self.adj[a]					) - 1, rcap, 0]					)







		def 					a_  (    self  :   List[str]       ,		UpperCAmelCase_  :   Union[str, Any]       ,		UpperCAmelCase_  :   List[Any]       ,		UpperCAmelCase_  :   Any					)       ->		List[str]:


						'''simple docstring'''







						if vertex == sink or not flow:
										return flow

						for i in range(self.ptr[vertex]       ,		len(self.adj[vertex]					)					):
										_UpperCAmelCase						:  Optional[int]     					=	self.adj[vertex][i]
										if self.lvl[e[0]] == self.lvl[vertex] + 1:
														_UpperCAmelCase						:  List[Any]     					=	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
										_UpperCAmelCase						:  Union[str, Any]     					=	self.ptr[vertex] + 1
						return 0







		def 					a_  (    self  :   str       ,		UpperCAmelCase_  :   str       ,		UpperCAmelCase_  :   Tuple					)       ->		int:


						'''simple docstring'''







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

														_UpperCAmelCase						:  Optional[int]     					=	self.depth_first_search(lowerCAmelCase__       ,		lowerCAmelCase__       ,		lowerCAmelCase__					)
														while p:
																		flow += p
																		_UpperCAmelCase						:  Any     					=	self.depth_first_search(lowerCAmelCase__       ,		lowerCAmelCase__       ,		lowerCAmelCase__					)

														if not self.lvl[sink]:
																		break

						return flow
UpperCAmelCase__			:   Optional[int]      			=    Dinic(10)
UpperCAmelCase__			:   str      			=    0
UpperCAmelCase__			:   int      			=    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))



from typing import Dict, Optional, Tuple

import torch
def   _lowerCAmelCase(						__A      ):
  UpperCAmelCase          =	boundaries[1] - boundaries[0]
  UpperCAmelCase          =	boundaries + step / 2
  UpperCAmelCase          =	torch.cat([bin_centers, (bin_centers[-1] + step).unsqueeze(-1      )] ,							dim=0      )
  return bin_centers
def   _lowerCAmelCase(						__A ,							__A ,							):
  UpperCAmelCase          =	_calculate_bin_centers(__A      )
  return (
      torch.sum(aligned_distance_error_probs * bin_centers ,							dim=-1      ),
      bin_centers[-1],
  )
def   _lowerCAmelCase(						__A ,							__A = 31 ,							__A = 64 ,							**__A ,							):
  UpperCAmelCase          =	torch.linspace(0 ,							__A ,							steps=(no_bins - 1) ,							device=logits.device      )

  UpperCAmelCase          =	torch.nn.functional.softmax(__A ,							dim=-1      )
  UpperCAmelCase   ,						UpperCAmelCase          =	_calculate_expected_aligned_error(
      alignment_confidence_breaks=__A ,							aligned_distance_error_probs=__A ,							)

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





def   _lowerCAmelCase(						__A ,							__A = None ,							__A = 31 ,							__A = 64 ,							__A = 1E-8 ,							**__A ,							):
  if residue_weights is None:
    UpperCAmelCase          =	logits.new_ones(logits.shape[-2]      )

  UpperCAmelCase          =	torch.linspace(0 ,							__A ,							steps=(no_bins - 1) ,							device=logits.device      )

  UpperCAmelCase          =	_calculate_bin_centers(__A      )
  torch.sum(__A      )
  UpperCAmelCase          =	logits.shape[-2]
  UpperCAmelCase          =	max(__A ,							19      )

  UpperCAmelCase          =	1.24 * (clipped_n - 15) ** (1.0 / 3) - 1.8

  UpperCAmelCase          =	torch.nn.functional.softmax(__A ,							dim=-1      )

  UpperCAmelCase          =	1.0 / (1 + (bin_centers**2) / (da**2))
  UpperCAmelCase          =	torch.sum(probs * tm_per_bin ,							dim=-1      )

  UpperCAmelCase          =	residue_weights / (eps + residue_weights.sum())
  UpperCAmelCase          =	torch.sum(predicted_tm_term * normed_residue_mask ,							dim=-1      )

  UpperCAmelCase          =	per_alignment * residue_weights

  UpperCAmelCase          =	(weighted == torch.max(__A      )).nonzero()[0]
  return per_alignment[tuple(__A      )]



