
from typing import Dict, Optional, Tuple

import torch


def  A			(   lowercase					)  ->    Union[str, Any]:
		'''simple docstring'''

		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  A			(   lowercase       ,			lowercase       ,			)  ->    Dict:
		'''simple docstring'''

		UpperCamelCase            =	_calculate_bin_centers(__A					)
		return (
		    torch.sum(aligned_distance_error_probs * bin_centers       ,			dim=-1					),
		    bin_centers[-1],
		)


def  A			(   lowercase       ,			lowercase = 31       ,			lowercase = 64       ,			**lowercase       ,			)  ->    Any:
		'''simple docstring'''

		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  A			(   lowercase       ,			lowercase = None       ,			lowercase = 31       ,			lowercase = 64       ,			lowercase = 1e-8       ,			**lowercase       ,			)  ->    Any:
		'''simple docstring'''

		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            =	1.2_4 * (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					)]



lowerCAmelCase__							=			float("inf")






class     __magic_name__     :


 def __init__(    self		:			List[str]      ,    lowerCAmelCase__		:			Dict     )     ->   List[Any]:
   UpperCAmelCase          =	[0] * n
   UpperCAmelCase          =	[0] * n
   UpperCAmelCase          =	[0] * n
   UpperCAmelCase          =	[[] for _ in range(lowerCAmelCase__     )]


 def _UpperCamelCase						(    self		:			List[Any]      ,    lowerCAmelCase__		:			Tuple      ,    lowerCAmelCase__		:			Dict      ,    lowerCAmelCase__		:			str      ,    lowerCAmelCase__		:			Optional[Any]=0     )     ->   Any:
   self.adj[a].append([b, len(self.adj[b]     ), c, 0]     )
   self.adj[b].append([a, len(self.adj[a]     ) - 1, rcap, 0]     )


 def _UpperCamelCase						(    self		:			List[str]      ,    lowerCAmelCase__		:			Union[str, Any]      ,    lowerCAmelCase__		:			List[Any]      ,    lowerCAmelCase__		:			Any     )     ->   List[str]:
   if vertex == sink or not flow:
     return flow

   for i in range(self.ptr[vertex]      ,    len(self.adj[vertex]     )     ):
     UpperCAmelCase          =	self.adj[vertex][i]
     if self.lvl[e[0]] == self.lvl[vertex] + 1:
       UpperCAmelCase          =	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          =	self.ptr[vertex] + 1
   return 0


 def _UpperCamelCase						(    self		:			str      ,    lowerCAmelCase__		:			str      ,    lowerCAmelCase__		:			Tuple     )     ->   int:
   UpperCAmelCase   ,						UpperCAmelCase          =	0, source
   for l in range(3_1     ):  # noqa: E741  l = 30 maybe faster for random data
     while True:
       UpperCAmelCase   ,						UpperCAmelCase          =	[0] * len(self.q     ), [0] * len(self.q     )
       UpperCAmelCase   ,						UpperCAmelCase   ,						UpperCAmelCase          =	0, 1, 1
       while qi < qe and not self.lvl[sink]:
         UpperCAmelCase          =	self.q[qi]
         qi += 1
         for e in self.adj[v]:
           if not self.lvl[e[0]] and (e[2] - e[3]) >> (3_0 - l):
             UpperCAmelCase          =	e[0]
             qe += 1
             UpperCAmelCase          =	self.lvl[v] + 1

       UpperCAmelCase          =	self.depth_first_search(lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__     )
       while p:
         flow += p
         UpperCAmelCase          =	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))



