"""simple docstring"""







from __future__ import annotations

import random

# Adjacency list representation of this graph:
# https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
_SCREAMING_SNAKE_CASE	:		str   =   {
    '''1''': ['''2''', '''3''', '''4''', '''5'''],
    '''2''': ['''1''', '''3''', '''4''', '''5'''],
    '''3''': ['''1''', '''2''', '''4''', '''5''', '''10'''],
    '''4''': ['''1''', '''2''', '''3''', '''5''', '''6'''],
    '''5''': ['''1''', '''2''', '''3''', '''4''', '''7'''],
    '''6''': ['''7''', '''8''', '''9''', '''10''', '''4'''],
    '''7''': ['''6''', '''8''', '''9''', '''10''', '''5'''],
    '''8''': ['''6''', '''7''', '''9''', '''10'''],
    '''9''': ['''6''', '''7''', '''8''', '''10'''],
    '''10''': ['''6''', '''7''', '''8''', '''9''', '''3'''],
}



def       A__    (	lowercase_     :	dict[str, list[str]]						)  ->							set[tuple[str, str]]:
   __lowerCamelCase    		=					{node: {node} for node in graph}

   __lowerCamelCase    		=					{node: graph[node][:] for node in graph}

   while len(lowercase_						) > 2:
      # Choose a random edge.
      __lowerCamelCase    		=					random.choice(list(graph_copy.keys()						)						)
      __lowerCamelCase    		=					random.choice(graph_copy[u]						)

      # Contract edge (u, v) to new node uv
      __lowerCamelCase    		=					u + v
      __lowerCamelCase    		=					list(set(graph_copy[u] + graph_copy[v]						)						)
      uv_neighbors.remove(lowercase_						)
      uv_neighbors.remove(lowercase_						)
      __lowerCamelCase    		=					uv_neighbors
      for neighbor in uv_neighbors:
         graph_copy[neighbor].append(lowercase_						)

      __lowerCamelCase    		=					set(contracted_nodes[u].union(contracted_nodes[v]						)						)

      # Remove nodes u and v.
      del graph_copy[u]
      del graph_copy[v]
      for neighbor in uv_neighbors:
         if u in graph_copy[neighbor]:
            graph_copy[neighbor].remove(lowercase_						)
         if v in graph_copy[neighbor]:
            graph_copy[neighbor].remove(lowercase_						)

    # Find cutset.
   __lowerCamelCase    		=					[contracted_nodes[node] for node in graph_copy]
   return {
       (node, neighbor)
       for node in groups[0]
       for neighbor in graph[node]
       if neighbor in groups[1]
   }


if __name__ == "__main__":
     print(partition_graph(TEST_GRAPH))







"""simple docstring"""






import requests

try:
						from django.contrib.auth import authenticate, login
						from django.shortcuts import redirect, render
except ImportError:
						lowerCAmelCase__    :    Union[str, Any]			=      print



def     a_		(   lowerCamelCase			):
				# Enter your recaptcha secret key here
				UpperCAmelCase__			 =				'secretKey'
				UpperCAmelCase__			 =				'https://www.google.com/recaptcha/api/siteverify'

				# when method is not POST, direct user to login page
				if request.method != "POST":
								return render(lowerCamelCase   ,     'login.html'			)

				# from the frontend, get username, password, and client_key
				UpperCAmelCase__			 =				request.POST.get('username'			)
				UpperCAmelCase__			 =				request.POST.get('password'			)
				UpperCAmelCase__			 =				request.POST.get('g-recaptcha-response'			)

				# post recaptcha response to Google's recaptcha api
				UpperCAmelCase__			 =				requests.post(lowerCamelCase   ,     data={'secret': secret_key, 'response': client_key}			)
				# if the recaptcha api verified our keys
				if response.json().get('success'   ,     lowerCamelCase			):
								# authenticate the user
								UpperCAmelCase__			 =				authenticate(lowerCamelCase   ,     username=lowerCamelCase   ,     password=lowerCamelCase			)
								if user_in_database:
												login(lowerCamelCase   ,     lowerCamelCase			)
												return redirect('/your-webpage'			)
				return render(lowerCamelCase   ,     'login.html'			)



