
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
_lowerCamelCase :       Union[str, Any]     					=    {
    '''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]]:
			_snake_case						=    {node: {node} for node in graph}

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

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

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

						_snake_case						=    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.
			_snake_case						=    [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))

import random
import sys

_lowerCamelCase :       Tuple     					=    '''ABCDEFGHIJKLMNOPQRSTUVWXYZ'''






def  a_	( )				->						None:
			_snake_case						=    input('Enter message: '				)
			_snake_case						=    'LFWOAYUISVKMNXPBDCRJTQEGHZ'
			_snake_case						=    input('Encrypt/Decrypt [e/d]: '				)

			check_valid_key(__lowercase				)

			if resp.lower().startswith('e'				):
						_snake_case						=    'encrypt'
						_snake_case						=    encrypt_message(__lowercase ,      __lowercase				)
			elif resp.lower().startswith('d'				):
						_snake_case						=    'decrypt'
						_snake_case						=    decrypt_message(__lowercase ,      __lowercase				)

			print(f'''\n{mode.title()}ion: \n{translated}'''				)






def  a_	( __lowercase     :			str				)				->						None:
			_snake_case						=    list(__lowercase				)
			_snake_case						=    list(__lowercase				)
			key_list.sort()
			letters_list.sort()

			if key_list != letters_list:
						sys.exit('Error in the key or symbol set.'				)






def  a_	( __lowercase     :			str ,      __lowercase     :			str				)				->						str:
			return translate_message(__lowercase ,      __lowercase ,      'encrypt'				)






def  a_	( __lowercase     :			str ,      __lowercase     :			str				)				->						str:
			return translate_message(__lowercase ,      __lowercase ,      'decrypt'				)






def  a_	( __lowercase     :			str ,      __lowercase     :			str ,      __lowercase     :			str				)				->						str:
			_snake_case						=    ''
			_snake_case						=    LETTERS
			_snake_case						=    key

			if mode == "decrypt":
						_snake_case			,      _snake_case						=    chars_b, chars_a

			for symbol in message:
						if symbol.upper() in chars_a:
									_snake_case						=    chars_a.find(symbol.upper()				)
									if symbol.isupper():
												translated += chars_b[sym_index].upper()
									else:
												translated += chars_b[sym_index].lower()
						else:
									translated += symbol

			return translated






def  a_	( )				->						str:
			_snake_case						=    list(__lowercase				)
			random.shuffle(__lowercase				)
			return "".join(__lowercase				)


if __name__ == "__main__":
			main()