






# using dfs for finding eulerian path traversal






def 					snake_case	(  lowerCamelCase					,	lowerCamelCase					,	lowerCamelCase					,	lowerCamelCase=None       ):




	'''simple docstring'''







	__lowercase   							=	(path or []) + [u]
	for v in graph[u]:
		if visited_edge[u][v] is False:
			__lowercase							,    __lowercase   							=	True, True
			__lowercase   							=	dfs(_snake_case					,	_snake_case					,	_snake_case					,	_snake_case       )
	return path





def 					snake_case	(  lowerCamelCase					,	lowerCamelCase       ):




	'''simple docstring'''







	__lowercase   							=	0
	__lowercase   							=	-1
	for i in range(_snake_case       ):
		if i not in graph.keys():
			continue
		if len(graph[i]       ) % 2 == 1:
			odd_degree_nodes += 1
			__lowercase   							=	i
	if odd_degree_nodes == 0:
		return 1, odd_node
	if odd_degree_nodes == 2:
		return 2, odd_node
	return 3, odd_node





def 					snake_case	(  lowerCamelCase					,	lowerCamelCase       ):




	'''simple docstring'''







	__lowercase   							=	[[False for _ in range(max_node + 1       )] for _ in range(max_node + 1       )]
	__lowercase							,    __lowercase   							=	check_circuit_or_path(_snake_case					,	_snake_case       )
	if check == 3:
		print("""graph is not Eulerian"""       )
		print("""no path"""       )
		return
	__lowercase   							=	1
	if check == 2:
		__lowercase   							=	odd_node
		print("""graph has a Euler path"""       )
	if check == 1:
		print("""graph has a Euler cycle"""       )
	__lowercase   							=	dfs(_snake_case					,	_snake_case					,	_snake_case       )
	print(_snake_case       )





def 					snake_case	(  ):




	'''simple docstring'''







	__lowercase   							=	{1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
	__lowercase   							=	{1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
	__lowercase   							=	{1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
	__lowercase   							=	{1: [2, 3], 2: [1, 3], 3: [1, 2]}
	__lowercase   							=	{
	    1: [],
	    2: []
	    # all degree is zero
	}
	__lowercase   							=	10
	check_euler(_snake_case					,	_snake_case       )
	check_euler(_snake_case					,	_snake_case       )
	check_euler(_snake_case					,	_snake_case       )
	check_euler(_snake_case					,	_snake_case       )
	check_euler(_snake_case					,	_snake_case       )


if __name__ == "__main__":
						main()






def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:bytes				)  ->     str:
   return "".join([hex(_snake_case				)[2:].zfill(2				).upper() for byte in list(_snake_case				)]				)

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:str				)  ->     bytes:
   # Check data validity, following RFC3548
   # https://www.ietf.org/rfc/rfc3548.txt
   if (len(_snake_case				) % 2) != 0:
      raise ValueError(
          '''Base16 encoded data is invalid:
Data does not have an even number of hex digits.'''				)
   # Check the character set - the standard base16 alphabet
   # is uppercase according to RFC3548 section 6
   if not set(_snake_case				) <= set('''0123456789ABCDEF'''				):
      raise ValueError(
          '''Base16 encoded data is invalid:
Data is not uppercase hex or it contains invalid characters.'''				)
   # For every two hexadecimal digits (= a byte), turn it into an integer.
   # Then, string the result together into bytes, and return it.
   return bytes(int(data[i] + data[i + 1]	,   16				) for i in range(0	,   len(_snake_case				)	,   2				)				)


if __name__ == "__main__":
   import doctest

   doctest.testmod()



