






"""simple docstring"""




# using dfs for finding eulerian path traversal



def    UpperCamelCase						(	_A,   _A,   _A,   _A=None			):






						"""simple docstring"""







						__magic_name__      :       Dict       						= (path or []) + [u]
						for v in graph[u]:
												if visited_edge[u][v] is False:
																		__magic_name__						,__magic_name__      :       Tuple       						= True, True
																		__magic_name__      :       Dict       						= dfs(UpperCamelCase__,   UpperCamelCase__,   UpperCamelCase__,   UpperCamelCase__			)
						return path

def    UpperCamelCase						(	_A,   _A			):






						"""simple docstring"""







						__magic_name__      :       Dict       						= 0
						__magic_name__      :       Dict       						= -1
						for i in range(UpperCamelCase__			):
												if i not in graph.keys():
																		continue
												if len(graph[i]			) % 2 == 1:
																		odd_degree_nodes += 1
																		__magic_name__      :       Union[str, Any]       						= i
						if odd_degree_nodes == 0:
												return 1, odd_node
						if odd_degree_nodes == 2:
												return 2, odd_node
						return 3, odd_node

def    UpperCamelCase						(	_A,   _A			):






						"""simple docstring"""







						__magic_name__      :       str       						= [[False for _ in range(max_node + 1			)] for _ in range(max_node + 1			)]
						__magic_name__						,__magic_name__      :       Optional[Any]       						= check_circuit_or_path(UpperCamelCase__,   UpperCamelCase__			)
						if check == 3:
												print("""graph is not Eulerian"""			)
												print("""no path"""			)
												return
						__magic_name__      :       Optional[Any]       						= 1
						if check == 2:
												__magic_name__      :       int       						= odd_node
												print("""graph has a Euler path"""			)
						if check == 1:
												print("""graph has a Euler cycle"""			)
						__magic_name__      :       Dict       						= dfs(UpperCamelCase__,   UpperCamelCase__,   UpperCamelCase__			)
						print(UpperCamelCase__			)

def    UpperCamelCase						(	):






						"""simple docstring"""







						__magic_name__      :       List[Any]       						= {1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
						__magic_name__      :       Dict       						= {1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
						__magic_name__      :       int       						= {1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
						__magic_name__      :       Optional[int]       						= {1: [2, 3], 2: [1, 3], 3: [1, 2]}
						__magic_name__      :       str       						= {
						    1: [],
						    2: []
						    # all degree is zero
						}
						__magic_name__      :       Dict       						= 10
						check_euler(UpperCamelCase__,   UpperCamelCase__			)
						check_euler(UpperCamelCase__,   UpperCamelCase__			)
						check_euler(UpperCamelCase__,   UpperCamelCase__			)
						check_euler(UpperCamelCase__,   UpperCamelCase__			)
						check_euler(UpperCamelCase__,   UpperCamelCase__			)


if __name__ == "__main__":
		main()








import sys

from .dependency_versions_table import deps
from .utils.versions import require_version, require_version_core


# define which module versions we always want to check at run time
# (usually the ones defined in `install_requires` in setup.py)
#
# order specific notes:
# - tqdm must be checked before tokenizers

__magic_name__:					int							=     "python tqdm regex requests packaging filelock numpy tokenizers".split()
if sys.version_info < (3, 7):
		pkgs_to_check_at_runtime.append("dataclasses")
if sys.version_info < (3, 8):
		pkgs_to_check_at_runtime.append("importlib_metadata")

for pkg in pkgs_to_check_at_runtime:
		if pkg in deps:
				if pkg == "tokenizers":
						# must be loaded here, or else tqdm check may fail
						from .utils import is_tokenizers_available

						if not is_tokenizers_available():
								continue  # not required, check version only if installed

				require_version_core(deps[pkg])
		else:
				raise ValueError(F"""can't find {pkg} in {deps.keys()}, check dependency_versions_table.py""")

def    UpperCamelCase						(	_A,   _A=None			):






						"""simple docstring"""







						require_version(deps[pkg],   _A			)
