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