CYCLE_LIMIT = 3


def rem_routes(routes):
    loop_routes = routes
    while len(loop_routes) > 0:
        circ, paths, loop_routes = largest_loop(loop_routes)
        if not circ:
            break
    partial_paths = []
    partial_routes = loop_routes
    while len(partial_routes) > 0:
        lp = longest_path(partial_routes)
        partial_paths.append((lp[-1].dst, lp[0].src))
        partial_routes = [x for x in partial_routes if x not in lp]
    return partial_paths


def route_deps(routes):
    routes_map = {}
    for r in routes:
        if r.src in routes_map:
            routes_map[r.src].append(r)
        else:
            routes_map[r.src] = [r]
        if r.dst not in routes_map:
            routes_map[r.dst] = []
    return routes_map


def largest_loop(routes):
    deps = route_deps(routes)
    circ_paths = [find_loop(r.src, r.src, deps, set(), []) for r in routes]
    circ, paths = max(circ_paths, key=lambda p: len(p[1]))
    # print filter(lambda p:not p[0],circ_paths)
    rem_paths = [x for x in routes if x not in paths]
    return (circ, paths, rem_paths)


def longest_path(routes):
    def route_path(r, deps):
        if r.dst not in deps or len(deps[r.dst]) == 0:
            return [r]
        all_dep_paths = [([r] + route_path(rt, deps)) for rt in deps[r.dst]]
        rp = max(all_dep_paths, key=lambda p: len(p))
        return rp
    deps = route_deps(routes)
    all_paths = [route_path(r, deps) for r in routes]
    longest = max(all_paths, key=len)
    return longest


def find_loop(elem, dep_elem, deps, checked, path):
    found_loop = False
    if dep_elem not in checked and dep_elem in deps:
        checked.add(dep_elem)
        for c in deps[dep_elem]:
            path.append(c)
            if elem == c.dst and len(path) <= CYCLE_LIMIT:
                found_loop = True
                break
            (loop, path) = find_loop(elem, c.dst, deps, checked, path)
            if loop:
                found_loop = True
                break
            else:
                del(path[-1])
    return (found_loop, path)