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 = filter(lambda x:x not in lp,partial_routes)
    return partial_paths

def route_deps(routes):
    routes_map = {}
    for r in routes:
        if routes_map.has_key(r.src):
            routes_map[r.src].append(r)
        else:
            routes_map[r.src]= [r]
        if not routes_map.has_key(r.dst):
            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 = filter(lambda x:x not in paths,routes)
    return (circ,paths,rem_paths)

def longest_path(routes):
    def route_path(r,deps):
        if not deps.has_key(r.dst) 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 deps.has_key(dep_elem):
        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)