import math, collections
SLD2 = {'co', 'com', 'net', 'org', 'gov', 'edu', 'ac'}
def split(q):
    q = q.rstrip('.').lower()
    labels = q.split('.')
    k = 3 if len(labels) >= 3 and len(labels[-1]) == 2 and labels[-2] in SLD2 else 2
    if len(labels) <= k: return q, ''
    return '.'.join(labels[-k:]), '.'.join(labels[:-k])
def chars(s): return [c for c in s if c != '.']
def H(counter):
    n = sum(counter.values())
    return -sum(v / n * math.log2(v / n) for v in counter.values()) if n else 0.0
def norm(counter):
    n = sum(counter.values()); return {k: v / n for k, v in counter.items()} if n else {}
def jsd(p, q):
    keys = sorted(set(p) | set(q)); s = 0.0
    for k in keys:
        a = p.get(k, 0.0); b = q.get(k, 0.0); m = (a + b) / 2
        if a > 0: s += 0.5 * a * math.log2(a / m)
        if b > 0: s += 0.5 * b * math.log2(b / m)
    return s
def groups_from(pairs):
    g = collections.defaultdict(set)
    for host, q in pairs:
        base, sub = split(q)
        if sub: g[(host, base)].add(sub)
    return g
def features(g):
    dists = {k: norm(collections.Counter(c for s in subs for c in chars(s))) for k, subs in g.items()}
    keys = sorted(dists); N = len(keys)
    tot = collections.defaultdict(float)
    for k in keys:
        for c, v in dists[k].items(): tot[c] += v
    out = {}
    for k in keys:
        subs = g[k]
        ref = {c: (tot[c] - dists[k].get(c, 0.0)) / (N - 1) for c in tot} if N > 1 else {}
        ref = {c: v for c, v in ref.items() if v > 1e-15}
        cnt = collections.Counter(c for s in subs for c in chars(s))
        out[k] = dict(U=len(subs), H=H(cnt), JSD=jsd(dists[k], ref) if ref else 0.0,
                      L=sum(len(s) for s in subs) / len(subs), maxlab=max(max(len(x) for x in s.split('.')) for s in subs))
    return out