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constexpr ll maxEdges = 128;
using cycle = bitset<maxEdges>;
struct cylces {
ll n;
vector<vector<pair<ll, ll>>> adj;
vector<bool> seen;
vector<cycle> paths, base;
vector<pair<ll, ll>> edges;
cylces(ll n) : n(n), adj(n), seen(n), paths(n) {}
void addEdge(ll a, ll b) {
adj[a].push_back({b, sz(edges)});
adj[b].push_back({a, sz(edges)});
edges.push_back({a, b});
}
void addBase(cycle cur) {
for (cycle o : base) {
o ^= cur;
if (o._Find_first() > cur._Find_first()) cur = o;
}
if (cur.any()) base.push_back(cur);
}
void findBase(ll c = 0, ll p = -1, cycle cur = {}) {
if (n == 0) return;
if (seen[c]) {
addBase(cur ^ paths[c]);
} else {
seen[c] = true;
paths[c] = cur;
for (auto e : adj[c]) {
if (e.first == p) continue;
cur[e.second].flip();
findBase(e.first, c, cur);
cur[e.second].flip();
}}}
//cycle must be constrcuted from base
bool isCycle(cycle cur) {
if (cur.none()) return false;
init(n);
for (ll i = 0; i < sz(edges); i++) {
if (cur[i]) {
cur[i] = false;
if (findSet(edges[i].first) ==
findSet(edges[i].second)) break;
unionSets(edges[i].first, edges[i].second);
}}
return cur.none();
};
ll count() {
findBase();
ll res = 0;
for (ll i = 1; i < (1ll << sz(base)); i++) {
cycle cur;
for (ll j = 0; j < sz(base); j++) {
if (((i >> j) & 1) != 0) cur ^= base[j];
if (isCycle(cur)) res++;
}
return res;
}
};
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