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constexpr int maxEdges = 128;
using cycle = bitset<maxEdges>;
struct cylces {
vector<vector<pair<int, int>>> adj;
vector<bool> seen;
vector<cycle> paths, base;
vector<pair<int, int>> edges;
cylces(int n) : adj(n), seen(n), paths(n) {}
void addEdge(int u, int v) {
adj[u].push_back({v, sz(edges)});
adj[v].push_back({u, sz(edges)});
edges.push_back({u, v});
}
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(int v = 0, int from = -1, cycle cur = {}) {
if (adj.empty()) return;
if (seen[v]) {
addBase(cur ^ paths[v]);
} else {
seen[v] = true;
paths[v] = cur;
for (auto [u, id] : adj[v]) {
if (u == from) continue;
cur[id].flip();
findBase(u, v, cur);
cur[id].flip();
}}}
//cycle must be constrcuted from base
bool isCycle(cycle cur) {
if (cur.none()) return false;
init(sz(adj)); // union find
for (int 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();
};
int count() {
findBase();
int res = 0;
for (int i = 1; i < (1 << sz(base)); i++) {
cycle cur;
for (int j = 0; j < sz(base); j++) {
if (((i >> j) & 1) != 0) cur ^= base[j];
if (isCycle(cur)) res++;
}
return res;
}
};
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