#include #include using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; // https://ei1333.github.io/library/graph/flow/gabow-edmonds.hpp #line 1 "graph/flow/gabow-edmonds.hpp" // https://qiita.com/Kutimoti_T/items/5b579773e0a24d650bdf /** * @brief Gabow Edmonds(一般グラフの最大マッチング) * @docs docs/gabow-edmonds.md */ struct GabowEdmonds { struct edge { int to, idx; }; vector< vector< edge > > g; vector< pair< int, int > > edges; vector< int > mate, label, first; queue< int > que; GabowEdmonds(int n) : g(n + 1), mate(n + 1), label(n + 1, -1), first(n + 1) {} void add_edge(int u, int v) { ++u, ++v; g[u].push_back((edge) {v, (int) (edges.size() + g.size())}); g[v].push_back((edge) {u, (int) (edges.size() + g.size())}); edges.emplace_back(u, v); } int find(int x) { if(label[first[x]] < 0) return first[x]; first[x] = find(first[x]); return first[x]; } void rematch(int v, int w) { int t = mate[v]; mate[v] = w; if(mate[t] != v) return; if(label[v] < (int)g.size()) { mate[t] = label[v]; rematch(label[v], t); } else { int x = edges[label[v] - g.size()].first; int y = edges[label[v] - g.size()].second; rematch(x, y); rematch(y, x); } } void assign_label(int x, int y, int num) { int r = find(x); int s = find(y); int join = 0; if(r == s) return; label[r] = -num; label[s] = -num; while(true) { if(s != 0) swap(r, s); r = find(label[mate[r]]); if(label[r] == -num) { join = r; break; } label[r] = -num; } int v = first[x]; while(v != join) { que.push(v); label[v] = num; first[v] = join; v = first[label[mate[v]]]; } v = first[y]; while(v != join) { que.push(v); label[v] = num; first[v] = join; v = first[label[mate[v]]]; } } bool augment_check(int u) { que = queue< int >(); first[u] = 0; label[u] = 0; que.push(u); while(!que.empty()) { int x = que.front(); que.pop(); for(auto e : g[x]) { int y = e.to; if(mate[y] == 0 && y != u) { mate[y] = x; rematch(x, y); return true; } else if(label[y] >= 0) { assign_label(x, y, e.idx); } else if(label[mate[y]] < 0) { label[mate[y]] = x; first[mate[y]] = y; que.push(mate[y]); } } } return false; } vector< pair< int, int > > max_matching() { for(int i = 1; i < (int)g.size(); i++) { if(mate[i] != 0) continue; if(augment_check(i)) label.assign(g.size(), -1); } vector< pair< int, int > > ret; for(int i = 1; i < (int)g.size(); i++) { if(i < mate[i]) ret.emplace_back(i - 1, mate[i] - 1); } return ret; } }; int main() { ios::sync_with_stdio(false); cin.tie(0); int n, m; cin >> n >> m; GabowEdmonds g(2 * n); VI deg(n); rep(_, m) { int u, v; cin >> u >> v; u--, v--; rep(i, 2) rep(j, 2) g.add_edge(2 * u + i, 2 * v + j); deg[u]++; deg[v]++; } int ans = 2 * g.max_matching().size(); if (ans == 2 * (n - 1) && *min_element(all(deg)) == 0) { ans -= 2; } cout << ans - n << '\n'; }