#include using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; constexpr int INF = 0x3f3f3f3f; constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL; constexpr double EPS = 1e-8; constexpr int MOD = 998244353; // constexpr int MOD = 1000000007; constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1}; constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1}; constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1}; template inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; } template inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << fixed << setprecision(20); } } iosetup; template struct MinimumCostSTFlow { struct Edge { int dst, rev; T cap; U cost; explicit Edge(const int dst, const T cap, const U cost, const int rev) : dst(dst), rev(rev), cap(cap), cost(cost) {} }; const U uinf; std::vector> graph; explicit MinimumCostSTFlow(const int n, const U uinf = std::numeric_limits::max()) : uinf(uinf), graph(n), tinf(std::numeric_limits::max()), n(n), has_negative_edge(false), prev_v(n, -1), prev_e(n, -1), dist(n), potential(n, 0) {} void add_edge(const int src, const int dst, const T cap, const U cost) { has_negative_edge |= cost < 0; graph[src].emplace_back(dst, cap, cost, graph[dst].size()); graph[dst].emplace_back(src, 0, -cost, graph[src].size() - 1); } U solve(const int s, const int t, T flow) { if (flow == 0) [[unlikely]] return 0; U res = 0; has_negative_edge ? bellman_ford(s) : dijkstra(s); while (true) { if (dist[t] == uinf) return uinf; res += calc(s, t, &flow); if (flow == 0) break; dijkstra(s); } return res; } U solve(const int s, const int t) { U res = 0; T flow = tinf; bellman_ford(s); while (potential[t] < 0 && dist[t] != uinf) { res += calc(s, t, &flow); dijkstra(s); } return res; } std::pair minimum_cost_maximum_flow(const int s, const int t, const T flow) { if (flow == 0) [[unlikely]] return {0, 0}; T f = flow; U cost = 0; has_negative_edge ? bellman_ford(s) : dijkstra(s); while (dist[t] != uinf) { cost += calc(s, t, &f); if (f == 0) break; dijkstra(s); } return {flow - f, cost}; } private: const T tinf; const int n; bool has_negative_edge; std::vector prev_v, prev_e; std::vector dist, potential; std::priority_queue, std::vector>, std::greater>> que; void bellman_ford(const int s) { std::fill(dist.begin(), dist.end(), uinf); dist[s] = 0; bool is_updated = true; for (int step = 0; step < n && is_updated; ++step) { is_updated = false; for (int i = 0; i < n; ++i) { if (dist[i] == uinf) continue; for (int j = 0; std::cmp_less(j, graph[i].size()); ++j) { const Edge& e = graph[i][j]; if (e.cap > 0 && dist[e.dst] > dist[i] + e.cost) { dist[e.dst] = dist[i] + e.cost; prev_v[e.dst] = i; prev_e[e.dst] = j; is_updated = true; } } } } assert(!is_updated); for (int i = 0; i < n; ++i) { if (dist[i] != uinf) potential[i] += dist[i]; } } void dijkstra(const int s) { std::fill(dist.begin(), dist.end(), uinf); dist[s] = 0; que.emplace(0, s); while (!que.empty()) { const auto [d, ver] = que.top(); que.pop(); if (dist[ver] < d) continue; for (int i = 0; std::cmp_less(i, graph[ver].size()); ++i) { const Edge& e = graph[ver][i]; const U nxt = dist[ver] + e.cost + potential[ver] - potential[e.dst]; if (e.cap > 0 && dist[e.dst] > nxt) { dist[e.dst] = nxt; prev_v[e.dst] = ver; prev_e[e.dst] = i; que.emplace(dist[e.dst], e.dst); } } } for (int i = 0; i < n; ++i) { if (dist[i] != uinf) potential[i] += dist[i]; } } U calc(const int s, const int t, T* flow) { T f = *flow; for (int v = t; v != s; v = prev_v[v]) { f = std::min(f, graph[prev_v[v]][prev_e[v]].cap); } *flow -= f; for (int v = t; v != s; v = prev_v[v]) { Edge& e = graph[prev_v[v]][prev_e[v]]; e.cap -= f; graph[v][e.rev].cap += f; } return potential[t] * f; } }; template struct WeightedBipartiteMatching { explicit WeightedBipartiteMatching(const int left, const int right) : is_built(false), left(left), right(right), mcf(left + right + 2) {} void add_edge(const int src, const int dst, const T cost) { mcf.add_edge(src, left + dst, 1, -cost); } T solve() { assert(!is_built); is_built = true; const int s = left + right, t = left + right + 1; for (int i = 0; i < left; ++i) { mcf.add_edge(s, i, 1, 0); } for (int i = 0; i < right; ++i) { mcf.add_edge(left + i, t, 1, 0); } return -mcf.minimum_cost_maximum_flow(s, t, left).second; } std::vector matching() const { assert(is_built); std::vector res(left, -1); for (int i = 0; i < left; ++i) { for (const auto& e : mcf.graph[i]) { if (e.cap == 0 && left <= e.dst && e.dst < left + right) { res[i] = e.dst - left; break; } } } return res; } private: bool is_built; const int left, right; MinimumCostSTFlow mcf; }; int main() { int n, m; cin >> n >> m; vector is_good(n, vector(n, 0)); while (m--) { int u, v; cin >> u >> v; --u; --v; is_good[u][v] = true; } WeightedBipartiteMatching wbm(n, n); REP(i, n) FOR(j, i + 1, n) { wbm.add_edge(i, j, is_good[i][j] ? 2 : 0); wbm.add_edge(j, i, is_good[i][j] ? 2 : 0); } const int ans = wbm.solve() - n; cout << (ans == n - 1 ? n - 2 : ans) << '\n'; return 0; }