// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll using pii = pair; #define rep(i, n) if (const int _rep_n = n; true) for (int i = 0; i < _rep_n; i++) #define rep1(i, n) if (const int _rep_n = n; true) for (int i = 1; i <= _rep_n; i++) #define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i, n) for (int i = (int)(n); i >= 1; i--) #define loop(i, a, B) for (int i = a; i B; i++) #define loopR(i, a, B) for (int i = a; i B; i--) #define all(x) begin(x), end(x) #define allR(x) rbegin(x), rend(x) #define pb push_back #define eb emplace_back #define fst first #define snd second template auto constexpr inf_ = numeric_limits::max()/2-1; auto constexpr INF32 = inf_; auto constexpr INF64 = inf_; auto constexpr INF = inf_; #ifdef LOCAL #include "debug.hpp" #define oj_local(x, y) (y) #else #define dump(...) (void)(0) #define debug if (0) #define oj_local(x, y) (x) #endif template struct pque : priority_queue, Comp> { vector &data() { return this->c; } void clear() { this->c.clear(); } }; template using pque_max = pque>; template using pque_min = pque>; template ::value, int> = 0> ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ::value, int> = 0> ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ())), class = typename enable_if::value>::type> istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; } template ostream& operator<<(ostream& os, pair const& p) { return os << p.first << " " << p.second; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } template ostream& operator<<(ostream& os, tuple const& t) { bool f = true; apply([&](auto&&... x) { ((os << (f ? f = false, "" : " ") << x), ...); }, t); return os; } template istream& operator>>(istream& is, tuple& t) { apply([&](auto&&... x) { ((is >> x), ...); }, t); return is; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define def(name, ...) auto name = MakeFixPoint() | [&](auto &&name, __VA_ARGS__) template struct FixPoint_d : private F { const char* const name; constexpr FixPoint_d(F&& f, const char* name) : F(forward(f)), name(name) {} template constexpr auto operator()(T&&... x) const { auto ret = F::operator()(*this, forward(x)...); #ifdef LOCAL cerr << name << to_s(tuple(x...)) << " -> " << to_s(ret) << '\n'; #endif return ret; } }; struct MakeFixPoint_d { const char* const name; MakeFixPoint_d(const char* name) : name(name) {} template constexpr auto operator|(F&& f) const { return FixPoint_d(forward(f), name); } }; #ifdef LOCAL #define def_d(name, ...) auto name = MakeFixPoint_d(#name) | [&](auto &&name, __VA_ARGS__) #else #define def_d def #endif template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << '\n'; exit(0); } template constexpr bool chmin(T& x, U const& y) { return x > (T)y ? x = (T)y, true : false; } template constexpr bool chmax(T& x, U const& y) { return x < (T)y ? x = (T)y, true : false; } template constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits::value_type{}); } template ()))> constexpr auto min(T const& a) { return *min_element(begin(a), end(a)); } template ()))> constexpr auto max(T const& a) { return *max_element(begin(a), end(a)); } template constexpr T min(set const& st) { assert(st.size()); return *st.begin(); } template constexpr T max(set const& st) { assert(st.size()); return *prev(st.end()); } template constexpr T min(multiset const& st) { assert(st.size()); return *st.begin(); } template constexpr T max(multiset const& st) { assert(st.size()); return *prev(st.end()); } constexpr ll max(signed x, ll y) { return max(x, y); } constexpr ll max(ll x, signed y) { return max(x, y); } constexpr ll min(signed x, ll y) { return min(x, y); } constexpr ll min(ll x, signed y) { return min(x, y); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x) - begin(v); } template int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x) - begin(v); } constexpr ll mod(ll x, ll m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; } constexpr ll div_floor(ll x, ll y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); } constexpr ll div_ceil(ll x, ll y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); } constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 }; constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 }; template vector iota(int n, Comp comp) { vector idx(n); iota(begin(idx), end(idx), 0); stable_sort(begin(idx), end(idx), comp); return idx; } constexpr int popcnt(ll x) { return __builtin_popcountll(x); } mt19937_64 seed_{random_device{}()}; template Int rand(Int a, Int b) { return uniform_int_distribution(a, b)(seed_); } i64 irand(i64 a, i64 b) { return rand(a, b); } // [a, b] u64 urand(u64 a, u64 b) { return rand(a, b); } // template void shuffle(It l, It r) { shuffle(l, r, seed_); } template V &operator--(V &v) { for (auto &x : v) --x; return v; } template V &operator++(V &v) { for (auto &x : v) ++x; return v; } bool next_product(vector &v, int m) { repR (i, v.size()) if (++v[i] < m) return true; else v[i] = 0; return false; } bool next_product(vector &v, vector const& s) { repR (i, v.size()) if (++v[i] < s[i]) return true; else v[i] = 0; return false; } template int sort_unique(Vec &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); return v.size(); } template int sort_unique(Vec &v, Comp comp) { sort(begin(v), end(v), comp); v.erase(unique(begin(v), end(v)), end(v)); return v.size(); } template auto prefix_sum(It l, It r) { vector s = { 0 }; while (l != r) s.emplace_back(s.back() + *l++); return s; } template auto suffix_sum(It l, It r) { vector s = { 0 }; while (l != r) s.emplace_back(*--r + s.back()); reverse(s.begin(), s.end()); return s; } template T pop(vector &a) { auto x = a.back(); a.pop_back(); return x; } template T pop_back(vector &a) { auto x = a.back(); a.pop_back(); return x; } template T pop(priority_queue &a) { auto x = a.top(); a.pop(); return x; } template T pop(queue &a) { auto x = a.front(); a.pop(); return x; } template T pop_front(deque &a) { auto x = a.front(); a.pop_front(); return x; } template T pop_back(deque &a) { auto x = a.back(); a.pop_back(); return x; } template T pop_front(set &a) { auto x = *a.begin(); a.erase(a.begin()); return x; } template T pop_back(set &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; } template T pop_front(multiset &a) { auto it = a.begin(); auto x = *it; a.erase(it); return x; } template T pop_back(multiset &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; } template pair, vector> unzip(vector> const& c) { vector a; vector b; for (auto const& [x, y] : c) { a.push_back(x); b.push_back(y); } return { a, b }; } template pair, vector> unzip(map const& c) { vector a; vector b; for (auto const& [x, y] : c) { a.push_back(x); b.push_back(y); } return { a, b }; } // <<< // >>> min cost b-flow // https://misawa.github.io/others/flow/lets_use_capacity_scaling.html template struct MinCostFlow { // capacity scaling struct Edge { int32_t from, to, rev; Flow cap, flow; Cost cost; Edge(int from, int to, int rev, Flow cap, Cost cost) : from(from), to(to), rev(rev), cap(cap), flow(0), cost(cost) {} }; vector> g; vector> es; vector b; vector p, dist; vector pv, pe, S, T; int V, E = 0; Cost max_dist; MinCostFlow(int V = 0) : g(V), b(V), p(V), pv(V, -1), pe(V, -1), V(V) {} int add_edge(int from, int to, Flow lower_cap, Flow upper_cap, Cost cost) { assert(0 <= from and from < V); assert(0 <= to and to < V); assert(lower_cap <= upper_cap); es.emplace_back(from, g[from].size()); g[from].emplace_back(from, to, g[to].size() + (from == to ? 1 : 0), upper_cap, cost); g[to].emplace_back(to, from, g[from].size()-1, -lower_cap, -cost); return E++; } Edge edge(int id) const { assert(0 <= id); assert(id < (int)es.size()); auto [from, idx] = es[id]; return g[from][idx]; } template static constexpr bool chmin(T &x, T const& y) { return x > y ? (x = y, true) : false; }; void push(Edge &e, Flow f) { e.flow += f; g[e.to][e.rev].flow -= f; b[e.from] -= f; b[e.to] += f; } Flow rcap(Edge const& e) const { return e.cap - e.flow; } Cost rcost(Edge const& e) const { return e.cost + p[e.from] - p[e.to]; } pair run() { p.resize(V); for (auto &es : g) for (auto &e : es) if (rcap(e) < 0) push(e, rcap(e)); Flow inf_flow = 1; for (auto &es : g) for (auto &e : es) inf_flow = max(inf_flow, rcap(e)); Flow delta = 1; while (delta <= inf_flow) delta <<= 1; for (delta >>= 1; delta; delta >>= 1) { S.clear(); T.clear(); for (auto &es : g) { for (auto &e : es) { if (rcost(e) < 0 and rcap(e) >= delta) { push(e, rcap(e)); } } } for (int32_t x = 0; x < V; x++) { if (b[x] >= +delta) S.push_back(x); if (b[x] <= -delta) T.push_back(x); } while (dual(delta)) primal(delta); } Cost ans = 0; for (auto [from, idx] : es) { auto const& e = g[from][idx]; ans += e.flow * e.cost; } return { ans, S.empty() and T.empty() }; } bool dual(Flow delta) { using P = pair; static auto comp = [](P const& p, P const& q) { return p.first > q.first; }; using PQ = priority_queue, decltype(comp)>; struct pque : PQ { pque() : PQ(comp) {} void clear() { this->c.clear(); } }; static pque pq; static auto const inf_cost = max(numeric_limits::max(), numeric_limits::max()); dist.assign(V, inf_cost); pv.assign(V, -1); pe.assign(V, -1); S.erase(remove_if(begin(S), end(S), [&](int x) { return b[x] < +delta; }), end(S)); T.erase(remove_if(begin(T), end(T), [&](int x) { return b[x] > -delta; }), end(T)); if (T.empty()) return false; pq.clear(); for (int s : S) pq.emplace(dist[s] = 0, s); max_dist = 0; size_t cnt = 0; while (pq.size()) { auto [d, x] = pq.top(); pq.pop(); if (dist[x] < d) continue; max_dist = d; if (b[x] <= -delta and ++cnt >= T.size()) break; for (size_t i = 0; i < g[x].size(); i++) { auto const& e = g[x][i]; if (rcap(e) >= delta and chmin(dist[e.to], d + rcost(e))) { pv[e.to] = x, pe[e.to] = i; pq.emplace(dist[e.to], e.to); } } } for (int x = 0; x < V; x++) p[x] += min(dist[x], max_dist); return cnt > 0; } void primal(Flow delta) { for (int t : T) { if (dist[t] > max_dist) continue; Flow f = -b[t]; int x; for (x = t; pv[x] >= 0 and f >= delta; x = pv[x]) { chmin(f, rcap(g[pv[x]][pe[x]])); } chmin(f, b[x]); if (f < delta) continue; x = t; while (true) { auto &y = pv[x]; if (y < 0) break; push(g[y][pe[x]], f); x = y, y = -1; } } } // tuple max_flow(int s, int t) { // assert(s != t); // Flow inf_flow = abs(b[s]); // for (auto const& e : g[s]) inf_flow += max(e.cap, 0); // add_edge(t, s, 0, inf_flow, 0); // auto pop = [&]() { // g[s].pop_back(); // g[t].pop_back(); // es.pop_back(); // }; // auto [cost, ok] = run(); // if (not ok) { // pop(); // return { 0, cost, false }; // } // inf_flow = abs(b[s]); // for (auto const& e : g[s]) inf_flow += rcap(e); // b[s] += inf_flow, b[t] -= inf_flow; // tie(cost, ok) = run(); // b[s] -= inf_flow, b[t] += inf_flow; // pop(); // return { b[t], cost, true }; // } #ifdef LOCAL friend string to_s(MinCostFlow a) { string ret = "\n"; ret += "V = " + to_s(a.V) + ", E = " + to_s(a.E) + "\n"; for (int id = 0; id < a.E; id++) { auto [from, idx] = a.es[id]; auto const& e = a.g[from][idx]; auto const& r = a.g[e.to][e.rev]; ret += to_s(id) + " : "; ret += to_s(e.from) + "->" + to_s(e.to) + ", "; ret += "flow " + to_s(e.flow) + " in [" + to_s(-r.cap) + ", " + to_s(e.cap) + "], "; ret += "cost " + to_s(e.cost) + "\n"; } return ret; } #endif }; // <<< int32_t main() { int n, m; cin >> n >> m; auto adj = make_v(n, n); rep (i, m) { int a, b; cin >> a >> b; --a, --b; adj[a][b] = adj[b][a] = 1; } MinCostFlow g(2*n); rep (i, n) rep (j, n) { if (i == j) continue; g.add_edge(i, n+j, 0, 1, 1-adj[i][j]); } rep (i, n) { g.b[i] = 1; g.b[n+i] = -1; } auto [cost, ok] = g.run(); assert(ok); dump(cost); cout << n-cost*2 << '\n'; }