#include using namespace std; using lint = long long; using pi = array; #define sz(a) ((int)(a).size()) #define all(a) (a).begin(), (a).end() const int MAXN = 10005 + 1; struct gm { // 1-based Vertex index int vis[MAXN], par[MAXN], orig[MAXN], match[MAXN], aux[MAXN], t, N; vector conn[MAXN]; queue Q; void addEdge(int u, int v) { u++; v++; conn[u].push_back(v); conn[v].push_back(u); } void init(int n) { N = n; t = 0; for (int i = 0; i <= n; ++i) { conn[i].clear(); match[i] = aux[i] = par[i] = 0; } } void augment(int u, int v) { int pv = v, nv; do { pv = par[v]; nv = match[pv]; match[v] = pv; match[pv] = v; v = nv; } while (u != pv); } int lca(int v, int w) { ++t; while (true) { if (v) { if (aux[v] == t) return v; aux[v] = t; v = orig[par[match[v]]]; } swap(v, w); } } void blossom(int v, int w, int a) { while (orig[v] != a) { par[v] = w; w = match[v]; if (vis[w] == 1) Q.push(w), vis[w] = 0; orig[v] = orig[w] = a; v = par[w]; } } bool bfs(int u) { fill(vis + 1, vis + 1 + N, -1); iota(orig + 1, orig + N + 1, 1); Q = queue(); Q.push(u); vis[u] = 0; while (!Q.empty()) { int v = Q.front(); Q.pop(); for (int x : conn[v]) { if (vis[x] == -1) { par[x] = v; vis[x] = 1; if (!match[x]) return augment(u, x), true; Q.push(match[x]); vis[match[x]] = 0; } else if (vis[x] == 0 && orig[v] != orig[x]) { int a = lca(orig[v], orig[x]); blossom(x, v, a); blossom(v, x, a); } } } return false; } int Match() { int ans = 0; // find random matching (not necessary, constant improvement) vector V(N - 1); iota(V.begin(), V.end(), 1); shuffle(V.begin(), V.end(), mt19937(0x94949)); for (auto x : V) if (!match[x]) { for (auto y : conn[x]) if (!match[y]) { match[x] = y, match[y] = x; ++ans; break; } } for (int i = 1; i <= N; ++i) if (!match[i] && bfs(i)) ++ans; return ans; } } gm; int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int n, m; cin >> n >> m; gm.init(2 * n); set isol; for (int i = 0; i < m; i++) { int u, v; cin >> u >> v; u--; v--; gm.addEdge(u, v); gm.addEdge(u, v + n); gm.addEdge(u + n, v); gm.addEdge(u + n, v + n); isol.insert(u); isol.insert(v); } int mtch = gm.Match(); if (mtch == n - 1 && sz(isol) == n - 1) mtch--; cout << mtch * 2 - n << "\n"; }