#include #define overload4(_1, _2, _3, _4, name, ...) name #define rep1(i, n) for (ll i = 0; i < ll(n); ++i) #define rep2(i, s, n) for (ll i = ll(s); i < ll(n); ++i) #define rep3(i, s, n, d) for(ll i = ll(s); i < ll(n); i+=d) #define rep(...) overload4(__VA_ARGS__,rep3,rep2,rep1)(__VA_ARGS__) #define rrep1(i, n) for (ll i = ll(n)-1; i >= 0; i--) #define rrep2(i, n, t) for (ll i = ll(n)-1; i >= (ll)t; i--) #define rrep3(i, n, t, d) for (ll i = ll(n)-1; i >= (ll)t; i-=d) #define rrep(...) overload4(__VA_ARGS__,rrep3,rrep2,rrep1)(__VA_ARGS__) #define all(a) a.begin(),a.end() #define rall(a) a.rbegin(),a.rend() #define SUM(a) accumulate(all(a),0LL) #define MIN(a) *min_element(all(a)) #define MAX(a) *max_element(all(a)) #define SZ(a) int(a.size()) #define popcount(x) __builtin_popcountll(x) #define pf push_front #define pb push_back #define ef emplace_front #define eb emplace_back #define ppf pop_front #define ppb pop_back #ifdef __LOCAL #define debug(...) { cout << #__VA_ARGS__; cout << ": "; print(__VA_ARGS__); cout << flush; } #else #define debug(...) void(0); #endif #define INT(...) int __VA_ARGS__;scan(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;scan(__VA_ARGS__) #define STR(...) string __VA_ARGS__;scan(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;scan(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;scan(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;scan(__VA_ARGS__) using namespace std; using ll = long long; using ld = long double; using P = pair; using LP = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vd = vector; using vvd = vector; using vs = vector; using vc = vector; using vvc = vector; using vb = vector; using vvb = vector; using vp = vector

; using vvp = vector; template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second; } template ostream &operator<<(ostream &os, const pair &p) { return os << '{' << p.first << ", " << p.second << '}'; } template istream &operator>>(istream &is, tuple &t) { return is >> get<0>(t) >> get<1>(t) >> get<2>(t); } template ostream &operator<<(ostream &os, const tuple &t) { return os << '{' << get<0>(t) << ", " << get<1>(t) << ", " << get<2>(t) << '}'; } template istream &operator>>(istream &is, vector &v) { for (T &t : v) { is >> t; } return is; } template ostream &operator<<(ostream &os, const vector &v) { os << '['; rep(i, v.size()) os << v[i] << (i == int(v.size() - 1) ? "" : ", "); return os << ']'; } template ostream &operator<<(ostream &os, const set &st) { os << '{'; auto it = st.begin(); while (it != st.end()) { os << (it == st.begin() ? "" : ", ") << *it; it++; } return os << '}'; } template void vecout(const vector &v, char div = '\n') { rep(i, v.size()) cout << v[i] << (i == int(v.size() - 1) ? '\n' : div); } template bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } void scan() {} template void scan(Head &head, Tail &... tail) { cin >> head; scan(tail...); } template void print(const T &t) { cout << t << '\n'; } template void print(const Head &head, const Tail &... tail) { cout << head << ' '; print(tail...); } template void fin(const T &... a) { print(a...); exit(0); } struct Init_io { Init_io() { ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); cout << boolalpha << fixed << setprecision(15); cerr << boolalpha << fixed << setprecision(15); } } init_io; const string yes[] = {"no", "yes"}; const string Yes[] = {"No", "Yes"}; const string YES[] = {"NO", "YES"}; const int inf = 1001001001; const ll linf = 1001001001001001001; template vector cumsum(const vector &v, bool shift_one = true) { int n = v.size(); vector res; if (shift_one) { res.resize(n + 1); rep(i, n) res[i + 1] = res[i] + v[i]; } else { res.resize(n); if (n) { res[0] = v[0]; rep(i, 1, n) res[i] = res[i - 1] + v[i]; } } return res; } vvi graph(int n, int m, bool directed = false, int origin = 1) { vvi G(n); rep(_, m) { INT(u, v); u -= origin, v -= origin; G[u].pb(v); if (!directed) G[v].pb(u); } return G; } template vector>> weighted_graph(int n, int m, bool directed = false, int origin = 1) { vector>> G(n); rep(_, m) { int u, v; T w; scan(u, v, w); u -= origin, v -= origin; G[u].eb(v, w); if (!directed) G[v].eb(u, w); } return G; } class unionfind { int n; vector par, rank; public: unionfind(int n) : n(n), par(n, -1), rank(n, 0) {} int root(int x) { if (par[x] < 0) return x; else return par[x] = root(par[x]); } bool is_root(int x) { return root(x) == x; } bool same(int x, int y) { return root(x) == root(y); }; bool merge(int x, int y) { x = root(x); y = root(y); if (x == y) return false; if (rank[x] < rank[y]) swap(x, y); if (rank[x] == rank[y]) rank[x]++; par[x] += par[y]; par[y] = x; return true; } int size(int x) { return -par[root(x)]; }; vi roots() { vi res; rep(i, n) if (root(i) == i) res.pb(i); return res; } bool connected() { return roots().size() == 1; } }; int main() { INT(n, m); vvi row(n), col(n); rep(_, m) { INT(r, c); --r, --c; row[r].pb(c); col[c].pb(r); } unionfind uf(n); rep(i, n) { rep(j, row[i].size() - 1) uf.merge(row[i][j], row[i][j + 1]); } map mp; rep(i, n) mp[uf.root(i)].pb(i); vp ls; int rem = n; for (auto[_, v] : mp) { set st; for (int i : v) { for (int j : col[i]) st.insert(j); } ls.eb(v.size(), st.size()); rem -= st.size(); } debug(rem, ls); sort(all(ls)); int ans = inf; int r = 0, c = 0; rep(i, ls.size()) { r += ls[i].first; c += ls[i].second; chmin(ans, r * c + (n - r) * (n - rem - c) + rem * min(r, n - r)); } fin(ans - m); }