#pragma region template #include #include #include using namespace std; // clang-format off using ll = long long; using vl = vector; using vvl = vector; using ld = long double; using vld = vector; using vvld = vector; using pll = pair; using vpll = vector; using vvpll = vector; using vb = vector; using vvb = vector>; using vs = vector; using mll = map; template using V = vector; template using VV = V>; template using VVV = V>; template using max_heap = priority_queue; template using min_heap = priority_queue, greater>; constexpr ll inf = 3001001000100100100LL; #define endl '\n' #define _overload(_1, _2, _3, name, ...) name #define rep(...) _overload(__VA_ARGS__, _rep, _rep2,)(__VA_ARGS__) #define repc(...) _overload(__VA_ARGS__, _repc, _repc2,)(__VA_ARGS__) #define repr(...) _overload(__VA_ARGS__, _repr, _repr2,)(__VA_ARGS__) #define reprc(...) _overload(__VA_ARGS__, _reprc, _reprc2,)(__VA_ARGS__) #define _rep(i,k,n) for(ll i=(k) , i##_xxxx=(n); i < i##_xxxx; ++i) #define _repc(i,k,n) for(ll i=(k) , i##_xxxx=(n); i <=i##_xxxx; ++i) #define _repr(i,k,n) for(ll i=(n)-1, i##_xxxx=(k); i >=i##_xxxx; --i) #define _reprc(i,k,n) for(ll i=(n) , i##_xxxx=(k); i >=i##_xxxx; --i) #define _rep2(i,n) _rep(i,0,n) #define _repc2(i,n) _repc(i,1,n) #define _repr2(i,n) _repr(i,0,n) #define _reprc2(i,n) _reprc(i,1,n) #define rall(o) rbegin(o), rend(o) #define all(o) begin(o), end(o) template ll sz(const C& c) { return static_cast(c.size()); } template bool chmax(T& m, const T& v){ if (m < v){ m = v; return true; } return false; } template bool chmin(T& m, const T& v){ if (v < m){ m = v; return true; } return false; } template T cdiv(const T& a, const T& b){ return (a + b - 1) / b; } template T rdiv(const T& a, const T& b){ return (a + b / 2) / b; } template string join(const T& v, const S& sep ){ stringstream ss; bool f = false; for (const auto& e : v){ if (f) ss << sep; f = true; ss << e;} return ss.str(); } template string join(const T& v, const S& sep, const U& ...args){ stringstream ss; bool f = false; for (const auto& c : v){ if (f) ss << sep; f = true; ss << join(c, args...); } return ss.str(); } ostream& operator<<(ostream& os, const __int128_t& val){ os << (ll)val; return os; } // template ::edge> ostream& operator<<(ostream& os, const atcoder::mf_graph<__int128>::edge& e) { auto [from, to, cap, flow] = e; os << '(' << from << "->" << to << " : " << flow << "/" << cap << ')'; return os; } template ostream& operator<<(ostream& os, const vector& seq){ os << '[' << join(seq, ",") << ']'; return os; } template ostream& operator<<(ostream& os, const vector>& seq){ os << '[' << join(seq, ",\n ") << ']'; return os; } template ostream& operator<<(ostream& os, const deque& seq){ os << '[' << join(seq, ",") << ']'; return os; } template ostream& operator<<(ostream& os, const set& seq){ os << '{' << join(seq, ",") << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_set& seq){ os << '{' << join(seq, ",") << '}'; return os; } template ostream& operator<<(ostream& os, const map& seq){ os << '{'; bool f = false; for (const auto& e : seq){ if (f) os << ','; f = true; os << e.first << ":" << e.second; } os << '}'; return os; } template ostream& operator<<(ostream& os, const pair& pa){ os << '(' << pa.first << ',' << pa.second << ')'; return os; } #if LOCAL #define _overload5(_1, _2, _3, _4, _5, name, ...) name #define debug(...) _overload5(__VA_ARGS__, _d5, _d4, _d3, _d2, _d1, )(__VA_ARGS__) #define _pp0(x, ...) #x " =", x #define _pp(x, ...) ", "#x " =", x // ,pp(__VA_ARGS__) #define _d1(x1) _debug(_pp0(x1), __LINE__) #define _d2(x1, x2) _debug(_pp0(x1), _pp(x2), __LINE__) #define _d3(x1, x2, x3) _debug(_pp0(x1), _pp(x2), _pp(x3), __LINE__) // #define debug(...) _debug(__VA_ARGS__, __LINE__) #else #define debug(...) #endif void print() { std::cout << '\n'; } template void print(const S& a){ std::cout << a << '\n'; } template void _debug(const S& a){ std::cerr << "(L:" << std::setw(3) << a << ")\n"; } template void print(const S& a, const T&... args){ std::cout << a << ' '; print(args...); } template void _debug(const S& a, const T&... args){ std::cerr << a << ' '; _debug(args...); } struct setup_main { setup_main() { std::cin.tie(nullptr); std::ios::sync_with_stdio(false); std::cout << fixed << setprecision(15); } } setup_main_; // clang-format on #pragma endregion template struct PSP { struct Variable { ll id, flip; Variable(ll i = 0, bool f = false) : id(i), flip(f) {} Variable operator~() { return Variable(id, !flip); } }; using S = Variable; ll n; vector> cost1; vector>>> cost2; vector var; PSP(){}; PSP(ll n_) : n(n_) { cost1.resize(n, vector(2, 0)); cost2.resize(n, vector(n, vector(2, vector(2, 0)))); var.reserve(n); rep(i, n) var.emplace_back(i); }; void add_constraint(S x, Cost cost) { cost1[x.id][!x.flip] += cost; } void add_constraint(S x, S y, Cost cost) { if (x.id > y.id) swap(x, y), cost = -cost; cost2[x.id][y.id][!x.flip][!y.flip] += cost; }; Cost solve() { Cost sum = 0; // find flips vector> cost2_rest(n, vector(n)); atcoder::dsu d(2 * n); rep(i, n) rep(j, n) { vector>& v(cost2[i][j]); Cost c = v[0][1] + v[1][0] - v[0][0] - v[1][1]; cost1[i][0] += v[0][0]; cost1[i][1] += v[1][0]; if (c < 0) { cost1[j][1] += v[0][1] - v[0][0]; cost2_rest[i][j] -= c; } else { cost1[j][1] += v[1][1] - v[1][0]; cost2_rest[i][j] += c; } if (c > 0) { // 劣モジュラ d.merge(i, j); d.merge(i + n, j + n); } else if (c < 0) { // 非劣モジュラ d.merge(i, n + j); d.merge(n + i, j); } // c=0ならflipは自由 } rep(i, n) if (d.same(i, n + i)) return -1; vl flip(2 * n, -1); rep(i, 2 * n) { ll p = d.leader(i); if (flip[p] == -1) flip[p] = 0; flip[i] = flip[p]; flip[d.leader((n + i) % (2 * n))] = 1 - flip[p]; debug(flip, i); } debug(sum); debug(flip); debug(cost1); debug(cost2_rest); // min-cut atcoder::mf_graph graph(n + 2); ll s = n, t = n + 1; rep(i, n) { // cost1 if (!flip[i]) swap(cost1[i][0], cost1[i][1]); if (cost1[i][0] >= cost1[i][1]) { graph.add_edge(s, i, cost1[i][0] - cost1[i][1]); sum += cost1[i][1]; } else { graph.add_edge(i, t, cost1[i][1] - cost1[i][0]); sum += cost1[i][0]; } } rep(i, n) rep(j, n) { if (flip[j]) graph.add_edge(i, j, cost2_rest[i][j]); else graph.add_edge(i, j, -cost2_rest[i][j]); } ll f = graph.flow(s, t); debug(sum, f); debug(graph.edges()); debug(graph.min_cut(s)); return sum + f; } }; template struct Compress { vector inv; Compress(vector a = {}) : inv(a) {} void push(T val) { inv.push_back(val); } void compress() { sort(all(inv)); inv.erase(unique(all(inv)), inv.end()); } ll zip(T val) { return lower_bound(all(inv), val) - inv.begin(); } T unzip(ll idx) { assert(0 <= idx and idx < sz(inv)); return inv[idx]; } size_t size() { return inv.size(); } }; #ifdef LOCAL const ll M = 10; #else const ll M = 500000; #endif void solve(ll H, ll W, vector>& A) { vvpll B(M + 1); rep(y, H) rep(x, W) { if (A[y][x] != 0) B[A[y][x]].emplace_back(y, x); } ll ans = 0; for (auto& v : B) { if (sz(v) == 0) continue; if (sz(v) == 1) { ans++; continue; } Compress row, col; for (auto&& [y, x] : v) { row.push(y); col.push(x); } row.compress(), col.compress(); ll h = row.size(), w = col.size(); PSP<__int128_t> psp(h + w); auto var = psp.var; rep(y, h) psp.add_constraint(y, 1); rep(x, w) psp.add_constraint(x + h, 1); for (auto [y, x] : v) { y = row.zip(y); x = col.zip(x); psp.add_constraint({y, false}, {x + h, false}, 100000); } ans += (ll)psp.solve(); } print(ans); } int main() { ll H, W; cin >> H >> W; vector> A(H, vector(W)); rep(j, H) { rep(i, W) { cin >> A[j][i]; } } solve(H, W, A); return 0; }