#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif template std::vector> transpose(const std::vector> &v) { const int H = v.size(), W = v[0].size(); std::vector> ret(W, std::vector(H)); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) ret[j][i] = v[i][j]; } return ret; } std::vector transpose(const std::vector &v) { const int H = v.size(), W = v[0].size(); std::vector ret(W, std::string(H, '\0')); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) ret[j][i] = v[i][j]; } return ret; } void answer(int x) { cout << x << '\n'; exit(0); } int main() { int H, W; cin >> H >> W; vector A(H, vector(W)); cin >> A; dbg(A); // REP(_, 2) { // for (size_t i = 0; i < A.size();) { // if (accumulate(ALL(A.at(i)), 0) == 0) { // A.erase(A.begin() + i); // } else { // ++i; // } // } // A = transpose(A); // } // dbg(A); // if (A.empty() or A.front().empty()) answer(0); // H = A.size(), W = A.front().size(); vector i2maxj(H, -1), j2maxi(W, -1); REP(i, H) REP(j, W) { if (A.at(i).at(j) == 1) { chmax(i2maxj.at(i), j); chmax(j2maxi.at(j), i); } } vector cs(H + 1, vector(W + 1)); REP(i, H) REP(j, W) { cs.at(i + 1).at(j + 1) = cs.at(i + 1).at(j) + cs.at(i).at(j + 1) - cs.at(i).at(j) + A.at(i).at(j); } dbg(i2maxj); dbg(j2maxi); // [ilo, ihi) * [jlo, jhi) auto sum = [&](int ilo, int ihi, int jlo, int jhi) { return cs.at(ihi).at(jhi) - cs.at(ilo).at(jhi) - cs.at(ihi).at(jlo) + cs.at(ilo).at(jlo); }; constexpr int inf = 1 << 27; vector dp(H, vector(W, inf)); IREP(x, H) IREP(y, W) { int nin = sum(x, H, y, W); if (!nin) { dp.at(x).at(y) = 0; continue; } vector xin(H); FOR(i, x, H) xin.at(i) = sum(i, i + 1, y, W) > 0; vector xin_cs(H + 1); REP(i, H) xin_cs.at(i + 1) = xin_cs.at(i) + xin.at(i); vector yin(W); FOR(j, y, W) yin.at(j) = sum(x, H, j, j + 1) > 0; vector yin_cs(W + 1); REP(j, W) yin_cs.at(j + 1) = yin_cs.at(j) + yin.at(j); vector x2yhi = i2maxj; IFOR(i, 1, H) chmax(x2yhi.at(i - 1), x2yhi.at(i)); // FOR(i, x, H) { // const int j = i2maxj.at(i); // if (j < y) continue; // while (x2y.size() and x2y.back().second <= y) x2y.pop_back(); // x2y.emplace_back(i, j); // } FOR(i, x, H) { // for (auto [i, j] : x2y) { const int j = x2yhi.at(i); int s = (xin_cs.at(i + 1) - xin_cs.at(x)) * (yin_cs.at(j + 1) - yin_cs.at(y)); if (i < H - 1) s += dp.at(i + 1).at(y); if (j < W - 1) s += dp.at(x).at(j + 1); chmin(dp.at(x).at(y), s); } // if (y + 1 < W and !sum(x, H, y, y + 1)) chmin(dp.at(x).at(y), dp.at(x).at(y + 1)); // if (x + 1 < H and !sum(x, x + 1, y, W)) chmin(dp.at(x).at(y), dp.at(x + 1).at(y)); } for (auto v : dp) dbg(v); int init = 0; for (auto v : A) init += accumulate(ALL(v), 0); cout << dp.at(0).at(0) - init << '\n'; }