// BEGIN: main.cpp #line 1 "main.cpp" // BEGIN: my_template.hpp #line 1 "my_template.hpp" #if defined(LOCAL) #include #else #if defined(__GNUC__) #include #pragma GCC optimize("Ofast,unroll-loops") #pragma GCC target("avx2,popcnt") #endif #include using namespace std; using ll = long long; using u8 = uint8_t; using u16 = uint16_t; using u32 = uint32_t; using u64 = uint64_t; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template constexpr T infty = 0; template <> constexpr int infty = 1'010'000'000; template <> constexpr ll infty = 2'020'000'000'000'000'000; template <> constexpr u32 infty = infty; template <> constexpr u64 infty = infty; template <> constexpr i128 infty = i128(infty) * 2'000'000'000'000'000'000; template <> constexpr double infty = numeric_limits::infinity(); template <> constexpr long double infty = numeric_limits::infinity(); using pi = pair; using vi = vector; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using pq_max = priority_queue; template using pq_min = priority_queue, greater>; #define vv(type, name, h, ...) \ vector> name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a) - 1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a) - 1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b) - 1; i >= ll(a); --i) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define all(x) (x).begin(), (x).end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } int popcnt_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); } int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); } int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); } int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template T kth_bit(int k) { return T(1) << k; } template bool has_kth_bit(T x, int k) { return x >> k & 1; } template struct all_bit { struct iter { UINT s; iter(UINT s) : s(s) {} int operator*() const { return lowbit(s); } iter &operator++() { s &= s - 1; return *this; } bool operator!=(const iter) const { return s != 0; } }; UINT s; all_bit(UINT s) : s(s) {} iter begin() const { return iter(s); } iter end() const { return iter(0); } }; template struct all_subset { static_assert(is_unsigned::value); struct iter { UINT s, t; bool ed; iter(UINT s) : s(s), t(s), ed(0) {} UINT operator*() const { return s ^ t; } iter &operator++() { (t == 0 ? ed = 1 : t = (t - 1) & s); return *this; } bool operator!=(const iter) const { return !ed; } }; UINT s; all_subset(UINT s) : s(s) {} iter begin() const { return iter(s); } iter end() const { return iter(0); } }; template T floor(T a, T b) { return a / b - (a % b && (a ^ b) < 0); } template T ceil(T x, T y) { return floor(x + y - 1, y); } template T bmod(T x, T y) { return x - y * floor(x, y); } template pair divmod(T x, T y) { T q = floor(x, y); return {q, x - q * y}; } constexpr ll TEN[] = { 1LL, 10LL, 100LL, 1000LL, 10000LL, 100000LL, 1000000LL, 10000000LL, 100000000LL, 1000000000LL, 10000000000LL, 100000000000LL, 1000000000000LL, 10000000000000LL, 100000000000000LL, 1000000000000000LL, 10000000000000000LL, 100000000000000000LL, 1000000000000000000LL, }; template T SUM(const U &A) { return std::accumulate(A.begin(), A.end(), T{}); } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) template inline long long LB(const C &c, const T &x) { return lower_bound(c.begin(), c.end(), x) - c.begin(); } template inline long long UB(const C &c, const T &x) { return upper_bound(c.begin(), c.end(), x) - c.begin(); } #define UNIQUE(x) \ sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit() template T POP(deque &que) { T a = que.front(); que.pop_front(); return a; } template T POP(priority_queue &que) { T a = que.top(); que.pop(); return a; } template T POP(vc &que) { T a = que.back(); que.pop_back(); return a; } template ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (llabs(ok - ng) > 1) { auto x = (ng + ok) / 2; (check(x) ? ok : ng) = x; } return ok; } template double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; (check(x) ? ok : ng) = x; } return (ok + ng) / 2; } template inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } // ? は -1 vc s_to_vi(const string &S, char first_char) { vc A(S.size()); FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); } return A; } template vc cumsum(const vc &A, int off = 1) { int N = A.size(); vc B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } // stable sort template vc argsort(const vc &A) { vc ids(len(A)); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); }); return ids; } // A[I[0]], A[I[1]], ... template vc rearrange(const vc &A, const vc &I) { vc B(len(I)); FOR(i, len(I)) B[i] = A[I[i]]; return B; } template void concat(vc &first, const Vectors &...others) { vc &res = first; (res.insert(res.end(), others.begin(), others.end()), ...); } #endif // END: my_template.hpp #line 2 "main.cpp" // BEGIN: other/io.hpp #line 1 "other/io.hpp" #define FASTIO // https://judge.yosupo.jp/submission/21623 namespace fastio { static constexpr uint32_t SZ = 1 << 17; char ibuf[SZ]; char obuf[SZ]; char out[100]; // pointer of ibuf, obuf uint32_t pil = 0, pir = 0, por = 0; struct Pre { char num[10000][4]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i][j] = n % 10 | '0'; n /= 10; } } } } constexpr pre; inline void load() { memmove(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin); pil = 0; if (pir < SZ) ibuf[pir++] = '\n'; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } void rd(char &c) { do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); } void rd(string &x) { x.clear(); char c; do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); do { x += c; if (pil == pir) load(); c = ibuf[pil++]; } while (!isspace(c)); } template void rd_real(T &x) { string s; rd(s); x = stod(s); } template void rd_integer(T &x) { if (pil + 100 > pir) load(); char c; do c = ibuf[pil++]; while (c < '-'); bool minus = 0; if constexpr (is_signed::value || is_same_v) { if (c == '-') { minus = 1, c = ibuf[pil++]; } } x = 0; while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; } if constexpr (is_signed::value || is_same_v) { if (minus) x = -x; } } template enable_if_t || is_same_v || is_same_v> rd( T &x) { rd_integer(x); } template enable_if_t || is_same_v> rd(T &x) { rd_real(x); } template void rd(pair &p) { rd(p.first), rd(p.second); } template void rd_tuple(T &t) { if constexpr (N < tuple_size::value) { auto &x = get(t); rd(x); rd_tuple(t); } } template void rd(tuple &tpl) { rd_tuple(tpl); } template void rd(array &x) { for (auto &d : x) rd(d); } template void rd(vc &x) { for (auto &d : x) rd(d); } void read() {} template void read(H &h, T &...t) { rd(h), read(t...); } // 先に用意(既出なら不要) inline void wt_range(const char *s, size_t n) { size_t i = 0; while (i < n) { if (por == SZ) flush(); size_t chunk = min(n - i, (size_t)(SZ - por)); memcpy(obuf + por, s + i, chunk); por += chunk; i += chunk; } } void wt(const char c) { if (por == SZ) flush(); obuf[por++] = c; } void wt(const char *s) { wt_range(s, strlen(s)); } void wt(const string &s) { wt_range(s.data(), s.size()); } template void wt_integer(T x) { if (por > SZ - 100) flush(); if (x < 0) { obuf[por++] = '-', x = -x; } int outi; for (outi = 96; x >= 10000; outi -= 4) { memcpy(out + outi, pre.num[x % 10000], 4); x /= 10000; } if (x >= 1000) { memcpy(obuf + por, pre.num[x], 4); por += 4; } else if (x >= 100) { memcpy(obuf + por, pre.num[x] + 1, 3); por += 3; } else if (x >= 10) { int q = (x * 103) >> 10; obuf[por] = q | '0'; obuf[por + 1] = (x - q * 10) | '0'; por += 2; } else obuf[por++] = x | '0'; memcpy(obuf + por, out + outi + 4, 96 - outi); por += 96 - outi; } template inline void wt_real(T x) { char buf[64]; // 有効数字 15 桁、通常/指数を自動選択(printf("%.15g") 相当) int n = std::snprintf(buf, sizeof(buf), "%.15g", (double)x); // (任意)-0 を 0 に正規化 if (n == 2 && buf[0] == '-' && buf[1] == '0') { buf[0] = '0'; n = 1; } wt_range(buf, (size_t)n); } template enable_if_t || is_same_v || is_same_v> wt( T x) { wt_integer(x); } template enable_if_t || is_same_v> wt(T x) { wt_real(x); } inline void wt(bool b) { wt(static_cast('0' + (b ? 1 : 0))); } template void wt(const pair &val) { wt(val.first); wt(' '); wt(val.second); } template void wt_tuple(const T &t) { if constexpr (N < tuple_size::value) { if constexpr (N > 0) wt(' '); wt(get(t)); wt_tuple(t); } } template void wt(const tuple &tpl) { wt_tuple(tpl); } template void wt(const array &val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } template void wt(const vector &val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } void print() { wt('\n'); } template void print(Head &&head, Tail &&...tail) { wt(head); if (sizeof...(Tail)) wt(' '); print(forward(tail)...); } // gcc expansion. called automaticall after main. void __attribute__((destructor)) _d() { flush(); } } // namespace fastio using fastio::flush; using fastio::print; using fastio::read; #if defined(LOCAL) #define HDR "[DEBUG:", __func__, __LINE__, "]" #define SHOW(...) \ SHOW_IMPL(__VA_ARGS__, SHOW8, SHOW7, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, \ SHOW1) \ (__VA_ARGS__) #define SHOW_IMPL(_1, _2, _3, _4, _5, _6, _7, _8, NAME, ...) NAME #define SHOW1(x) print(HDR, #x, "=", (x)), flush() #define SHOW2(x, y) print(HDR, #x, "=", (x), #y, "=", (y)), flush() #define SHOW3(x, y, z) \ print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z)), flush() #define SHOW4(x, y, z, w) \ print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush() #define SHOW5(x, y, z, w, v) \ print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", \ (v)), \ flush() #define SHOW6(x, y, z, w, v, u) \ print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", \ (v), #u, "=", (u)), \ flush() #define SHOW7(x, y, z, w, v, u, t) \ print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", \ (v), #u, "=", (u), #t, "=", (t)), \ flush() #define SHOW8(x, y, z, w, v, u, t, s) \ print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", \ (v), #u, "=", (u), #t, "=", (t), #s, "=", (s)), \ flush() #else #define SHOW(...) #endif #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define U32(...) \ u32 __VA_ARGS__; \ read(__VA_ARGS__) #define U64(...) \ u64 __VA_ARGS__; \ read(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ read(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ read(name) #define VV(type, name, h, w) \ vector> name(h, vector(w)); \ read(name) void YES(bool t = 1) { print(t ? "YES" : "NO"); } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void no(bool t = 1) { yes(!t); } void YA(bool t = 1) { print(t ? "YA" : "TIDAK"); } void TIDAK(bool t = 1) { YA(!t); } // END: other/io.hpp #line 3 "main.cpp" // BEGIN: other/fibonacci_search.hpp #line 1 "other/fibonacci_search.hpp" // returns: {fx, x} // [L, R) での極小値をひとつ求める、単峰は不要 template pair fibonacci_search(F f, ll L, ll R) { assert(L < R); --R; ll a = L, b = L + 1, c = L + 2, d = L + 3; int n = 0; while (d < R) { b = c, c = d, d = b + c - a, ++n; } auto get = [&](ll x) -> T { if (R < x) return infty; return (MINIMIZE ? f(x) : -f(x)); }; T ya = get(a), yb = get(b), yc = get(c), yd = get(d); // この中で極小ならば全体でも極小、を維持する FOR(n) { if (yb <= yc) { d = c, c = b, b = a + d - c; yd = yc, yc = yb, yb = get(b); } else { a = b, b = c, c = a + d - b; ya = yb, yb = yc, yc = get(c); } } ll x = a; T y = ya; if (chmin(y, yb)) x = b; if (chmin(y, yc)) x = c; if (chmin(y, yd)) x = d; if (MINIMIZE) return {y, x}; return {-y, x}; }// END: other/fibonacci_search.hpp #line 5 "main.cpp" // BEGIN: random/base.hpp #line 1 "random/base.hpp" u64 RNG_64() { static u64 x_ = u64(chrono::duration_cast(chrono::high_resolution_clock::now().time_since_epoch()).count()) * 10150724397891781847ULL; x_ ^= x_ << 7; return x_ ^= x_ >> 9; } u64 RNG(u64 lim) { return RNG_64() % lim; } ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); } // END: random/base.hpp #line 6 "main.cpp" /* c=a+bタイプの場合 c,dはどちらも2べき もともと2べきの場合 d|c */ ll F(ll a, ll b, ll c, ll d, ll LIM) { ll ANS = 0; // FOR(x, LIM + 1) { chmax(ANS, (a + x) * ((b - c * x) / d)); } if (c % d == 0) { ll bb = b / d; ll cc = c / d; // FOR(x, LIM + 1) { chmax(ANS, (a + x) * (bb - cc * x)); } auto f = [&](ll x) -> ll { return (a + x) * (bb - cc * x); }; chmax(ANS, fibonacci_search(f, 0, LIM + 1).fi); } else { assert(d % c == 0); ll bb = b / c; ll dd = d / c; // FOR(x, LIM + 1) { chmax(ANS, (a + x) * ((bb - x) / dd)); } // floor を保って x を最大化 // x == bb mod d として auto f = [&](ll x) -> ll { return (a + x) * ((bb - x) / dd); }; chmax(ANS, f(0)); chmax(ANS, f(LIM)); ll x0 = bb % dd; if (x0 <= LIM) { ll lim = (LIM - x0) / dd; auto g = [&](ll t) -> ll { ll x = x0 + t * dd; return f(x); }; chmax(ANS, fibonacci_search(g, 0, lim + 1).fi); } } return ANS; } ll solve(ll K, ll x, ll y, ll a, ll b, ll c) { a = 1LL << a; b = 1LL << b; c = 1LL << c; SHOW(K, x, y, a, b, c); /* x+=1 costa y+=1 costb xy+=1 costc */ chmin(c, a + b); ll ANS = 0; FOR(2) { swap(x, y), swap(a, b); if (c <= a) { ll t = K / c; chmax(ANS, (x + t) * (y + t)); continue; } /* x+=1 costa xy+=1 costc */ chmax(ANS, F(y, a * x + K, c - a, a, K / c)); // for (ll Y = 0; Y * c <= K; ++Y) { // ll X = (K - Y * c) / a; // chmax(ANS, (x + X + Y) * (y + Y)); // } } return ANS; } ll solve_old(ll K, ll x, ll y, ll a, ll b, ll c) { a = 1LL << a; b = 1LL << b; c = 1LL << c; /* x+=1 costa y+=1 costb xy+=1 costc */ chmin(c, a + b); ll ANS = 0; FOR(2) { swap(x, y), swap(a, b); for (ll Y = 0; Y * c <= K; ++Y) { ll X = (K - Y * c) / a; chmax(ANS, (x + X + Y) * (y + Y)); } } return ANS; } void test() { while (1) { ll K = RNG(0, 100); ll x = RNG(0, 100); ll y = RNG(0, 100); ll a = RNG(0, 10); ll b = RNG(0, 10); ll c = RNG(0, 10); chmin(a, c), chmin(b, c); ll god = solve_old(K, x, y, a, b, c); ll me = solve(K, x, y, a, b, c); if (god != me) { SHOW(K, x, y, a, b, c, god, me); } } } void solve() { LL(H, W, K); VV(ll, A, H, W); VV(ll, B, H, W); vi X(H, infty), Y(W, infty); vi SX(H), SY(W); FOR(x, H) FOR(y, W) chmin(X[x], B[x][y]), chmin(Y[y], B[x][y]); FOR(x, H) FOR(y, W) SX[x] += A[x][y], SY[y] += A[x][y]; ll ANS = 0; FOR(x, H) FOR(y, W) { chmax(ANS, solve(K, SX[x], SY[y], X[x], Y[y], B[x][y])); } print(ANS); } signed main() { // test(); solve(); } // END: main.cpp