//#pragma GCC optimize("Ofast") //#pragma GCC target("avx") //#undef LOCAL #include #include #include namespace atcoder { struct dsu { public: dsu() : _n(0) {} dsu(int n) : _n(n), parent_or_size(n, -1) {} int merge(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); int x = leader(a), y = leader(b); if (x == y) return x; if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y); parent_or_size[x] += parent_or_size[y]; parent_or_size[y] = x; return x; } bool same(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); return leader(a) == leader(b); } int leader(int a) { assert(0 <= a && a < _n); if (parent_or_size[a] < 0) return a; return parent_or_size[a] = leader(parent_or_size[a]); } int size(int a) { assert(0 <= a && a < _n); return -parent_or_size[leader(a)]; } std::vector> groups() { std::vector leader_buf(_n), group_size(_n); for (int i = 0; i < _n; i++) { leader_buf[i] = leader(i); group_size[leader_buf[i]]++; } std::vector> result(_n); for (int i = 0; i < _n; i++) { result[i].reserve(group_size[i]); } for (int i = 0; i < _n; i++) { result[leader_buf[i]].push_back(i); } result.erase( std::remove_if(result.begin(), result.end(), [&](const std::vector& v) { return v.empty(); }), result.end()); return result; } private: int _n; std::vector parent_or_size; }; } // namespace atcoder #include #include #include #include #include #include namespace atcoder { namespace internal { template struct simple_queue { std::vector payload; int pos = 0; void reserve(int n) { payload.reserve(n); } int size() const { return int(payload.size()) - pos; } bool empty() const { return pos == int(payload.size()); } void push(const T& t) { payload.push_back(t); } T& front() { return payload[pos]; } void clear() { payload.clear(); pos = 0; } void pop() { pos++; } }; } // namespace internal } // namespace atcoder namespace atcoder { template struct mf_graph { public: mf_graph() : _n(0) {} mf_graph(int n) : _n(n), g(n) {} int add_edge(int from, int to, Cap cap) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); assert(0 <= cap); int m = int(pos.size()); pos.push_back({from, int(g[from].size())}); int from_id = int(g[from].size()); int to_id = int(g[to].size()); if (from == to) to_id++; g[from].push_back(_edge{to, to_id, cap}); g[to].push_back(_edge{from, from_id, 0}); return m; } struct edge { int from, to; Cap cap, flow; }; edge get_edge(int i) { int m = int(pos.size()); assert(0 <= i && i < m); auto _e = g[pos[i].first][pos[i].second]; auto _re = g[_e.to][_e.rev]; return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap}; } std::vector edges() { int m = int(pos.size()); std::vector result; for (int i = 0; i < m; i++) { result.push_back(get_edge(i)); } return result; } void change_edge(int i, Cap new_cap, Cap new_flow) { int m = int(pos.size()); assert(0 <= i && i < m); assert(0 <= new_flow && new_flow <= new_cap); auto& _e = g[pos[i].first][pos[i].second]; auto& _re = g[_e.to][_e.rev]; _e.cap = new_cap - new_flow; _re.cap = new_flow; } Cap flow(int s, int t) { return flow(s, t, std::numeric_limits::max()); } Cap flow(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); assert(s != t); std::vector level(_n), iter(_n); internal::simple_queue que; auto bfs = [&]() { std::fill(level.begin(), level.end(), -1); level[s] = 0; que.clear(); que.push(s); while (!que.empty()) { int v = que.front(); que.pop(); for (auto e : g[v]) { if (e.cap == 0 || level[e.to] >= 0) continue; level[e.to] = level[v] + 1; if (e.to == t) return; que.push(e.to); } } }; auto dfs = [&](auto self, int v, Cap up) { if (v == s) return up; Cap res = 0; int level_v = level[v]; for (int& i = iter[v]; i < int(g[v].size()); i++) { _edge& e = g[v][i]; if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue; Cap d = self(self, e.to, std::min(up - res, g[e.to][e.rev].cap)); if (d <= 0) continue; g[v][i].cap += d; g[e.to][e.rev].cap -= d; res += d; if (res == up) return res; } level[v] = _n; return res; }; Cap flow = 0; while (flow < flow_limit) { bfs(); if (level[t] == -1) break; std::fill(iter.begin(), iter.end(), 0); Cap f = dfs(dfs, t, flow_limit - flow); if (!f) break; flow += f; } return flow; } std::vector min_cut(int s) { std::vector visited(_n); internal::simple_queue que; que.push(s); while (!que.empty()) { int p = que.front(); que.pop(); visited[p] = true; for (auto e : g[p]) { if (e.cap && !visited[e.to]) { visited[e.to] = true; que.push(e.to); } } } return visited; } private: int _n; struct _edge { int to, rev; Cap cap; }; std::vector> pos; std::vector> g; }; } // namespace atcoder #include #include #include #include #include namespace yosupo { namespace internal { int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } } // namespace internal int bsf(unsigned int n) { return __builtin_ctz(n); } int bsf(unsigned long n) { return __builtin_ctzl(n); } int bsf(unsigned long long n) { return __builtin_ctzll(n); } int bsr(unsigned int n) { return 8 * (int)sizeof(unsigned int) - 1 - __builtin_clz(n); } int bsr(unsigned long n) { return 8 * (int)sizeof(unsigned long) - 1 - __builtin_clzl(n); } int bsr(unsigned long long n) { return 8 * (int)sizeof(unsigned long long) - 1 - __builtin_clzll(n); } } // namespace yosupo namespace yosupo { struct Xoshiro256StarStar { public: using result_type = uint64_t; Xoshiro256StarStar() : Xoshiro256StarStar(0) {} explicit Xoshiro256StarStar(uint64_t seed) { for (int i = 0; i < 4; i++) { uint64_t z = (seed += 0x9e3779b97f4a7c15); z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9; z = (z ^ (z >> 27)) * 0x94d049bb133111eb; s[i] = z ^ (z >> 31); } } static constexpr result_type min() { return 0; } static constexpr result_type max() { return -1; } result_type operator()() { const uint64_t result_starstar = rotl(s[1] * 5, 7) * 9; const uint64_t t = s[1] << 17; s[2] ^= s[0]; s[3] ^= s[1]; s[1] ^= s[2]; s[0] ^= s[3]; s[2] ^= t; s[3] = rotl(s[3], 45); return result_starstar; } private: static uint64_t rotl(const uint64_t x, int k) { return (x << k) | (x >> (64 - k)); } std::array s; }; namespace internal { template uint64_t uniform(uint64_t upper, G& gen) { static_assert(std::is_same::value, ""); static_assert(G::min() == 0, ""); static_assert(G::max() == uint64_t(-1), ""); if (!(upper & (upper + 1))) { return gen() & upper; } int log = bsr(upper); uint64_t mask = (log == 63) ? ~0ULL : (1ULL << (log + 1)) - 1; while (true) { uint64_t r = gen() & mask; if (r <= upper) return r; } } } // namespace internal Xoshiro256StarStar& global_gen() { static Xoshiro256StarStar gen( std::chrono::steady_clock::now().time_since_epoch().count()); return gen; } template T uniform(T lower, T upper, G& gen) { return T(lower + internal::uniform(uint64_t(upper) - uint64_t(lower), gen)); } template T uniform(T lower, T upper) { return uniform(lower, upper, global_gen()); } template bool uniform_bool(G& gen) { return internal::uniform(1, gen) == 1; } bool uniform_bool() { return uniform_bool(global_gen()); } template std::pair uniform_pair(T lower, T upper, G& gen) { assert(upper - lower >= 1); T a, b; do { a = uniform(lower, upper, gen); b = uniform(lower, upper, gen); } while (a == b); if (a > b) std::swap(a, b); return {a, b}; } template std::pair uniform_pair(T lower, T upper) { return uniform_pair(lower, upper, global_gen()); } } // namespace yosupo using namespace atcoder; #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using uint = unsigned int; using ll = long long; using ull = unsigned long long; constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); } template using V = vector; template using VV = V>; #ifdef LOCAL ostream& operator<<(ostream& os, __int128_t x) { if (x < 0) { os << "-"; x *= -1; } if (x == 0) { return os << "0"; } string s; while (x) { s += char(x % 10 + '0'); x /= 10; } reverse(s.begin(), s.end()); return os << s; } ostream& operator<<(ostream& os, __uint128_t x) { if (x == 0) { return os << "0"; } string s; while (x) { s += char(x % 10 + '0'); x /= 10; } reverse(s.begin(), s.end()); return os << s; } template ostream& operator<<(ostream& os, const pair& p); template ostream& operator<<(ostream& os, const V& v); template ostream& operator<<(ostream& os, const deque& v); template ostream& operator<<(ostream& os, const array& a); template ostream& operator<<(ostream& os, const set& s); template ostream& operator<<(ostream& os, const map& m); template ostream& operator<<(ostream& os, const pair& p) { return os << "P(" << p.first << ", " << p.second << ")"; } template ostream& operator<<(ostream& os, const V& v) { os << "["; bool f = false; for (auto d : v) { if (f) os << ", "; f = true; os << d; } return os << "]"; } template ostream& operator<<(ostream& os, const deque& v) { os << "["; bool f = false; for (auto d : v) { if (f) os << ", "; f = true; os << d; } return os << "]"; } template ostream& operator<<(ostream& os, const array& a) { os << "["; bool f = false; for (auto d : a) { if (f) os << ", "; f = true; os << d; } return os << "]"; } template ostream& operator<<(ostream& os, const set& s) { os << "{"; bool f = false; for (auto d : s) { if (f) os << ", "; f = true; os << d; } return os << "}"; } template ostream& operator<<(ostream& os, const map& s) { os << "{"; bool f = false; for (auto p : s) { if (f) os << ", "; f = true; os << p.first << ": " << p.second; } return os << "}"; } struct PrettyOS { ostream& os; bool first; template auto operator<<(T&& x) { if (!first) os << ", "; first = false; os << x; return *this; } }; template void dbg0(T&&... t) { (PrettyOS{cerr, true} << ... << t); } #define dbg(...) \ do { \ cerr << __LINE__ << " : " << #__VA_ARGS__ << " = "; \ dbg0(__VA_ARGS__); \ cerr << endl; \ } while (false); #else #define dbg(...) #endif #include struct Scanner { int fd = -1; char line[(1 << 15) + 1]; size_t st = 0, ed = 0; void reread() { memmove(line, line + st, ed - st); ed -= st; st = 0; ed += ::read(fd, line + ed, (1 << 15) - ed); line[ed] = '\0'; } bool succ() { while (true) { if (st == ed) { reread(); if (st == ed) return false; } while (st != ed && isspace(line[st])) st++; if (st != ed) break; } if (ed - st <= 50) { bool sep = false; for (size_t i = st; i < ed; i++) { if (isspace(line[i])) { sep = true; break; } } if (!sep) reread(); } return true; } template ::value, int> = 0> bool read_single(T& ref) { if (!succ()) return false; while (true) { size_t sz = 0; while (st + sz < ed && !isspace(line[st + sz])) sz++; ref.append(line + st, sz); st += sz; if (!sz || st != ed) break; reread(); } return true; } template ::value>* = nullptr> bool read_single(T& ref) { if (!succ()) return false; bool neg = false; if (line[st] == '-') { neg = true; st++; } ref = T(0); while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); } if (neg) ref = -ref; return true; } template bool read_single(V& ref) { for (auto& d : ref) { if (!read_single(d)) return false; } return true; } void read() {} template void read(H& h, T&... t) { bool f = read_single(h); assert(f); read(t...); } int read_unsafe() { return 0; } template int read_unsafe(H& h, T&... t) { bool f = read_single(h); if (!f) return 0; return 1 + read_unsafe(t...); } Scanner(FILE* fp) : fd(fileno(fp)) {} }; struct Printer { public: template void write() {} template void write(const H& h, const T&... t) { if (F) write_single(' '); write_single(h); write(t...); } template void writeln(const T&... t) { write(t...); write_single('\n'); } Printer(FILE* _fp) : fp(_fp) {} ~Printer() { flush(); } private: static constexpr size_t SIZE = 1 << 15; FILE* fp; char line[SIZE], small[50]; size_t pos = 0; void flush() { fwrite(line, 1, pos, fp); pos = 0; } void write_single(const char& val) { if (pos == SIZE) flush(); line[pos++] = val; } template ::value>* = nullptr> void write_single(T val) { if (pos > (1 << 15) - 50) flush(); if (val == 0) { write_single('0'); return; } if (val < 0) { write_single('-'); val = -val; // todo min } size_t len = 0; while (val) { small[len++] = char(0x30 | (val % 10)); val /= 10; } for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; } pos += len; } void write_single(__int128 val) { if (pos > (1 << 15) - 50) flush(); if (val == 0) { write_single('0'); return; } if (val < 0) { write_single('-'); val = -val; // todo min } size_t len = 0; while (val) { small[len++] = char(0x30 | (val % 10)); val /= 10; } for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; } pos += len; } void write_single(const string& s) { for (char c : s) write_single(c); } void write_single(const char* s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) write_single(s[i]); } template void write_single(const V& val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write_single(' '); write_single(val[i]); } } }; struct StopWatch { bool f = false; clock_t st; void start() { f = true; st = clock(); } int msecs() { assert(f); return (clock()-st)*1000 / CLOCKS_PER_SEC; } }; Scanner sc = Scanner(stdin); Printer pr = Printer(stdout); using cent = __int128; struct E { int from, to, idx; cent c, d; }; int main() { StopWatch sw; sw.start(); int n, m; cent K; sc.read(n, m, K); V edges; for (int i = 0; i < m; i++) { int u, v; cent c, d; sc.read(u, v, c, d); u--; v--; edges.push_back({u, v, i, c, d}); } V costs; for (auto e : edges) { costs.push_back(e.c); } sort(costs.begin(), costs.end()); costs.erase(unique(costs.begin(), costs.end()), costs.end()); int k = int(costs.size()); const cent INF = cent(TEN(18)) * cent(TEN(9)); cent offset = 0; for (auto e : edges) { offset += e.c * e.d; } cent ans = 0; //for (int ph = 0; ph < 100; ph++) { while (sw.msecs() < 1800) { mf_graph g(m * k + 2); auto id = [&](int i, int j) { assert(0 <= i && i < m); assert(0 <= j && j < k); return i * k + j; }; int sv = m * k, tv = sv + 1; for (auto e : edges) { int i = e.idx; int bk = sv; for (int j = 0; j < k; j++) { int nw = id(i, j); g.add_edge(bk, nw, costs[j] * e.d); g.add_edge(nw, bk, INF); bk = nw; } g.add_edge(bk, tv, INF); int x = int(lower_bound(costs.begin(), costs.end(), e.c) - costs.begin()); if (x) g.add_edge(sv, id(i, x - 1), INF); } shuffle(edges.begin(), edges.end(), yosupo::global_gen()); //sort(edges.begin(), edges.end(), [&](E a, E b) { return a.c < b.c; }); using P = pair; VV

tr(n); V path; auto dfs = [&](auto self, int s, int bk, int t) -> bool { if (s == t) return true; for (auto e : tr[s]) { if (e.first == bk) continue; if (self(self, e.first, s, t)) { path.push_back(e.second); return true; } } return false; }; dsu d(n); for (auto e : edges) { int i = e.idx; if (d.same(e.from, e.to)) { path.clear(); bool f = dfs(dfs, e.from, -1, e.to); assert(f); for (auto u: path) { for (int j = 0; j < k; j++) { int my = id(i, j); int your = id(u, j); g.add_edge(your, my, INF); } } // continue; } // tree d.merge(e.from, e.to); tr[e.from].push_back({e.to, e.idx}); tr[e.to].push_back({e.from, e.idx}); int bk = sv; for (int j = 0; j < k; j++) { int nw = id(i, j); g.add_edge(bk, nw, TEN(18) - (costs[j] * K)); bk = nw; } } cent z = g.flow(sv, tv); auto cut = g.min_cut(sv); cent cur_ans = offset + cent(n - 1) * TEN(18) - z; dbg(z, cur_ans); ans = max(ans, cur_ans); /* for (auto& e : edges) { int i = e.idx; int bk = sv; bool ok = false; for (int j = 0; j < k; j++) { int nw = id(i, j); if (cut[bk] && !cut[nw]) { ok = true; e.c = costs[j]; break; } bk = nw; } assert(ok); }*/ } /* cent ans = offset; dsu d(n); for (auto& e : edges) { ans -= e.c * e.d; if (d.same(e.from, e.to)) continue; d.merge(e.from, e.to); ans += K * e.c; } dbg(offset, ans);*/ pr.writeln(ans); return 0; }