#ifndef HIDDEN_IN_VS // 折りたたみ用 // 警告の抑制 #define _CRT_SECURE_NO_WARNINGS // ライブラリの読み込み #include using namespace std; // 型名の短縮 using ll = long long; // -2^63 ~ 2^63 = 9 * 10^18(int は -2^31 ~ 2^31 = 2 * 10^9) using pii = pair; using pll = pair; using pil = pair; using pli = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vvvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vvvvl = vector; using vb = vector; using vvb = vector; using vvvb = vector; using vc = vector; using vvc = vector; using vvvc = vector; using vd = vector; using vvd = vector; using vvvd = vector; template using priority_queue_rev = priority_queue, greater>; using Graph = vvi; // 定数の定義 const double PI = acos(-1); const vi DX = { 1, 0, -1, 0 }; // 4 近傍(下,右,上,左) const vi DY = { 0, 1, 0, -1 }; int INF = 1001001001; ll INFL = 4004004003104004004LL; // (int)INFL = 1010931620; double EPS = 1e-15; // 入出力高速化 struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp; // 汎用マクロの定義 #define all(a) (a).begin(), (a).end() #define sz(x) ((int)(x).size()) #define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x)) #define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x)) #define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");} #define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順 #define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順 #define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順 #define repe(v, a) for(const auto& v : (a)) // a の全要素(変更不可能) #define repea(v, a) for(auto& v : (a)) // a の全要素(変更可能) #define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d ビット全探索(昇順) #define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て(昇順) #define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod #define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去 #define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了 #define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) // 半開矩形内判定 // 汎用関数の定義 template inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; } template inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新(更新されたら true を返す) template inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら true を返す) template inline T get(T set, int i) { return (set >> i) & T(1); } // 演算子オーバーロード template inline istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template inline istream& operator>>(istream& is, vector& v) { repea(x, v) is >> x; return is; } template inline vector& operator--(vector& v) { repea(x, v) --x; return v; } template inline vector& operator++(vector& v) { repea(x, v) ++x; return v; } #endif // 折りたたみ用 #if __has_include() #include using namespace atcoder; #ifdef _MSC_VER #include "localACL.hpp" #endif //using mint = modint1000000007; using mint = modint998244353; //using mint = modint; // mint::set_mod(m); namespace atcoder { inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; } inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; } } using vm = vector; using vvm = vector; using vvvm = vector; using vvvvm = vector; #endif #ifdef _MSC_VER // 手元環境(Visual Studio) #include "local.hpp" #else // 提出用(gcc) inline int popcount(int n) { return __builtin_popcount(n); } inline int popcount(ll n) { return __builtin_popcountll(n); } inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; } inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; } inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; } inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; } #define gcd __gcd #define dump(...) #define dumpel(v) #define dump_list(v) #define dump_mat(v) #define input_from_file(f) #define output_to_file(f) #define Assert(b) { if (!(b)) while (1) cout << "OLE"; } #endif // https://judge.yosupo.jp/submission/72030 から窃盗 // DSU_rollback struct Data { int time, u, par; // before `time`, `par` = par[u] }; struct DSU { vector par; vector change; DSU(int n) : par(n + 5, -1) {} // find root of x. // if par[x] < 0 then x is a root, and its tree has -par[x] nodes int getRoot(int x) { while (par[x] >= 0) x = par[x]; return x; } // join components containing x and y. // t should be current time. We use it to update `change`. bool join(int x, int y, int t) { x = getRoot(x); y = getRoot(y); if (x == y) return false; //union by rank if (par[x] < par[y]) swap(x, y); //now x's tree has less nodes than y's tree change.push_back({ t, y, par[y] }); par[y] += par[x]; change.push_back({ t, x, par[x] }); par[x] = y; return true; } // rollback all changes at time > t. void rollback(int t) { while (!change.empty() && change.back().time > t) { par[change.back().u] = change.back().par; change.pop_back(); } } }; // Directed MST // Copied from chemthan // Index from 0 using ll = long long; struct Edge { int u, v; // directed, u -> v ll cost; }; struct HeapNode { // lazy skew heap node Edge key; HeapNode* l, * r; ll delta; void prop() { key.cost += delta; if (l) l->delta += delta; if (r) r->delta += delta; delta = 0; } Edge top() { prop(); return key; } }; HeapNode* merge(HeapNode* a, HeapNode* b) { if (!a) return b; if (!b) return a; a->prop(); b->prop(); if (a->key.cost > b->key.cost) swap(a, b); swap(a->l, (a->r = merge(b, a->r))); return a; } void pop(HeapNode*& a) { a->prop(); a = merge(a->l, a->r); } // return {cost, parent[i]} // Not found -> return {-1, {}} pair> directed_mst(int n, int root, vector& edges) { DSU dsu(n); int dsu_time = 0; vector heap(n); for (const Edge& e : edges) { heap[e.v] = merge(heap[e.v], new HeapNode{ e }); } ll res = 0; vector seen(n, -1), path(n); seen[root] = root; vector Q(n), in(n, { -1, -1 }); deque>> cycs; for (int s = 0; s < n; ++s) { int u = s, qi = 0, w; while (seen[u] < 0) { if (!heap[u]) return { -1, {} }; Edge e = heap[u]->top(); heap[u]->delta -= e.cost; pop(heap[u]); Q[qi] = e; path[qi++] = u; seen[u] = s; res += e.cost; u = dsu.getRoot(e.u); if (seen[u] == s) { HeapNode* cyc = 0; int end = qi; int time = dsu_time; do { cyc = merge(cyc, heap[w = path[--qi]]); } while (dsu.join(u, w, ++dsu_time)); u = dsu.getRoot(u); heap[u] = cyc; seen[u] = -1; cycs.push_front({ u, time, {&Q[qi], &Q[end]} }); } } for (int i = 0; i < qi; i++) in[dsu.getRoot(Q[i].v)] = Q[i]; } for (auto& [u, t, comp] : cycs) { dsu.rollback(t); Edge inEdge = in[u]; for (auto& e : comp) in[dsu.getRoot(e.v)] = e; in[dsu.getRoot(inEdge.v)] = inEdge; } vector par(n); for (int i = 0; i < n; i++) par[i] = in[i].u; return { res, par }; } int main() { // input_from_file("input.txt"); // output_to_file("output.txt"); int n, m; cin >> n >> m; vvl cost(n, vl(n, INF)); rep(j, m) { int u, v; ll sc; cin >> u >> v >> sc; cost[u][v] = INF - sc; } vector edges; rep(s, n) rep(t, n) if (s != t) edges.push_back({ s, t, cost[s][t] }); ll cost_min = INFL; vi par_min; int root_min = -1; rep(root, n) { auto [total, par] = directed_mst(n, root, edges); if (chmin(cost_min, total)) { par_min = par; root_min = root; } } Graph g(n); rep(s, n) if (s != root_min) g[par_min[s]].push_back(s); cout << (ll)INF * (n - 1) - cost_min << endl; function dfs = [&](int s) { cout << s << endl; repe(t, g[s]) dfs(t); }; dfs(root_min); }