#include using namespace std; using ll = long long; #define rep(dst, N) for (int dst = 0; dst < (int)(N); ++dst) #define all(C) begin(C), end(C) #define dump(x) cerr << __LINE__ << ":\t" #x " = " << x << endl using Weight = int; using Capacity = int; struct Edge { int src, dst; Weight weight; Edge(int s, int d, Weight w) : src(s), dst(d), weight(w) {} }; using Edges = vector; using Graph = vector; using Array = vector; using Matrix = vector; vector tarjan_scc(const Graph &g) { int n = g.size(), sz = 0; Graph rg(n); vector stk, cmp(n, -1), added(n), visited(n), ord(n); for (auto &es : g) { for (auto &e : es) rg[e.dst].emplace_back(e.dst, e.src, e.weight); sz += es.size(); } stk.resize(n + sz); sz = 0; for (int i = 0; i < n; i++) { if (visited[i]) continue; int s = 0; stk[s++] = i; while (s != 0) { int v = stk[s - 1]; visited[v] = true; bool pushed = false; for (auto &e : g[v]) { int dst = e.dst; if (!visited[dst]) { stk[s++] = dst; pushed = true; } } if (pushed) continue; int t = stk[s - 1]; if (!added[t]) { added[t] = true; ord[n - ++sz] = t; } --s; } } int k = 0; for (int &u : ord) { if (cmp[u] != -1) continue; int s = 0; stk[s++] = u; while (s != 0) { int v = stk[--s]; cmp[v] = k; for (auto &e : rg[v]) { int d = e.dst; if (cmp[d] == -1) stk[s++] = d; } } ++k; } return cmp; } bool in_range(int x, int l, int r) { return l <= x && x <= r; } bool acyclic(const Graph &g) { vector a = tarjan_scc(g); sort(all(a)); a.erase(unique(all(a)), a.end()); return a.size() == g.size(); } void visit(const Graph &g, int u, int *vis) { if (vis[u]) return; vis[u] = true; for (auto &e : g[u]) visit(g, e.dst, vis); } bool all_reachable(const Graph &g, int u) { static int vis[100010]; memset(vis, 0, sizeof vis); visit(g, u, vis); int cnt = count(vis, vis + g.size(), true); return cnt == g.size(); } int N, M; Graph g, rg; int dpb[100010], dpr[100010]; int blue(int u) { int &res = dpb[u]; if (res != -1) return res; res = 0; for (auto &e : rg[u]) res = max(res, blue(e.dst) + e.weight); return res; } int red(int u) { int &res = dpr[u]; if (res != -1) return res; res = 1e9; for (auto &e : g[u]) res = min(res, red(e.dst) - e.weight); return res; } int main() { cin >> N >> M; assert(in_range(N, 3, 100000)); assert(in_range(M, 2, 500000)); g.assign(N, {}); rg.assign(N, {}); memset(dpb, -1, sizeof dpb); memset(dpr, -1, sizeof dpr); for (int i = 0; i < M; i++) { int A, B, C; cin >> A >> B >> C; assert(in_range(A, 0, N - 1)); assert(in_range(B, 0, N - 1)); assert(in_range(C, 0, 160 - 1)); g[A].emplace_back(A, B, C); rg[B].emplace_back(B, A, C); } assert(g[N - 1].size() == 0); assert(rg[0].size() == 0); assert(acyclic(g)); assert(acyclic(rg)); assert(all_reachable(g, 0)); assert(all_reachable(rg, N - 1)); blue(N - 1); dpr[N - 1] = dpb[N - 1]; red(0); int p = 0; for (int i = 0; i < N; i++) { if (dpb[i] != dpr[i]) ++p; } printf("%d %d/%d\n", blue(N - 1), p, N); }