// #include #include #include #include #include #define NDEBUG using i64 = long long; struct solve_t { std::vector> g; std::vector a, b, c; solve_t(int n): g(n) {} void add_edge(int u, int v, int w) { g[u].push_back(a.size()); g[v].push_back(a.size()); a.push_back(u); b.push_back(v); c.push_back(w); } i64 solve(int start = 0) { i64 answer = (i64)g.size() * ((i64)g.size() - 1); std::vector deleted(g.size()); auto solve = [&](auto&& solve, int root) -> void { static std::vector size(g.size()); auto calc_size = [&](auto&& dfs, int v, int par) -> int { size[v] = 1; for(int id: g[v]) { int to = v ^ a[id] ^ b[id]; if(to == par or deleted[to]) continue; size[v] += dfs(dfs, to, v); } return size[v]; }; calc_size(calc_size, root, -1); auto get_centroid = [&](auto&& dfs, int v, int par) -> int { for(int id: g[v]) { int to = v ^ a[id] ^ b[id]; if(to == par or deleted[to]) continue; if(size[to] > size[root] / 2) return dfs(dfs, to, v); } return v; }; int centroid = get_centroid(get_centroid, root, -1); // 分割統治 deleted[centroid] = true; for(int id: g[centroid]) { int to = centroid ^ a[id] ^ b[id]; if(deleted[to]) continue; solve(solve, to); } deleted[centroid] = false; calc_size(calc_size, centroid, -1); #ifndef NDEBUG printf("root: %d\n", root + 1); printf("centroid: %d\n", centroid + 1); for(auto e: deleted) printf("%d ", (int)e); puts(""); for(auto e: size) printf("%d ", e); puts(""); for(int id: g[centroid]) if(!deleted[a[id] ^ b[id] ^ centroid]) printf("%d ", (a[id] ^ b[id] ^ centroid) + 1); puts(""); #endif // [centroid-v] for(int id: g[centroid]) { int to = centroid ^ a[id] ^ b[id]; if(deleted[to]) continue; auto dfs = [&](auto&& dfs, int v, int par, int xor_val) -> void { if(!xor_val) { answer -= size[v]; return; } for(int id: g[v]) { int to = v ^ a[id] ^ b[id]; if(to == par or deleted[to]) continue; dfs(dfs, to, v, xor_val ^ c[id]); } }; dfs(dfs, to, centroid, c[id]); } // [u-centroid] for(int id: g[centroid]) { int to = centroid ^ a[id] ^ b[id]; if(deleted[to]) continue; std::map xor_path; xor_path[0] = 1; auto dfs = [&](auto&& dfs, int v, int par, int xor_val) -> void { if(xor_path[xor_val]) answer -= size[centroid] - size[to]; xor_path[xor_val]++; for(int id: g[v]) { int to = v ^ a[id] ^ b[id]; if(to == par or deleted[to]) continue; dfs(dfs, to, v, xor_val ^ c[id]); } xor_path[xor_val]--; }; dfs(dfs, to, centroid, c[id]); } // [u-centroid-v] for(int loop = 0; loop < 2; loop++) { std::map map; for(int id: g[centroid]) { int to = centroid ^ a[id] ^ b[id]; if(deleted[to]) continue; { // counting 0-xor paths std::map xor_path; xor_path[0] = 1; auto dfs = [&](auto&& dfs, int v, int par, int xor_val) -> void { if(!xor_path[xor_val]) answer -= map[xor_val]; xor_path[xor_val]++; for(int id: g[v]) { int to = v ^ a[id] ^ b[id]; if(to == par or deleted[to]) continue; dfs(dfs, to, v, xor_val ^ c[id]); }; xor_path[xor_val]--; }; dfs(dfs, to, centroid, c[id]); } { // mapping path xors std::map xor_path; auto dfs = [&](auto&& dfs, int v, int par, int xor_val) -> void { if(!xor_path[xor_val]) map[xor_val] += size[v]; xor_path[xor_val]++; for(int id: g[v]) { int to = v ^ a[id] ^ b[id]; if(to == par or deleted[to]) continue; dfs(dfs, to, v, xor_val ^ c[id]); }; xor_path[xor_val]--; }; dfs(dfs, to, centroid, c[id]); } } #ifndef NDEBUG printf("loop(%d): ", loop); for(auto [p, q]: map) printf("(%d: %lld), ", p, q); puts(""); printf("%lld\n", answer); #endif reverse(begin(g[centroid]), end(g[centroid])); } #ifndef NDEBUG puts(""); #endif }; solve(solve, start); return answer; } }; int main() { int n; scanf("%d", &n); solve_t solver(n); for(int i = 0; i < n - 1; i++) { int u, v, w; scanf("%d%d%d", &u, &v, &w); solver.add_edge(u - 1, v - 1, w); } printf("%lld\n", solver.solve()); }