#line 1 "main.cpp" #define PROBLEM "https://yukicoder.me/problems/no/1769" #line 1 "library/my_template.hpp" #if defined(LOCAL) #include #else #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #include using namespace std; using ll = long long; using pi = pair; using vi = vector; using u32 = unsigned int; using u64 = unsigned long long; using i128 = __int128; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using vvvvvc = vector>; template using pq = priority_queue; template using pqg = 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 FOR_subset(t, s) \ for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) #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); } // (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 ceil(T x, U y) { return (x > 0 ? (x + y - 1) / y : x / y); } template T floor(T x, U y) { return (x > 0 ? x / y : (x - y + 1) / y); } template pair divmod(T x, U y) { T q = floor(x, y); return {q, x - q * y}; } template T SUM(const vector &A) { T sum = 0; for (auto &&a: A) sum += a; return sum; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #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(pq &que) { T a = que.top(); que.pop(); return a; } template T POP(pqg &que) { assert(!que.empty()); T a = que.top(); que.pop(); return a; } template T POP(vc &que) { assert(!que.empty()); T a = que.back(); que.pop_back(); return a; } template ll binary_search(F check, ll ok, ll ng) { assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x)); } return ok; } template double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, 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 vector cumsum(vector &A, int off = 1) { int N = A.size(); vector 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 vector argsort(const vector &A) { vector 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; } #endif #line 1 "library/other/io.hpp" // based on yosupo's fastio #include namespace fastio { #define FASTIO // クラスが read(), print() を持っているかを判定するメタ関数 struct has_write_impl { template static auto check(T &&x) -> decltype(x.write(), std::true_type{}); template static auto check(...) -> std::false_type; }; template class has_write : public decltype(has_write_impl::check(std::declval())) { }; struct has_read_impl { template static auto check(T &&x) -> decltype(x.read(), std::true_type{}); template static auto check(...) -> std::false_type; }; template class has_read : public decltype(has_read_impl::check(std::declval())) {}; struct Scanner { FILE *fp; char line[(1 << 15) + 1]; size_t st = 0, ed = 0; void reread() { memmove(line, line + st, ed - st); ed -= st; st = 0; ed += fread(line + ed, 1, (1 << 15) - ed, fp); 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, int> = 0> 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 ::value>::type * = nullptr> inline bool read_single(T &x) { x.read(); return true; } bool read_single(double &ref) { string s; if (!read_single(s)) return false; ref = std::stod(s); return true; } bool read_single(char &ref) { string s; if (!read_single(s) || s.size() != 1) return false; ref = s[0]; return true; } template bool read_single(vector &ref) { for (auto &d: ref) { if (!read_single(d)) return false; } return true; } template bool read_single(pair &p) { return (read_single(p.first) && read_single(p.second)); } template void read_single_tuple(T &t) { if constexpr (N < std::tuple_size::value) { auto &x = std::get(t); read_single(x); read_single_tuple(t); } } template bool read_single(tuple &tpl) { read_single_tuple(tpl); return true; } void read() {} template void read(H &h, T &... t) { bool f = read_single(h); assert(f); read(t...); } Scanner(FILE *fp) : fp(fp) {} }; struct Printer { Printer(FILE *_fp) : fp(_fp) {} ~Printer() { flush(); } 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(const char val) { if (pos == SIZE) flush(); line[pos++] = val; } template ::value, int> = 0> void write(T val) { if (pos > (1 << 15) - 50) flush(); if (val == 0) { write('0'); return; } if (val < 0) { write('-'); 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(const string s) { for (char c: s) write(c); } void write(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) write(s[i]); } void write(const double x) { ostringstream oss; oss << fixed << setprecision(15) << x; string s = oss.str(); write(s); } void write(const long double x) { ostringstream oss; oss << fixed << setprecision(15) << x; string s = oss.str(); write(s); } template ::value>::type * = nullptr> inline void write(T x) { x.write(); } template void write(const vector val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write(' '); write(val[i]); } } template void write(const pair val) { write(val.first); write(' '); write(val.second); } template void write_tuple(const T t) { if constexpr (N < std::tuple_size::value) { if constexpr (N > 0) { write(' '); } const auto x = std::get(t); write(x); write_tuple(t); } } template bool write(tuple tpl) { write_tuple(tpl); return true; } template void write(const array val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write(' '); write(val[i]); } } void write(i128 val) { string s; bool negative = 0; if (val < 0) { negative = 1; val = -val; } while (val) { s += '0' + int(val % 10); val /= 10; } if (negative) s += "-"; reverse(all(s)); if (len(s) == 0) s = "0"; write(s); } }; Scanner scanner = Scanner(stdin); Printer printer = Printer(stdout); void flush() { printer.flush(); } void print() { printer.write('\n'); } template void print(Head &&head, Tail &&... tail) { printer.write(head); if (sizeof...(Tail)) printer.write(' '); print(forward(tail)...); } void read() {} template void read(Head &head, Tail &... tail) { scanner.read(head); read(tail...); } } // namespace fastio using fastio::print; using fastio::flush; using fastio::read; #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __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); } #line 4 "main.cpp" #line 2 "library/graph/base.hpp" template struct Edge { int frm, to; T cost; int id; }; template struct Graph { int N, M; using cost_type = T; using edge_type = Edge; vector edges; vector indptr; vector csr_edges; vc vc_deg, vc_indeg, vc_outdeg; bool prepared; class OutgoingEdges { public: OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {} const edge_type* begin() const { if (l == r) { return 0; } return &G->csr_edges[l]; } const edge_type* end() const { if (l == r) { return 0; } return &G->csr_edges[r]; } private: const Graph* G; int l, r; }; bool is_prepared() { return prepared; } constexpr bool is_directed() { return directed; } Graph() : N(0), M(0), prepared(0) {} Graph(int N) : N(N), M(0), prepared(0) {} void resize(int n) { N = n; } void add(int frm, int to, T cost = 1, int i = -1) { assert(!prepared); assert(0 <= frm && 0 <= to && to < N); if (i == -1) i = M; auto e = edge_type({frm, to, cost, i}); edges.eb(e); ++M; } // wt, off void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); } void read_graph(int M, bool wt = false, int off = 1) { for (int m = 0; m < M; ++m) { INT(a, b); a -= off, b -= off; if (!wt) { add(a, b); } else { T c; read(c); add(a, b, c); } } build(); } void read_parent(int off = 1) { for (int v = 1; v < N; ++v) { INT(p); p -= off; add(p, v); } build(); } void build() { assert(!prepared); prepared = true; indptr.assign(N + 1, 0); for (auto&& e: edges) { indptr[e.frm + 1]++; if (!directed) indptr[e.to + 1]++; } for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; } auto counter = indptr; csr_edges.resize(indptr.back() + 1); for (auto&& e: edges) { csr_edges[counter[e.frm]++] = e; if (!directed) csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id}); } } OutgoingEdges operator[](int v) const { assert(prepared); return {this, indptr[v], indptr[v + 1]}; } vc deg_array() { if (vc_deg.empty()) calc_deg(); return vc_deg; } pair, vc> deg_array_inout() { if (vc_indeg.empty()) calc_deg_inout(); return {vc_indeg, vc_outdeg}; } int deg(int v) { if (vc_deg.empty()) calc_deg(); return vc_deg[v]; } int in_deg(int v) { if (vc_indeg.empty()) calc_deg_inout(); return vc_indeg[v]; } int out_deg(int v) { if (vc_outdeg.empty()) calc_deg_inout(); return vc_outdeg[v]; } void debug() { print("Graph"); if (!prepared) { print("frm to cost id"); for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id); } else { print("indptr", indptr); print("frm to cost id"); FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id); } } private: void calc_deg() { assert(vc_deg.empty()); vc_deg.resize(N); for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++; } void calc_deg_inout() { assert(vc_indeg.empty()); vc_indeg.resize(N); vc_outdeg.resize(N); for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; } } }; #line 2 "library/graph/centroid.hpp" template vc find_centroids(GT& G) { int N = G.N; vc par(N, -1); vc V(N); vc sz(N); int l = 0, r = 0; V[r++] = 0; while (l < r) { int v = V[l++]; for (auto&& e: G[v]) if (e.to != par[v]) { par[e.to] = v; V[r++] = e.to; } } FOR_R(i, N) { int v = V[i]; sz[v] += 1; int p = par[v]; if (p != -1) sz[p] += sz[v]; } int M = N / 2; auto check = [&](int v) -> bool { if (N - sz[v] > M) return false; for (auto&& e: G[v]) { if (e.to != par[v] && sz[e.to] > M) return false; } return true; }; vc ANS; FOR(v, N) if (check(v)) ANS.eb(v); return ANS; } template struct Centroid_Decomposition { using edge_type = typename GT::edge_type; GT& G; int N; vc sz; vc par; vector cdep; // depth in centroid tree bool calculated; Centroid_Decomposition(GT& G) : G(G), N(G.N), sz(G.N), par(G.N), cdep(G.N, -1) { calculated = 0; build(); } private: int find(int v) { vc V = {v}; par[v] = -1; int p = 0; while (p < len(V)) { int v = V[p++]; sz[v] = 0; for (auto&& e: G[v]) { if (e.to == par[v] || cdep[e.to] != -1) continue; par[e.to] = v; V.eb(e.to); } } while (len(V)) { int v = V.back(); V.pop_back(); sz[v] += 1; if (p - sz[v] <= p / 2) return v; sz[par[v]] += sz[v]; } return -1; } void build() { assert(G.is_prepared()); assert(!G.is_directed()); assert(!calculated); calculated = 1; vc> st; st.eb(0, 0); while (!st.empty()) { auto [lv, v] = st.back(); st.pop_back(); auto c = find(v); cdep[c] = lv; for (auto&& e: G[c]) { if (cdep[e.to] == -1) { st.eb(lv + 1, e.to); } } } } public: /* root を重心とする木において、(v, path data v) の vector を、方向ごとに集めて返す ・0 番目:root からのパスすべて(root を含む) ・i番目:i 番目の方向 f: E x edge -> E */ template vc>> collect(int root, E root_val, F f) { vc>> res = {{{root, root_val}}}; for (auto&& e: G[root]) { int nxt = e.to; if (cdep[nxt] < cdep[root]) continue; vc> dat; int p = 0; dat.eb(nxt, f(root_val, e)); par[nxt] = root; while (p < len(dat)) { auto [v, val] = dat[p++]; for (auto&& e: G[v]) { if (e.to == par[v]) continue; if (cdep[e.to] < cdep[root]) continue; par[e.to] = v; dat.eb(e.to, f(val, e)); } } res.eb(dat); res[0].insert(res[0].end(), all(dat)); } return res; } vc>> collect_dist(int root) { auto f = [&](int x, auto e) -> int { return x + 1; }; return collect(root, 0, f); } // (V, H), V[i] は、H における頂点 i の G における番号 // 頂点は EulerTour 順に並ぶ、V は sort されているとは限らない pair, Graph> get_subgraph(int root) { static vc conv; while (len(conv) < N) conv.eb(-1); vc V; using cost_type = typename GT::cost_type; vc> edges; auto dfs = [&](auto& dfs, int v, int p) -> void { conv[v] = len(V); V.eb(v); for (auto&& e: G[v]) { int to = e.to; if (to == p) continue; if (cdep[to] < cdep[root]) continue; dfs(dfs, to, v); edges.eb(conv[v], conv[to], e.cost); } }; dfs(dfs, root, -1); int n = len(V); Graph H(n); for (auto&& [a, b, c]: edges) H.add(a, b, c); H.build(); for (auto&& v: V) conv[v] = -1; return {V, H}; } }; #line 3 "library/graph/tree.hpp" // HLD euler tour をとっていろいろ。 // 木以外、非連結でも dfs 順序や親がとれる。 template struct Tree { using Graph_type = GT; GT &G; using WT = typename GT::cost_type; int N; bool hld; vector LID, RID, head, V, parent; vc depth; vc depth_weighted; Tree(GT &G, int r = -1, bool hld = 1) : G(G), N(G.N), hld(hld), LID(G.N), RID(G.N), head(G.N, r), V(G.N), parent(G.N, -1), depth(G.N, -1), depth_weighted(G.N, 0) { assert(G.is_prepared()); int t1 = 0; if (r != -1) { dfs_sz(r, -1); dfs_hld(r, t1); } else { for (int r = 0; r < N; ++r) { if (parent[r] == -1) { head[r] = r; dfs_sz(r, -1); dfs_hld(r, t1); } } } } void dfs_sz(int v, int p) { auto &sz = RID; parent[v] = p; depth[v] = (p == -1 ? 0 : depth[p] + 1); sz[v] = 1; int l = G.indptr[v], r = G.indptr[v + 1]; auto &csr = G.csr_edges; // 使う辺があれば先頭にする for (int i = r - 2; i >= l; --i) { if (hld && depth[csr[i + 1].to] == -1) swap(csr[i], csr[i + 1]); } int hld_sz = 0; for (int i = l; i < r; ++i) { auto e = csr[i]; if (depth[e.to] != -1) continue; depth_weighted[e.to] = depth_weighted[v] + e.cost; dfs_sz(e.to, v); sz[v] += sz[e.to]; if (hld && chmax(hld_sz, sz[e.to]) && l < i) { swap(csr[l], csr[i]); } } } void dfs_hld(int v, int ×) { LID[v] = times++; RID[v] += LID[v]; V[LID[v]] = v; bool heavy = true; for (auto &&e: G[v]) { if (depth[e.to] <= depth[v]) continue; head[e.to] = (heavy ? head[v] : e.to); heavy = false; dfs_hld(e.to, times); } } vc heavy_path_at(int v) { vc P = {v}; while (1) { int a = P.back(); for (auto &&e: G[a]) { if (e.to != parent[a] && head[e.to] == v) { P.eb(e.to); break; } } if (P.back() == a) break; } return P; } int e_to_v(int eid) { auto e = G.edges[eid]; return (parent[e.frm] == e.to ? e.frm : e.to); } int ELID(int v) { return 2 * LID[v] - depth[v]; } int ERID(int v) { return 2 * RID[v] - depth[v] - 1; } /* k: 0-indexed */ int LA(int v, int k) { assert(k <= depth[v]); while (1) { int u = head[v]; if (LID[v] - k >= LID[u]) return V[LID[v] - k]; k -= LID[v] - LID[u] + 1; v = parent[u]; } } int LCA(int u, int v) { for (;; v = parent[head[v]]) { if (LID[u] > LID[v]) swap(u, v); if (head[u] == head[v]) return u; } } int lca(int u, int v) { return LCA(u, v); } int la(int u, int v) { return LA(u, v); } int subtree_size(int v) { return RID[v] - LID[v]; } int dist(int a, int b) { int c = LCA(a, b); return depth[a] + depth[b] - 2 * depth[c]; } WT dist(int a, int b, bool weighted) { assert(weighted); int c = LCA(a, b); return depth_weighted[a] + depth_weighted[b] - WT(2) * depth_weighted[c]; } // a is in b bool in_subtree(int a, int b) { return LID[b] <= LID[a] && LID[a] < RID[b]; } int jump(int a, int b, ll k) { if (k == 1) { if (a == b) return -1; return (in_subtree(b, a) ? LA(b, depth[b] - depth[a] - 1) : parent[a]); } int c = LCA(a, b); int d_ac = depth[a] - depth[c]; int d_bc = depth[b] - depth[c]; if (k > d_ac + d_bc) return -1; if (k <= d_ac) return LA(a, k); return LA(b, d_ac + d_bc - k); } vc collect_child(int v) { vc res; for (auto &&e: G[v]) if (e.to != parent[v]) res.eb(e.to); return res; } vc> get_path_decomposition(int u, int v, bool edge) { // [始点, 終点] の"閉"区間列。 vc> up, down; while (1) { if (head[u] == head[v]) break; if (LID[u] < LID[v]) { down.eb(LID[head[v]], LID[v]); v = parent[head[v]]; } else { up.eb(LID[u], LID[head[u]]); u = parent[head[u]]; } } if (LID[u] < LID[v]) down.eb(LID[u] + edge, LID[v]); elif (LID[v] + edge <= LID[u]) up.eb(LID[u], LID[v] + edge); reverse(all(down)); up.insert(up.end(), all(down)); return up; } vc restore_path(int u, int v) { vc P; for (auto &&[a, b]: get_path_decomposition(u, v, 0)) { if (a <= b) { FOR(i, a, b + 1) P.eb(V[i]); } else { FOR_R(i, b, a + 1) P.eb(V[i]); } } return P; } }; #line 2 "library/random/base.hpp" u64 RNG_64() { static uint64_t x_ = uint64_t(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); } #line 3 "library/ds/hashmap.hpp" // u64 -> Val template struct HashMap { int N; u64* keys; Val* vals; vc IDS; bitset<1 << LOG> used; const int shift; const u64 r = 11995408973635179863ULL; HashMap() : N(1 << LOG), keys(new u64[N]), vals(new Val[N]), shift(64 - __lg(N)) {} int hash(ll x) { static const u64 FIXED_RANDOM = std::chrono::steady_clock::now().time_since_epoch().count(); return (u64(x + FIXED_RANDOM) * r) >> shift; } int index(const u64& key) { int i = 0; for (i = hash(key); used[i] && keys[i] != key; (i += 1) &= (N - 1)) {} return i; } // [] した時点で要素は作られる Val& operator[](const u64& key) { int i = index(key); if (!used[i]) IDS.eb(i), used[i] = 1, keys[i] = key, vals[i] = Val{}; return vals[i]; } Val get(const u64& key, Val default_value) { int i = index(key); if (!used[i]) return default_value; return vals[i]; } bool count(const u64& key) { int i = index(key); return used[i] && keys[i] == key; } void reset() { for (auto&& i: IDS) used[i] = 0; IDS.clear(); } // f(key, val) template void enumerate_all(F f) { for (auto&& i: IDS) f(keys[i], vals[i]); } }; #line 9 "main.cpp" void solve() { LL(N); Graph G(N); G.read_tree(1); vi ANS(N); Centroid_Decomposition CD(G); HashMap> MP; FOR(root, N) { auto [conv, G] = CD.get_subgraph(root); const int N = G.N; // lca が 0 であるような path について解く vc A(N); FOR(v, N) { for (auto&& e: G[v]) A[e.to] = A[v] ^ e.cost; } Tree tree(G, 0, false); // 根以外の点に対して、dep=1 の LA vc par_1(N, -1); FOR(v, 1, N) { int p = tree.parent[v]; par_1[v] = (p == 0 ? v : par_1[p]); } // 色 -> 頂点集合 MP.reset(); FOR(v, 1, N) if (A[v] != A[0]) MP[A[v]].eb(v); // 根の次の点 -> 頂点の個数 vc CNT(N); FOR(v, N) if (par_1[v] == v) CNT[v] = tree.subtree_size(v); MP.enumerate_all([&](auto key, auto V) -> void { vc W; for (auto&& x: V) { if (len(W) && tree.in_subtree(x, W.back())) { continue; } W.eb(x); } V = W; // 到達可能な点の個数を更新 ll s = N; for (auto&& v: V) { int x = tree.subtree_size(v); CNT[par_1[v]] -= x; s -= x; } // 各 v からの答を計算 for (auto&& v: V) { ANS[conv[v]] += s - CNT[par_1[v]]; } for (auto&& v: V) { int x = tree.subtree_size(v); CNT[par_1[v]] += x; } }); // 根から進む場合 vc OK(N); OK[0] = 1; FOR(v, N) { if (!OK[v]) continue; for (auto&& e: G[v]) { if (A[e.to] == A[0]) continue; OK[e.to] = 1; } } ANS[conv[0]] += SUM(OK) - 1; } print(SUM(ANS)); } signed main() { solve(); return 0; }