#line 1 "/home/maspy/compro/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 u32 = unsigned int; using u64 = unsigned long long; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template constexpr T infty = 0; template <> constexpr int infty = 1'000'000'000; template <> constexpr ll infty = ll(infty) * infty * 2; template <> constexpr u32 infty = infty; template <> constexpr u64 infty = infty; template <> constexpr i128 infty = i128(infty) * infty; template <> constexpr double infty = infty; template <> constexpr long double infty = infty; using pi = pair; using vi = vector; 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); } int popcnt_mod_2(int x) { return __builtin_parity(x); } int popcnt_mod_2(u32 x) { return __builtin_parity(x); } int popcnt_mod_2(ll x) { return __builtin_parityll(x); } int popcnt_mod_2(u64 x) { return __builtin_parityll(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 floor(T a, T b) { return a / b - (a % b && (a ^ b) < 0); } template T ceil(T x, T y) { return floor(x + y - 1, y); } template T bmod(T x, T y) { return x - y * floor(x, y); } template pair divmod(T x, T y) { T q = floor(x, y); return {q, x - q * y}; } template T SUM(const vector &A) { T sm = 0; for (auto &&a: A) sm += a; return sm; } #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) { T a = que.top(); que.pop(); return a; } template T POP(vc &que) { T a = que.back(); que.pop_back(); return a; } template ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; (check(x) ? ok : ng) = x; } return ok; } template double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; (check(x) ? ok : ng) = 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 "/home/maspy/compro/library/other/io.hpp" #define FASTIO #include // https://judge.yosupo.jp/submission/21623 namespace fastio { static constexpr uint32_t SZ = 1 << 17; char ibuf[SZ]; char obuf[SZ]; char out[100]; // pointer of ibuf, obuf uint32_t pil = 0, pir = 0, por = 0; struct Pre { char num[10000][4]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i][j] = n % 10 | '0'; n /= 10; } } } } constexpr pre; inline void load() { memcpy(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin); pil = 0; if (pir < SZ) ibuf[pir++] = '\n'; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } void rd(char &c) { do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); } void rd(string &x) { x.clear(); char c; do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); do { x += c; if (pil == pir) load(); c = ibuf[pil++]; } while (!isspace(c)); } template void rd_real(T &x) { string s; rd(s); x = stod(s); } template void rd_integer(T &x) { if (pil + 100 > pir) load(); char c; do c = ibuf[pil++]; while (c < '-'); bool minus = 0; if constexpr (is_signed::value || is_same_v) { if (c == '-') { minus = 1, c = ibuf[pil++]; } } x = 0; while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; } if constexpr (is_signed::value || is_same_v) { if (minus) x = -x; } } void rd(int &x) { rd_integer(x); } void rd(ll &x) { rd_integer(x); } void rd(i128 &x) { rd_integer(x); } void rd(u32 &x) { rd_integer(x); } void rd(u64 &x) { rd_integer(x); } void rd(u128 &x) { rd_integer(x); } void rd(double &x) { rd_real(x); } void rd(long double &x) { rd_real(x); } void rd(f128 &x) { rd_real(x); } template void rd(pair &p) { return rd(p.first), rd(p.second); } template void rd_tuple(T &t) { if constexpr (N < std::tuple_size::value) { auto &x = std::get(t); rd(x); rd_tuple(t); } } template void rd(tuple &tpl) { rd_tuple(tpl); } template void rd(array &x) { for (auto &d: x) rd(d); } template void rd(vc &x) { for (auto &d: x) rd(d); } void read() {} template void read(H &h, T &... t) { rd(h), read(t...); } void wt(const char c) { if (por == SZ) flush(); obuf[por++] = c; } void wt(const string s) { for (char c: s) wt(c); } void wt(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) wt(s[i]); } template void wt_integer(T x) { if (por > SZ - 100) flush(); if (x < 0) { obuf[por++] = '-', x = -x; } int outi; for (outi = 96; x >= 10000; outi -= 4) { memcpy(out + outi, pre.num[x % 10000], 4); x /= 10000; } if (x >= 1000) { memcpy(obuf + por, pre.num[x], 4); por += 4; } else if (x >= 100) { memcpy(obuf + por, pre.num[x] + 1, 3); por += 3; } else if (x >= 10) { int q = (x * 103) >> 10; obuf[por] = q | '0'; obuf[por + 1] = (x - q * 10) | '0'; por += 2; } else obuf[por++] = x | '0'; memcpy(obuf + por, out + outi + 4, 96 - outi); por += 96 - outi; } template void wt_real(T x) { ostringstream oss; oss << fixed << setprecision(15) << double(x); string s = oss.str(); wt(s); } void wt(int x) { wt_integer(x); } void wt(ll x) { wt_integer(x); } void wt(i128 x) { wt_integer(x); } void wt(u32 x) { wt_integer(x); } void wt(u64 x) { wt_integer(x); } void wt(u128 x) { wt_integer(x); } void wt(double x) { wt_real(x); } void wt(long double x) { wt_real(x); } void wt(f128 x) { wt_real(x); } template void wt(const pair val) { wt(val.first); wt(' '); wt(val.second); } template void wt_tuple(const T t) { if constexpr (N < std::tuple_size::value) { if constexpr (N > 0) { wt(' '); } const auto x = std::get(t); wt(x); wt_tuple(t); } } template void wt(tuple tpl) { wt_tuple(tpl); } template void wt(const array val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } template void wt(const vector val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } void print() { wt('\n'); } template void print(Head &&head, Tail &&... tail) { wt(head); if (sizeof...(Tail)) wt(' '); print(forward(tail)...); } // gcc expansion. called automaticall after main. void __attribute__((destructor)) _d() { flush(); } } // namespace fastio using fastio::read; using fastio::print; using fastio::flush; #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define U32(...) \ u32 __VA_ARGS__; \ read(__VA_ARGS__) #define U64(...) \ u64 __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 3 "main.cpp" #line 1 "/home/maspy/compro/library/ds/removable_queue.hpp" template struct Removable_Queue { using QUE = QUE_TYPE; using T = typename QUE::value_type; QUE que, rm_que; Removable_Queue() {} Removable_Queue(vc& dat) : que(all(dat)) {} void push(T x) { que.push(x); } int size() { return len(que) - len(rm_que); } bool empty() { return size() == 0; } T pop() { refresh(); return POP(que); } T top() { refresh(); return que.top(); } void remove(T x) { rm_que.push(x); } private: void refresh() { while (len(rm_que) && rm_que.top() == que.top()) { rm_que.pop(), que.pop(); } } }; #line 5 "main.cpp" // 各 heavy path を head が左, tail が右となるように splay tree で持つ. // ユーザーが直接呼ぶ可能性があるものだけ int でも実装 template struct LinkCutTree { using VX = typename Node::VX; using np = Node *; int n; Node *nodes; LinkCutTree(int n = 0) : n(n) { nodes = new Node[NODES]; FOR(i, n) nodes[i] = Node(i); } Node *operator[](int v) { return &nodes[v]; } // パスを表す splay tree の根になっているかどうか // underlying tree ではない bool is_root(Node *c) { return state(c) == 0; } // underlying tree の根 Node *get_root(Node *c) { expose(c); while (c->l) { c->push(); c = c->l; } splay(c); return c; } // underlying tree の根 int get_root(int c) { return get_root(&nodes[c])->idx; } // parent(c)==p となるように link. void link(Node *c, Node *p) { evert(c); evert(p); // no edge -> heavy edge c->p = p; p->r = c; p->update(); } // parent(c)==p となるように link. void link(int c, int p) { return link(&nodes[c], &nodes[p]); } void cut(Node *a, Node *b) { evert(a); expose(b); assert(!b->p); assert((b->l) == a); // heavy edge -> no edge b->l->p = nullptr; b->l = nullptr; b->update(); } void cut(int a, int b) { return cut(&nodes[a], &nodes[b]); } // c を underlying tree の根とする. // c は splay tree の根にもなる. void evert(Node *c) { expose(c); c->reverse(); c->push(); } // c を underlying tree の根とする. // c は splay tree の根にもなる. void evert(int c) { evert(&nodes[c]); } Node *lca(Node *u, Node *v) { assert(get_root(u) == get_root(v)); expose(u); return expose(v); } int lca(int u, int v) { return lca(&nodes[u], &nodes[v])->idx; } Node *jump(Node *u, Node *v, int k) { evert(v); expose(u); assert(0 <= k && k < (u->size)); while (1) { u->push(); int rs = (u->r ? u->r->size : 0); if (k < rs) { u = u->r; continue; } if (k == rs) { break; } k -= rs + 1; u = u->l; } splay(u); return u; } int jump(int u, int v, int k) { auto c = jump((*this)[u], (*this)[v], k); return c->idx; } // [root, c] がひとつの splay tree になるように変更する. // c が右端で splay tree の根という状態になる. // path query はこの状態で c の data を見る. virtual Node *expose(Node *c) { Node *now = c; Node *rp = nullptr; // 今まで作ったパス while (now) { splay(now); // heavy -> light, light -> heavy. if (now->r) { now->add_light(now->r, now->r->x); } if (rp) { now->erase_light(rp, rp->x); } now->r = rp; now->update(); rp = now; now = now->p; } splay(c); return rp; } // [root, c] がひとつの splay tree になるように変更する. // c が右端で splay tree の根という状態になる. // path query はこの状態で c の data を見る. int expose(int c) { Node *x = expose(&nodes[c]); if (!x) return -1; return x->idx; } Node *get_parent(Node *x) { expose(x); if (!x->l) return nullptr; x = x->l; while (x->r) x = x->r; return x; } int get_parent(int x) { Node *p = get_parent((*this)[x]); return (p ? p->idx : -1); } // splay tree 内で完結する操作. 特に heavy, light 構造は変わらない. // light edge のポインタは変更されうる void rotate(Node *n) { // n を根に近づける Node *pp, *p, *c; p = n->p; pp = p->p; if (p->l == n) { c = n->r; n->r = p; p->l = c; } else { c = n->l; n->l = p; p->r = c; } p->update(), n->update(); if (pp) { if (pp->l == p) pp->l = n; elif (pp->r == p) pp->r = n; else { // light edge pointer が p から n に変わる // 集約値は変わらないので場合によっては省略可能 pp->erase_light(p, n->x); pp->add_light(n, n->x); } } n->p = pp; p->p = n; if (c) c->p = p; } inline int state(Node *n) { if (!n->p) return 0; if (n->p->l == n) return 1; if (n->p->r == n) return -1; return 0; } // splay tree 内で完結する操作. 特に heavy, light 構造は変わらない. // light pointer は rotate 内でケア void splay(Node *c) { c->push(); while (!is_root(c)) { Node *p = c->p; Node *pp = (p ? p->p : nullptr); if (state(p) == 0) { p->push(), c->push(); rotate(c); } elif (state(c) == state(p)) { pp->push(), p->push(), c->push(); rotate(p); rotate(c); } else { pp->push(), p->push(), c->push(); rotate(c); rotate(c); } } } void set_vdata(Node *c, VX x) { evert(c); c->set_vdata(x); } void set_vdata(int c, VX x) { set_vdata((*this)[c], x); } vc collect_heavy_path(int v) { np c = (*this)[v]; while (!is_root(c)) c = c->p; vc res; auto dfs = [&](auto &dfs, np c, bool rev) -> void { if (!rev) { if (c->l) dfs(dfs, c->l, rev ^ c->rev); res.eb(c->idx); if (c->r) dfs(dfs, c->r, rev ^ c->rev); } else { if (c->r) dfs(dfs, c->r, rev ^ c->rev); res.eb(c->idx); if (c->l) dfs(dfs, c->l, rev ^ c->rev); } }; dfs(dfs, c, false); return res; } void debug(int N) { print("idx,p,lch,rch,rev"); auto f = [&](np c) -> int { return (c ? c->idx : -1); }; FOR(i, N) { print(i, f((*this)[i]->p), f((*this)[i]->l), f((*this)[i]->r), (*this)[i]->rev); } } }; // Data は rev を反映済のものをもつ struct Node { using VX = ll; using MX = int; using X = ll; Node *l, *r, *p; int idx, size; // size は heavy path の頂点数 bool rev; VX vx = 0; MX mx; X x = 0; Node(int i = 0) : l(nullptr), r(nullptr), p(nullptr), idx(i), size(1), rev(0) {} void update() { size = 1; x = vx; if (l) { size += l->size, x += l->x; } if (r) { size += r->size, x += r->x; } } void push() { if (rev) { if (l) l->reverse(); if (r) r->reverse(); rev = 0; } } // data の reverse も行う void reverse() { rev ^= 1; swap(l, r); } // LCT 内で expose, update を行うのでここは変更だけ void set_vdata(VX x) { vx = x; } // c がこの時点では update されていないかもしれないが, x は正常なものが入る // c->x 等は使わないように注意する // c->idx を持っておくと探索できることがある void add_light(Node *c, X x) {} void erase_light(Node *c, X x) {} }; void solve() { LL(N); LinkCutTree LCT(2 * N - 1); FOR(e, N - 1) { LL(a, b, c); int idx = N + e; LCT.set_vdata(idx, c); LCT.link(a, idx), LCT.link(b, idx); } auto dist = [&](int a, int b) -> ll { LCT.evert(a); LCT.expose(b); return LCT[b]->x; }; auto solve_1 = [&]() -> void { LL(u, v, w, x); // uv -> vw(x) ll e = LCT.jump(u, v, 1); LCT.cut(u, e), LCT.cut(e, v); LCT.set_vdata(e, x); LCT.link(v, e), LCT.link(e, w); }; auto solve_2 = [&]() -> void { LL(K); VEC(int, X, K); // 頂点インデックス順で dfs したときの euler 順にソートできる // jump の計算のときに evert しているので LCA 取得前に evert しなおすこと int r = X[0]; sort(all(X), [&](auto a, auto b) -> bool { if (a == b) return false; LCT.evert(r); int c = LCT.lca(a, b); if (a == c) return true; if (b == c) return false; int x = LCT.jump(c, a, 1); int y = LCT.jump(c, b, 1); return x < y; }); X.eb(X[0]); ll ANS = 0; FOR(k, K) { ANS += dist(X[k], X[k + 1]); } ANS /= 2; print(ANS); }; LL(Q); FOR(Q) { LL(t); if (t == 1) solve_1(); if (t == 2) solve_2(); } } signed main() { solve(); return 0; }