#include #pragma GCC diagnostic ignored "-Wsign-compare" #pragma GCC diagnostic ignored "-Wsign-conversion" //!===========================================================!// //! dP dP dP !// //! 88 88 88 !// //! 88aaaaa88a .d8888b. .d8888b. .d888b88 .d8888b. 88d888b. !// //! 88 88 88ooood8 88' '88 88' '88 88ooood8 88' '88 !// //! 88 88 88. ... 88. .88 88. .88 88. ... 88 !// //! dP dP '88888P' '88888P8 '88888P8 '88888P' dP !// //!===========================================================!// using ld = long double; using ll = long long; using ull = unsigned long long; std::mt19937 mt{std::random_device{}()}; template constexpr T INF = std::numeric_limits::max() / 4; template constexpr T MOD = static_cast(1000000007); template constexpr F PI() { return 3.1415926535897932385; } #define SHOW(...) (std::cerr << "(" << #__VA_ARGS__ << ") = ("), HogeHogeSansuu(__VA_ARGS__), std::cerr << ")" << std::endl; struct has_debugPrint_impl { template static auto check(T&& x) -> decltype(x.debugPrint(), std::true_type{}); template static auto check(...) -> std::false_type; }; template class has_debugPrint : public decltype(has_debugPrint_impl::check(std::declval())) { }; template struct HogeHogeDump { template static void dump(const T& x) { x.debugPrint(); } }; template <> struct HogeHogeDump { template static void dump(const T& x) { std::cerr << x; } }; void HogeHogeSansuu() { ; } template void HogeHogeSansuu(const T& x) { HogeHogeDump::value>::dump(x); } template void HogeHogeSansuu(const T& x, Args... args) { HogeHogeDump::value>::dump(x), std::cerr << ",", HogeHogeSansuu(args...); } template bool chmin(T& a, const T& b) { return a = std::min(a, b), a == b; } template bool chmax(T& a, const T& b) { return a = std::max(a, b), a == b; } template void For(const T s, const T t, const F f) { for (T i = s; i != t; i += T(s < t ? 1 : -1)) { f(i); } } template void Rep(const T N, const F f) { For(0, N, f); } template void RRep(const T N, const F f) { For(N - 1, -1, f); } template std::vector Vec(const std::size_t n, T v) { return std::vector(n, v); } template auto Vec(const std::size_t n, Args... args) { return std::vector(n, Vec(args...)); } template constexpr T PopCount(const T u) { unsigned long long v = static_cast(u); return v = (v & 0x5555555555555555ULL) + (v >> 1 & 0x5555555555555555ULL), v = (v & 0x3333333333333333ULL) + (v >> 2 & 0x3333333333333333ULL), v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL, static_cast(v * 0x0101010101010101ULL >> 56 & 0x7f); } template constexpr T log2p1(const T u) { unsigned long long v = static_cast(u); return v = static_cast(v), v |= (v >> 1), v |= (v >> 2), v |= (v >> 4), v |= (v >> 8), v |= (v >> 16), v |= (v >> 32), PopCount(v); } template constexpr bool ispow2(const T v) { return (v << 1) == (T(1) << (log2p1(v))); } template constexpr T ceil2(const T v) { return ispow2(v) ? v : T(1) << log2p1(v); } template constexpr T floor2(const T v) { return v == 0 ? T(0) : ispow2(v) ? v : T(1) << (log2p1(v) - 1); } template struct Accum { template Accum(const InIt first, const InIt last) : accum(std::size_t(std::distance(first, last))) { std::partial_sum(first, last, accum.begin()); } T sum(const std::size_t i) const { return i == 0 ? T(0) : accum[i - 1]; } T sum(const std::size_t l, const std::size_t r) const { return sum(r) - sum(l); } std::vector accum; }; template struct Accum2D { Accum2D(const std::vector>& t) : accum{t} { for (std::size_t i = 0; i < accum.size(); i++) { for (std::size_t j = 1; j < accum[i].size(); j++) { accum[i][j] += accum[i][j - 1]; } } for (std::size_t i = 1; i < accum.size(); i++) { for (std::size_t j = 0; j < accum[i].size(); j++) { accum[i][j] += accum[i - 1][j]; } } } T sum(const std::size_t y, const std::size_t x) const { return y == 0 or x == 0 ? T(0) : accum[y - 1][x - 1]; } T sum(const std::size_t ymin, const std::size_t ysup, const std::size_t xmin, const std::size_t xsup) const { return sum(ysup, xsup) - sum(ymin, xmin); } std::vector> accum; }; template struct Zip { template Zip(const InIt first, const InIt last) : unzip(std::size_t(std::distance(first, last))) { std::copy(first, last, unzip), std::sort(unzip.begin(), unzip.end()), unzip.erase(std::unique(unzip.begin(), unzip.end()), unzip.end()); for (std::size_t i = 0; i < unzip.size(); i++) { zip[unzip[i]] = i; } } std::vector unzip; std::map zip; }; template std::ostream& operator<<(std::ostream& os, const std::array& v) { os << "["; for (const auto& e : v) { os << e << ","; } return (os << "]" << std::endl); } template std::ostream& operator<<(std::ostream& os, const std::deque& v) { os << "["; for (const auto& e : v) { os << e << ","; } return (os << "]" << std::endl); } template std::ostream& operator<<(std::ostream& os, const std::multimap& v) { os << "["; for (const auto& e : v) { os << "<" << e.first << ": " << e.second << ">,"; } return (os << "]" << std::endl); } template std::ostream& operator<<(std::ostream& os, const std::multiset& v) { os << "["; for (const auto& e : v) { os << e << ","; } return (os << "]" << std::endl); } template std::ostream& operator<<(std::ostream& os, const std::map& v) { os << "["; for (const auto& e : v) { os << "<" << e.first << ": " << e.second << ">,"; } return (os << "]" << std::endl); } template std::ostream& operator<<(std::ostream& os, const std::pair& v) { return (os << "<" << v.first << "," << v.second << ">"); } template std::ostream& operator<<(std::ostream& os, const std::priority_queue& v) { auto q = v; os << "["; while (not q.empty()) { os << q.top() << ",", q.pop(); } return os << "]\n"; } template std::ostream& operator<<(std::ostream& os, const std::queue& v) { auto q = v; os << "["; while (not q.empty()) { os << q.front() << ",", q.pop(); } return os << "]\n"; } template std::ostream& operator<<(std::ostream& os, const std::set& v) { os << "["; for (const auto& e : v) { os << e << ","; } return (os << "]" << std::endl); } template std::ostream& operator<<(std::ostream& os, const std::stack& v) { auto q = v; os << "["; while (not q.empty()) { os << q.top() << ",", q.pop(); } return os << "]\n"; } template std::ostream& operator<<(std::ostream& os, const std::unordered_multimap& v) { os << "["; for (const auto& e : v) { os << "<" << e.first << ": " << e.second << ">,"; } return (os << "]" << std::endl); } template std::ostream& operator<<(std::ostream& os, const std::unordered_multiset& v) { os << "["; for (const auto& e : v) { os << e << ","; } return (os << "]" << std::endl); } template std::ostream& operator<<(std::ostream& os, const std::unordered_map& v) { os << "["; for (const auto& e : v) { os << "<" << e.first << ": " << e.second << ">,"; } return (os << "]" << std::endl); } template std::ostream& operator<<(std::ostream& os, const std::unordered_set& v) { os << "["; for (const auto& e : v) { os << e << ","; } return (os << "]" << std::endl); } template std::ostream& operator<<(std::ostream& os, const std::vector& v) { os << "["; for (const auto& e : v) { os << e << ","; } return (os << "]" << std::endl); } //!=================================================!// //! .88888. dP !// //! d8' '88 88 !// //! 88 88d888b. .d8888b. 88d888b. 88d888b. !// //! 88 YP88 88' '88 88' '88 88' '88 88' '88 !// //! Y8. .88 88 88. .88 88. .88 88 88 !// //! '88888' dP '88888P8 88Y888P' dP dP !// //! 88 !// //! dP !// //!=================================================!// struct Graph { Graph(const std::size_t v) : V{v}, edge(v), rev_edge(v) {} void addEdge(const std::size_t from, const std::size_t to) { edge[from].push_back(to), rev_edge[to].push_back(from); } const std::vector& operator[](const std::size_t i) const { return edge[i]; } void debugPrint() const { std::cerr << "[\n"; for (std::size_t i = 0; i < V; i++) { for (const std::size_t to : edge[i]) { std::cerr << i << "->" << to << "\n"; } } std::cerr << "]\n"; } const std::size_t V; std::vector> edge, rev_edge; }; //!===================================================================!// //! dP dP oo dP !// //! 88 88 88 !// //! 88 .d8888b. dP dP dP 88 dP 88d888b. 88 .dP !// //! 88 88' '88 88 88 88 88 88 88' '88 88888" !// //! 88 88. .88 88.88b.88' 88 88 88 88 88 '8b. !// //! 88888888P '88888P' 8888P Y8P 88888888P dP dP dP dP 'YP !// //!===================================================================!// class LowLink { private: using P = std::pair; const std::size_t V; std::vector

bridges; std::vector ord, low, arts; std::vector isart; public: LowLink(const Graph& g) : V(g.V), ord(V, V), low(V, 0), isart(V, false) { std::size_t num = 0; auto dfs = [&](auto&& self, const std::size_t s, const std::size_t prev) -> void { ord[s] = low[s] = num++; std::size_t child = 0; for (const std::size_t to : g.edge[s]) { if (to == prev) { continue; } if (ord[to] != V) { low[s] = std::min(low[s], ord[to]); } else { child++, self(self, to, s), isart[s] = isart[s] | (prev != V and low[to] >= ord[s]), low[s] = std::min(low[s], low[to]); if (this->isBridge(s, to)) { bridges.push_back({std::minmax(s, to)}); } } } isart[s] = isart[s] | (prev == V and child >= 2); if (isart[s]) { arts.push_back(s); } }; for (std::size_t i = 0; i < V; i++) { if (ord[i] != V) { continue; } dfs(dfs, i, V); } } bool isBridge(const std::size_t i, const std::size_t j) const { return (ord[i] < ord[j]) ? ord[i] < low[j] : ord[j] < low[i]; } bool isArt(const std::size_t i) const { return isart[i]; } const std::vector

& getBridges() const { return bridges; } const std::vector& getArts() const { return arts; } }; //!======================================================================================!// //! 888888ba oo a88888b. !// //! 88 '8b d8' '88 !// //! a88aaaa8P' dP .d8888b. .d8888b. 88d888b. 88 .d8888b. 88d8b.d8b. 88d888b. !// //! 88 '8b. 88 88' '"" 88' '88 88' '88 88 88' '88 88''88''88 88' '88 !// //! 88 .88 88 88. ... 88. .88 88 88 Y8. .88 88. .88 88 88 88 88. .88 !// //! 88888888P dP '88888P' '88888P' dP dP Y88888P' '88888P' dP dP dP 88Y888P' !// //! 88 !// //! dP !// //!======================================================================================!// class BCC { public: BCC(const Graph& g) : V{g.V}, comp(V, V), lowlink(g) { auto dfs = [&](auto&& self, const std::size_t s) -> void { comp[s] = comp_num; for (const std::size_t to : g.edge[s]) { if (comp[to] != V or lowlink.isBridge(s, to)) { continue; } self(self, to); } }; for (std::size_t i = 0; i < V; i++) { if (comp[i] != V) { continue; } dfs(dfs, i), comp_num++; } } Graph toTree() const { Graph tree(comp_num); for (const auto& p : lowlink.getBridges()) { tree.addEdge(comp[p.first], comp[p.second]), tree.addEdge(comp[p.second], comp[p.first]); } return tree; } const std::vector& getComp() const { return comp; } private: std::size_t V, comp_num = 0; std::vector comp; const LowLink lowlink; }; //!==================================!// //! dP dP dP 888888ba !// //! 88 88 88 88 '8b !// //! 88aaaaa88a 88 88 88 !// //! 88 88 88 88 88 !// //! 88 88 88 88 .8P !// //! dP dP 88888888P 8888888P !// //!==================================!// class HLD { public: HLD(Graph& g, const std::size_t r = 0) : par(g.V, g.V), top(g.V, g.V), in(g.V, g.V), out(g.V, g.V) { const std::size_t N = g.V; std::vector sz(N, 1); auto dfs1 = [&](auto&& self, const std::size_t s, const std::size_t p) -> std::size_t { par[s] = p; for (std::size_t& to : g.edge[s]) { if (p == to) { continue; } sz[s] += self(self, to, s); if (sz[to] > sz[g.edge[s][0]]) { std::swap(to, g.edge[s][0]); } } return sz[s]; }; dfs1(dfs1, r, N); top[r] = r; auto dfs2 = [&](auto&& self, const std::size_t s, const std::size_t p, std::size_t& ind) -> void { in[s] = ind++; for (const std::size_t to : g.edge[s]) { if (to == p) { continue; } top[to] = (to == g.edge[s][0] ? top[s] : to); self(self, to, s, ind); } out[s] = ind; }; std::size_t ind = 0; dfs2(dfs2, r, N, ind); } std::size_t at(const std::size_t v) const { return in[v]; } std::pair sub(const std::size_t v) const { return {in[v], out[v]}; } std::vector> path(std::size_t u, std::size_t v, const bool edgeWeight = false) const { using P = std::pair; std::vector

head, tail; for (std::size_t pu = top[u], pv = top[v]; pu != pv;) { if (in[pu] < in[pv]) { tail.push_back({in[pv], in[v]}); v = par[pv], pv = top[v]; } else { tail.push_back({in[u], in[pu]}); u = par[pu], pu = top[u]; } } if (edgeWeight) { if (std::abs((int)in[u] - (int)in[v]) >= 1) { head.push_back(in[u] < in[v] ? P{in[u] + 1, in[v]} : P{in[u], in[v] + 1}); } } else { head.push_back({in[u], in[v]}); } std::reverse(tail.begin(), tail.end()); for (const auto& p : tail) { head.push_back(p); } return head; } private: std::vector par, top, in, out; }; //!===================================================================!// //! .d88888b d888888P !// //! 88. "' 88 !// //! 'Y88888b. .d8888b. .d8888b. 88 88d888b. .d8888b. .d8888b. !// //! '8b 88ooood8 88' '88 88 88' '88 88ooood8 88ooood8 !// //! d8' .8P 88. ... 88. .88 88 88 88. ... 88. ... !// //! Y88888P '88888P' '8888P88 dP dP '88888P' '88888P' !// //! .88 !// //! d8888P !// //!===================================================================!// template class SegTree { public: using BaseMonoid = Monoid; using T = typename Monoid::T; SegTree(const std::size_t N, const T initial = Monoid::id()) : size(N), half(ceil2(size)), value(half << 1, Monoid::id()) { if (initial != Monoid::id()) { std::fill(value.begin() + half, value.end(), initial); for (std::size_t i = half - 1; i >= 1; i--) { up(i); } } } template SegTree(const InIt first, const InIt last) : size(std::distance(first, last)), half(ceil2(size)), value(half << 1, Monoid::id()) { std::copy(first, last, value.begin() + half); for (std::size_t i = half - 1; i >= 1; i--) { up(i); } } T get(const std::size_t a) const { return value[a + half]; } void set(std::size_t a, const T& val) { value[a += half] = val; while (a >>= 1) { up(a); } } T accumulate(std::size_t L, std::size_t R) const { T accl = Monoid::id(), accr = Monoid::id(); for (L += half, R += half; L < R; L >>= 1, R >>= 1) { if (L & 1) { accl = acc(accl, value[L++]); } if (R & 1) { accr = acc(value[--R], accr); } } return acc(accl, accr); } template std::size_t partitionPoint(const std::size_t L, const std::size_t R, const Pred& pred) const { auto prec = [&](auto&& self, const std::size_t index, const std::size_t left, const std::size_t right, const T& offset) -> std::pair { if (right <= L or R <= left or pred(acc(offset, value[index]))) { return {Monoid::id(), R}; } if (index >= half) { return {value[index], index - half}; } const std::pair lans = self(self, index << 1, left, (left + right) >> 1, offset); if (lans.second != R) { return lans; } return self(self, index << 1 | 1, (left + right) >> 1, right, acc(offset, lans.first)); }; return prec(prec, 1, 0, half, Monoid::id()).second; } void debugPrint() const { std::cerr << "["; for (std::size_t i = half; i < half + size; i++) { std::cerr << value[i] << (i + 1 == half + size ? "" : ","); } std::cerr << "]\n"; } private: void up(const std::size_t i) { value[i] = acc(value[i << 1], value[i << 1 | 1]); } const std::size_t size, half; std::vector value; const Monoid acc{}; }; //!============================================!// //! 8888ba.88ba oo !// //! 88 '8b '8b !// //! 88 88 88 .d8888b. dP 88d888b. !// //! 88 88 88 88' '88 88 88' '88 !// //! 88 88 88 88. .88 88 88 88 !// //! dP dP dP '88888P8 dP dP dP !// //!============================================!// struct Monoid { using T = std::pair; T operator()(const T& a, const T& b) const { return std::max(a, b); } static constexpr T id() { return T{-1, -1}; } }; int main() { std::cin.tie(nullptr); std::ios::sync_with_stdio(false); int N, M, Q; std::cin >> N >> M >> Q; Graph g(N); Rep(M, [&](const int) { int A, B; std::cin >> A >> B, A--, B--, g.addEdge(A, B), g.addEdge(B, A); }); BCC bcc(g); const auto comp = bcc.getComp(); auto t = bcc.toTree(); HLD hld(t); std::vector v(t.V); std::vector> Qs(t.V); for (int i = 0; i < t.V; i++) { v[i] = {-1LL, i}, Qs[i].push(-1LL); } SegTree seg(v.begin(), v.end()); Rep(Q, [&](const int) { int T; std::cin >> T; if (T == 1) { int U; ll W; std::cin >> U >> W, U--; const std::size_t c = hld.at(comp[U]); Qs[c].push(W), seg.set(c, {Qs[c].top(), c}); } else { int S, T; std::cin >> S >> T, S--, T--; const auto range = hld.path(comp[S], comp[T]); Monoid::T max = {-INF, -1}; for (const auto& p : range) { const auto q = std::minmax(p.first, p.second); const std::size_t l = q.first, r = q.second + 1; chmax(max, seg.accumulate(l, r)); } if (max.first != -1LL) { Qs[max.second].pop(), seg.set(max.second, {Qs[max.second].top(), max.second}); } std::cout << max.first << std::endl; } }); return 0; }