//████████╗██╗███╗░░██╗ ██╗░░░░░███████╗
//╚══██╔══╝██║████╗░██║ ██║░░░░░██╔════╝
//░░░██║░░░██║██╔██╗██║ ██║░░░░░█████╗░░
//░░░██║░░░██║██║╚████║ ██║░░░░░██╔══╝░░
//░░░██║░░░██║██║░╚███║ ███████╗███████╗
//░░░╚═╝░░░╚═╝╚═╝░░╚══╝ ╚══════╝╚══════╝
// __________________
// | ________________ |
// || ____ ||
// || /\ | ||
// || /__\ | ||
// || / \ |____ ||
// ||________________||
// |__________________|
// \###################\
// \###################\
// \ ____ \
// \_______\___\_______\
// An AC a day keeps the doctor away.
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <ctime>
#include <cassert>
#include <complex>
#include <string>
#include <cstring>
#include <chrono>
#include <random>
#include <bitset>
#include <iomanip>
#include <functional>
#include <numeric>
#include <stack>
#include <array>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using namespace std;
template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define vt vector
#define all(x) begin(x), end(x)
#define allr(x) rbegin(x), rend(x)
#define ub upper_bound
#define lb lower_bound
#define db double
#define ld long db
#define ll long long
#define ull unsigned long long
#define vll vt<ll>
#define vvll vt<vll>
#define pll pair<ll, ll>
#define vpll vt<pll>
#define vvpll vt<vpll>
#define vc vt<char>
#define vvc vt<vc>
#define vi vt<int>
#define vvi vt<vi>
#define vvvi vt<vvi>
#define pii pair<int, int>
#define vpii vt<pii>
#define vs vt<string>
#define vvs vt<vs>
#define vb vt<bool>
#define vvb vt<vb>
#define vvpii vt<vpii>
#define vd vt<db>
#define ar(x) array<int, x>
#define var(x) vt<ar(x)>
#define vvar(x) vt<var(x)>
#define al(x) array<ll, x>
#define vall(x) vt<al(x)>
#define vvall(x) vt<vall(x)>
#define mset(m, v) memset(m, v, sizeof(m))
#define pb push_back
#define ff first
#define ss second
#define sv string_view
#define MP make_pair
#define MT make_tuple
#define rsz resize
#define sum(x) (ll)accumulate(all(x), 0LL)
#define srt(x) sort(all(x))
#define srtR(x) sort(allr(x))
#define srtU(x) sort(all(x)), (x).erase(unique(all(x)), (x).end())
#define SORTED(x) is_sorted(all(x))
#define rev(x) reverse(all(x))
#define MAX(a) *max_element(all(a))
#define MIN(a) *min_element(all(a))
#define ROTATE(a, p) rotate(begin(a), begin(a) + p, end(a))
#define i128 __int128
//SGT DEFINE
#define lc i * 2 + 1
#define rc i * 2 + 2
#define lp lc, left, middle
#define rp rc, middle + 1, right
#define entireTree 0, 0, n - 1
#define midPoint left + (right - left) / 2
#define pushDown push(i, left, right)
#define iter int i, int left, int right
#define IOS ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
struct custom {
static const uint64_t C = 0x9e3779b97f4a7c15; const uint32_t RANDOM = std::chrono::steady_clock::now().time_since_epoch().count();
size_t operator()(uint64_t x) const { return __builtin_bswap64((x ^ RANDOM) * C); }
size_t operator()(const std::string& s) const { size_t hash = std::hash<std::string>{}(s); return hash ^ RANDOM; } };
template <class K, class V> using umap = std::unordered_map<K, V, custom>; template <class K> using uset = std::unordered_set<K, custom>;
template<class T> using max_heap = priority_queue<T>;
template<class T> using min_heap = priority_queue<T, vector<T>, greater<T>>;
template<typename T, size_t N>
istream& operator>>(istream& is, array<T, N>& arr) {
for (size_t i = 0; i < N; i++) { is >> arr[i]; } return is;
}
template<typename T, size_t N>
istream& operator>>(istream& is, vector<array<T, N>>& vec) {
for (auto &arr : vec) { is >> arr; } return is;
}
inline std::ostream& operator<<(std::ostream& os, i128 x) {
if(x == 0) { os << '0'; return os; } if(x < 0) { os << '-'; x = -x; }
string s; while (x > 0) { int digit = int(x % 10); s.pb(char('0' + digit)); x /= 10; }
rev(s); os << s; return os;
}
template <typename T1, typename T2> istream &operator>>(istream& in, pair<T1, T2>& input) { return in >> input.ff >> input.ss; }
template <typename T> istream &operator>>(istream &in, vector<T> &v) { for (auto &el : v) in >> el; return in; }
template<class T>
void output_vector(vt<T>& a, int off_set = 0) {
int n = a.size();
for(int i = off_set; i < n; i++) {
cout << a[i] << (i == n - 1 ? '\n' : ' ');
}
}
template<typename T, typename Compare>
vi closest_left(const vt<T>& a, Compare cmp) {
int n = a.size(); vi closest(n); iota(all(closest), 0);
for (int i = 0; i < n; i++) {
auto& j = closest[i];
while(j && cmp(a[i], a[j - 1])) j = closest[j - 1];
}
return closest;
}
template<typename T, typename Compare> // auto right = closest_right<int>(a, std::less<int>());
vi closest_right(const vt<T>& a, Compare cmp) {
int n = a.size(); vi closest(n); iota(all(closest), 0);
for (int i = n - 1; i >= 0; i--) {
auto& j = closest[i];
while(j < n - 1 && cmp(a[i], a[j + 1])) j = closest[j + 1];
}
return closest;
}
template<typename T, typename V = string>
vt<pair<T, int>> encode(const V& s) {
vt<pair<T, int>> seg;
for(auto& ch : s) {
if(seg.empty() || ch != seg.back().ff) seg.pb({ch, 1});
else seg.back().ss++;
}
return seg;
}
template<typename K, typename V>
auto operator<<(std::ostream &o, const std::map<K, V> &m) -> std::ostream& {
o << "{"; int i = 0;
for (const auto &[key, value] : m) { if (i++) o << " , "; o << key << " : " << value; }
return o << "}";
}
#ifdef LOCAL
#define debug(x...) debug_out(#x, x)
void debug_out(const char* names) { std::cerr << std::endl; }
template <typename T, typename... Args>
void debug_out(const char* names, T value, Args... args) {
const char* comma = strchr(names, ',');
std::cerr << "[" << (comma ? std::string(names, comma) : names) << " = " << value << "]";
if (sizeof...(args)) { std::cerr << ", "; debug_out(comma + 1, args...); }
else { std::cerr << std::endl; }
}
template<typename T1, typename T2>
std::ostream& operator<<(std::ostream& o, const std::pair<T1, T2>& p) { return o << "{" << p.ff << " , " << p.ss << "}"; }
auto operator<<(auto &o, const auto &x) -> decltype(end(x), o) {
o << "{"; int i = 0; for (const auto &e : x) { if (i++) o << " , "; o << e; } return o << "}";
} // remove for leetcode
#include <sys/resource.h>
#include <sys/time.h>
void printMemoryUsage() {
struct rusage usage;
getrusage(RUSAGE_SELF, &usage);
double memoryMB = usage.ru_maxrss / 1024.0;
cerr << "Memory usage: " << memoryMB << " MB" << "\n";
}
#define startClock clock_t tStart = clock();
#define endClock std::cout << std::fixed << std::setprecision(10) << "\nTime Taken: " << (double)(clock() - tStart) / CLOCKS_PER_SEC << " seconds" << std::endl;
#else
#define debug(...)
#define startClock
#define endClock
#endif
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
#define eps 1e-9
#define M_PI 3.14159265358979323846
const static string pi = "3141592653589793238462643383279";
const static ll INF = 1LL << 62;
const static int inf = 1e9 + 100;
const static int MK = 20;
const static int MX = 1e5 + 5;
ll gcd(ll a, ll b) { while (b != 0) { ll temp = b; b = a % b; a = temp; } return a; }
ll lcm(ll a, ll b) { return (a / gcd(a, b)) * b; }
ll floor(ll a, ll b) { if(b < 0) a = -a, b = -b; if (a >= 0) return a / b; return a / b - (a % b ? 1 : 0); }
ll ceil(ll a, ll b) { if (b < 0) a = -a, b = -b; if (a >= 0) return (a + b - 1) / b; return a / b; }
int pct(ll x) { return __builtin_popcountll(x); }
ll have_bit(ll x, int b) { return x & (1LL << b); }
int min_bit(ll x) { return __builtin_ctzll(x); }
int max_bit(ll x) { return 63 - __builtin_clzll(x); }
const vvi dirs = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}, {1, 1}, {-1, -1}, {1, -1}, {-1, 1}}; // UP, DOWN, LEFT, RIGHT
const vvi knight_dirs = {{-2, -1}, {-2, 1}, {-1, -2}, {-1, 2}, {1, -2}, {1, 2}, {2, -1}, {2, 1}}; // knight dirs
const vc dirChar = {'U', 'D', 'L', 'R'};
int modExpo(ll base, ll exp, ll mod) { ll res = 1; base %= mod; while(exp) { if(exp & 1) res = (res * base) % mod; base = (base * base) % mod; exp >>= 1; } return res; }
ll extended_gcd(ll a, ll b, ll &x, ll &y) { if (b == 0) { x = 1; y = 0; return a; } ll d = extended_gcd(b, a % b, y, x); y -= (a / b) * x; return d; }
ll modInv(ll a, ll m) { ll x, y; ll g = extended_gcd(a, m, x, y); if (g != 1) { return -1; } x %= m; if (x < 0) x += m; return x; }
int modExpo_on_string(ll a, string exp, int mod) { ll b = 0; for(auto& ch : exp) b = (b * 10 + (ch - '0')) % (mod - 1); return modExpo(a, b, mod); }
ll sum_even_series(ll n) { return (n / 2) * (n / 2 + 1);}
ll sum_odd_series(ll n) {return n - sum_even_series(n);} // sum of first n odd number is n ^ 2
ll sum_of_square(ll n) { return n * (n + 1) * (2 * n + 1) / 6; } // sum of 1 + 2 * 2 + 3 * 3 + 4 * 4 + ... + n * n
string make_lower(const string& t) { string s = t; transform(all(s), s.begin(), [](unsigned char c) { return tolower(c); }); return s; }
string make_upper(const string&t) { string s = t; transform(all(s), s.begin(), [](unsigned char c) { return toupper(c); }); return s; }
ll sqrt(ll n) { ll t = sqrtl(n); while(t * t < n) t++; while(t * t > n) t--; return t;}
bool is_perm(ll sm, ll square_sum, ll len) {return sm == len * (len + 1) / 2 && square_sum == len * (len + 1) * (2 * len + 1) / 6;} // determine if an array is a permutation base on sum and square_sum
bool is_vowel(char c) {return c == 'a' || c == 'e' || c == 'u' || c == 'o' || c == 'i';}
template<typename T = int>
class GRAPH {
public:
int n, m;
vvi dp;
vi parent, subtree;
vi tin, tout, low, ord, depth;
vll depth_by_weight;
vvi weight;
int timer = 0;
vt<unsigned> in_label, ascendant;
vi par_head;
unsigned cur_lab = 1;
vt<vt<T>> adj;
GRAPH() {}
GRAPH(const vt<vt<T>>& graph, int root = 0) {
adj = graph;
n = graph.size();
m = log2(n) + 1;
// depth_by_weight.rsz(n);
// weight.rsz(n, vi(m));
dp.rsz(n, vi(m, -1));
depth.rsz(n);
parent.rsz(n, -1);
subtree.rsz(n, 1);
tin.rsz(n);
tout.rsz(n);
ord.rsz(n);
dfs(root);
init();
in_label.rsz(n);
ascendant.rsz(n);
par_head.rsz(n + 1);
sv_dfs1(root);
ascendant[root] = in_label[root];
sv_dfs2(root);
}
void dfs(int node, int par = -1) {
tin[node] = timer++;
ord[tin[node]] = node;
for (auto& nei : adj[node]) {
if (nei == par) continue;
depth[nei] = depth[node] + 1;
// depth_by_weight[nei] = depth_by_weight[node] + w;
// weight[nei][0] = w;
dp[nei][0] = node;
parent[nei] = node;
dfs(nei, node);
subtree[node] += subtree[nei];
}
tout[node] = timer - 1;
}
bool is_ancestor(int par, int child) { return tin[par] <= tin[child] && tin[child] <= tout[par]; }
void init() {
for (int j = 1; j < m; ++j) {
for (int i = 0; i < n; ++i) {
int p = dp[i][j - 1];
if(p == -1) continue;
//weight[i][j] = max(weight[i][j - 1], weight[p][j - 1]);
dp[i][j] = dp[p][j - 1];
}
}
}
void sv_dfs1(int u, int p = -1) {
in_label[u] = cur_lab++;
for(auto& v : adj[u]) if (v != p) {
sv_dfs1(v, u);
if(std::__countr_zero(in_label[v]) > std::__countr_zero(in_label[u]))
in_label[u] = in_label[v];
}
}
void sv_dfs2(int u, int p = -1) {
for(auto& v : adj[u]) if (v != p) {
ascendant[v] = ascendant[u];
if(in_label[v] != in_label[u]) {
par_head[in_label[v]] = u;
ascendant[v] += in_label[v] & -in_label[v];
}
sv_dfs2(v, u);
}
}
int lift(int u, unsigned j) const {
unsigned k = std::__bit_floor(ascendant[u] ^ j);
return k == 0 ? u : par_head[(in_label[u] & -k) | k];
}
int lca(int a, int b) {
if(is_ancestor(a, b)) return a;
if(is_ancestor(b, a)) return b;
auto [x, y] = std::minmax(in_label[a], in_label[b]);
unsigned j = ascendant[a] & ascendant[b] & -std::__bit_floor((x - 1) ^ y);
a = lift(a, j);
b = lift(b, j);
return depth[a] < depth[b] ? a : b;
}
int path_queries(int u, int v) { // lca in logn
if(depth[u] < depth[v]) swap(u, v);
int res = 0;
int diff = depth[u] - depth[v];
for(int i = 0; i < m; i++) {
if(diff & (1 << i)) {
res = max(res, weight[u][i]);
u = dp[u][i];
}
}
if(u == v) return res;
for(int i = m - 1; i >= 0; --i) {
if(dp[u][i] != dp[v][i]) {
res = max({res, weight[u][i], weight[v][i]});
u = dp[u][i];
v = dp[v][i];
}
}
return max({res, weight[u][0], weight[v][0]});
}
int dist(int u, int v) {
int a = lca(u, v);
return depth[u] + depth[v] - 2 * depth[a];
}
ll dist_by_weight(int u, int v) {
int a = lca(u, v);
return depth_by_weight[u] + depth_by_weight[v] - 2 * depth_by_weight[a];
}
int kth_ancestor(int u, ll k) {
if(u < 0 || k > depth[u]) return -1;
for(int i = 0; i < m && u != -1; ++i) {
if(k & (1LL << i)) {
u = (u >= 0 ? dp[u][i] : -1);
}
}
return u;
}
int kth_ancestor_on_path(int u, int v, ll k) {
int d = dist(u, v);
if(k >= d) return v;
int w = lca(u, v);
int du = depth[u] - depth[w];
if(k <= du) return kth_ancestor(u, k);
int rem = k - du;
int dv = depth[v] - depth[w];
return kth_ancestor(v, dv - rem);
}
int kth_downward(int v, ll k) {
if(k < 1 || k > depth[v] + 1) return -1;
ll steps_up = depth[v] - (k - 1);
return kth_ancestor(v, steps_up);
}
int max_intersection(int a, int b, int c) { // # of common intersection between path(a, c) OR path(b, c)
auto cal = [&](int u, int v, int goal){
return (dist(u, goal) + dist(v, goal) - dist(u, v)) / 2 + 1;
};
int res = 0;
res = max(res, cal(a, b, c));
res = max(res, cal(a, c, b));
res = max(res, cal(b, c, a));
return res;
}
int intersection(int a, int b, int c, int d) { // common edges between path[a, b] OR path[c, d]
int r1 = lca(a, b), r2 = lca(c, d);
int q = depth[r1] > depth[r2] ? r1 : r2;
int p = lca(a, c), t = lca(a, d);
if (depth[t] > depth[p]) p = t;
t = lca(b,c); if (depth[t] > depth[p]) p = t;
t = lca(b,d); if (depth[t] > depth[p]) p = t;
if (depth[p] < depth[q]) return 0;
return depth[p] - depth[q];
}
bool is_continuous_chain(int a, int b, int c, int d) { // determine if path[a, b][b, c][c, d] don't have any intersection
return dist(a, b) <= dist(a, c) && dist(d, c) <= dist(d, b) && intersection(a, b, c, d) == 0;
}
int rooted_lca(int a, int b, int c) { return lca(a, c) ^ lca(a, b) ^ lca(b, c); }
int next_on_path(int u, int v) { // closest_next_node from u to v
if(u == v) return -1;
if(is_ancestor(u, v)) return kth_ancestor(v, depth[v] - depth[u] - 1);
return parent[u];
}
void reroot(int root) {
fill(all(parent), -1);
timer = 0;
dfs(root);
init();
cur_lab = 1;
sv_dfs1(root);
ascendant[root] = in_label[root];
sv_dfs2(root);
}
int comp_size(int c,int v){
if(parent[v] == c) return subtree[v];
return n - subtree[c];
}
int rooted_lca_potential_node(int a, int b, int c) { // # of nodes where rooted at will make lca(a, b) = c
if(rooted_lca(a, b, c) != c) return 0;
int v1 = next_on_path(c, a);
int v2 = next_on_path(c, b);
return n - (v1 == -1 ? 0 : comp_size(c, v1)) - (v2 == -1 ? 0 : comp_size(c, v2));
}
vi get_path(int u, int v) { // get every node in path [u, v]
vi path1, path2;
int c = lca(u, v);
while(u != c) {
path1.pb(u);
u = parent[u];
}
while(v != c) {
path2.pb(v);
v = parent[v];
}
rev(path2);
path1.pb(c);
path1.insert(end(path1), all(path2));
return path1;
}
};
struct Reachability_Tree {
struct DSU {
vi p, r;
DSU(int n): p(n), r(n, 0) { iota(all(p), 0); }
int find(int x) {
return p[x] == x ? x : p[x] = find(p[x]);
}
bool same(int a, int b) {
return find(a) == find(b);
}
void merge(int a, int b) {
a = find(a); b = find(b);
if(a == b) return;
p[b] = a;
if(r[a] == r[b]) r[a]++;
}
};
int n;
vi weight;
GRAPH<int> g;
DSU root;
int rt;
vvi graph;
Reachability_Tree(int n) : n(n), root(n * 2), rt(n - 1), graph(n * 2), weight(n * 2) {}
void add_edge(int u, int v, int w = 0) {
if(root.same(u, v)) return;
rt++;
weight[rt] = w;
graph[rt].pb(root.find(u));
graph[rt].pb(root.find(v));
root.merge(rt, u);
root.merge(rt, v);
}
bool built = false;
void init(var(3)& edges) {
built = true;
sort(all(edges), [](const ar(3)& a, const ar(3)& b) {return a[2] < b[2];});
for(auto& [u, v, w] : edges) {
add_edge(u, v, w);
}
g = GRAPH<int>(graph, rt);
}
void build() {
built = true;
g = GRAPH<int>(graph, rt);
}
int lca_query(int u, int v) {
if(!built) build();
int c = g.lca(u, v);
return weight[c];
}
};
void solve() {
int n, m, q; cin >> n >> m >> q;
var(3) edges;
for(int i = 0; i < m; i++) {
int u, v, w; cin >> u >> v >> w;
u--, v--;
edges.pb({u, v, w});
}
Reachability_Tree root(n);
root.init(edges);
while(q--) {
int u, v; cin >> u >> v;
u--, v--;
cout << root.lca_query(u, v) << '\n';
}
}
signed main() {
// careful for overflow, check for long long, use unsigned long long for random generator
// when mle, look if problem require read in file, typically old problems
IOS;
startClock
//generatePrime();
int t = 1;
//cin >> t;
for(int i = 1; i <= t; i++) {
//cout << "Case #" << i << ": ";
solve();
}
endClock
#ifdef LOCAL
printMemoryUsage();
#endif
return 0;
}
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Tin Le tin_le