#ifndef hwe
#include "swap.h"
#endif
#include <bits/stdc++.h>
using namespace std;
#define POPCOUNT(n) (__builtin_popcountll((n)))
#define CLZ(n) (__builtin_clzll((n)))
#define CTZ(n) (__builtin_ctzll((n)))
#define LOG(n) (63 - __builtin_clzll((n)))
#define BIT(n, i) (((n) >> (i)) & 1ll)
#define MASK(i) (1ll << (i))
#define FLIP(n, i) ((n) ^ (1ll << (i)))
#define ON(n, i) ((n) | MASK(i))
#define OFF(n, i) ((n) & ~MASK(i))
#define Int __int128
#define fi first
#define se second
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef pair<long long, int> pli;
typedef pair<int, long long> pil;
typedef vector<pair<int, int>> vii;
typedef vector<pair<long long, long long>> vll;
typedef vector<pair<long long, int>> vli;
typedef vector<pair<int, long long>> vil;
template <class T1, class T2> bool maximize(T1 &x, T2 y) {
if (x < y) {
x = y;
return true;
}
return false;
}
template <class T1, class T2> bool minimize(T1 &x, T2 y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <class T> void remove_duplicate(vector<T> &ve) {
sort (ve.begin(), ve.end());
ve.resize(unique(ve.begin(), ve.end()) - ve.begin());
}
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
long long random(long long l, long long r) {
return uniform_int_distribution<long long>(l, r)(rng);
}
unsigned long long random(unsigned long long l, unsigned long long r) {
return uniform_int_distribution<unsigned long long>(l, r)(rng);
}
template <class T> T random(T r) {
return rng() % r;
}
const int N = 1e5 + 5, LG = 18;
const int MOD = 1e9 + 7;
const int inf = 1e9;
const long long INF = 1e18;
vector<int> adj[N];
int up[N][LG], dep[N], w[N], costEdge[N][LG], costThree[N][LG];
struct Edge {
int u, v, w;
Edge(int _u = 0, int _v = 0, int _w = 0) {
u = _u, v = _v, w = _w;
}
} edges[N + N];
struct DSU {
vector<int> lab;
DSU() {}
void resize(int n) {
lab.assign(n + 1, -1);
}
int find_set(int p) {
return lab[p] < 0 ? p : lab[p] = find_set(lab[p]);
}
bool same_set(int u, int v) {
return find_set(u) == find_set(v);
}
bool join(int u, int v) {
u = find_set(u), v = find_set(v);
if (u != v) {
if (lab[u] > lab[v]) swap(u, v);
lab[u] += lab[v], lab[v] = u;
return true;
}
return false;
}
} dsu;
void dfs(int u, int fa) {
for (auto id : adj[u]) {
int v = edges[id].u ^ edges[id].v ^ u;
if (v == fa) continue;
up[v][0] = u, costEdge[v][0] = edges[id].w, costThree[v][0] = w[v];
for (int i = 1; i < LG; ++i) {
up[v][i] = up[up[v][i - 1]][i - 1];
costEdge[v][0] = max(costEdge[v][i - 1], costEdge[up[v][i - 1]][i - 1]);
costThree[v][0] = min(costThree[v][i - 1], costThree[up[v][i - 1]][i - 1]);
}
dfs(v, u);
}
}
void init(int n, int m, vector<int> U, vector<int> V, vector<int> W) {
for (int i = 0; i < m; ++i) {
edges[i] = Edge(U[i], V[i], W[i]);
adj[U[i]].emplace_back(W[i]);
adj[V[i]].emplace_back(W[i]);
}
for (int i = 0; i < n; ++i) {
if (adj[i].size() < 3) w[i] = inf + 69;
sort (adj[i].begin(), adj[i].end());
w[i] = adj[i][2];
}
sort (edges, edges + m, [&](Edge x, Edge y) {
return x.w < y.w;
});
dsu.resize(n);
for (int i = 0; i < m; ++i) {
auto [u, v, w] = edges[i];
if (dsu.join(u, v)) {
adj[u].emplace_back(i);
adj[v].emplace_back(i);
}
}
dfs(0, -1);
}
int getMinimumFuelCapacity(int u, int v) {
if (dep[u] < dep[v]) swap(u, v);
int delta = dep[u] - dep[v], maxEdge = 0, minThree = inf + 69;
for (int i = 0; MASK(i) <= delta; ++i) if (BIT(delta, i)) {
maximize(maxEdge, costEdge[u][i]);
minimize(minThree, costThree[u][i]);
u = up[u][i];
}
if (u == v) {
minimize(minThree, w[u]);
return max(maxEdge, minThree);
}
for (int i = LOG(dep[u]); i >= 0; --i)
if (up[u][i] != up[v][i]) {
maximize(maxEdge, max(costEdge[u][i], costEdge[v][i]));
minimize(minThree, min(costThree[u][i], costThree[v][i]));
u = up[u][i], v = up[v][i];
}
maximize(maxEdge, max(costEdge[u][0], costEdge[v][0]));
minimize(minThree, min(costThree[u][0], costThree[v][0]));
return max(maxEdge, minThree);
}
#ifdef hwe
signed main() {
ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
return 0;
}
#endif
