//happier ending for folks like us?
//yani in AC nashe, yak yak kesaii ke in APIO dadan dast ma
//PAIN
#include "swap.h"
#include <bits/stdc++.h>
using namespace std;
const int N = 4e5 + 15, M = 2e5 + 5, L = 21, INF = 0x3f3f3f3f;
int p[N], dpr[N], pr[N][L], ext[N], P[N], h[N], rt, D[N], deg[N];
vector<int> adj[N], Wtmp;
inline void smin(int &a, int b) {a = min(a, b);}
void dfs(int v) {
for (int i = 1; i < L; i++) pr[v][i] = pr[pr[v][i - 1]][i - 1];
for (auto u: adj[v]) {
pr[u][0] = v;
h[u] = h[v] + 1;
dfs(u);
smin(ext[v], ext[u]);
}
}
int gpr(int u) {return dpr[u] == u ? u : dpr[u] = gpr(dpr[u]);}
bool merge(int u, int v, int id) {
int tu = u, tv = v;
deg[tu]++, deg[tv]++;
u = gpr(u), v = gpr(v);
if (u == v) return false;
dpr[u] = dpr[v] = id + M;
D[id + M] = max({D[u], D[v], deg[tu], deg[tv]});
adj[id + M].push_back(u);
adj[id + M].push_back(v);
return true;
}
void init(int n, int m, std::vector<int> U, std::vector<int> V, std::vector<int> W) {
iota(p, p + m, 0);
sort(p, p + m, [&](const int x, const int y) {return W[x] < W[y];});
iota(dpr, dpr + N, 0);
memset(ext, 0x3f, sizeof ext);
Wtmp = W;
for (int i = 0; i < m; i++) {
const int id = p[i];
if (!merge(U[id], V[id], id)) {
smin(ext[U[id]], W[id]);
smin(ext[V[id]], W[id]);
}
}
rt = gpr(0), pr[rt][0] = rt, dfs(rt);
}
int LCA(int X, int Y) {
for (int i = L - 1; i >= 0; i--) if (pr[Y][i] != pr[X][i]) Y = pr[Y][i], X = pr[X][i];
return pr[X][0];
}
int getMinimumFuelCapacity(int X, int Y) {
if (h[X] < h[Y]) swap(X, Y);
while (h[Y] < h[X]) X = pr[X][__lg(h[X] - h[Y])];
int w = INF, lca = LCA(X, Y);
for (int i = L - 1; i >= 0; i--) if (pr[Y][i] != pr[X][i] || D[pr[X][i]] <= 2) Y = pr[Y][i], X = pr[X][i];
smin(w, (D[pr[X][0]] > 2 ? Wtmp[pr[X][0] - M] : INF));
if (h[X] <= h[lca]) smin(w, max(Wtmp[X - M], ext[X]));
return w >= INF ? -1 : w;
}
