/*************************************
* author: marvinthang *
* created: 09.11.2023 08:43:17 *
*************************************/
#include "swap.h"
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define left ___left
#define right ___right
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
#define MASK(i) (1LL << (i))
#define BIT(x, i) ((x) >> (i) & 1)
#define __builtin_popcount __builtin_popcountll
#define ALL(v) (v).begin(), (v).end()
#define REP(i, n) for (int i = 0, _n = (n); i < _n; ++i)
#define REPD(i, n) for (int i = (n); i-- > 0; )
#define FOR(i, a, b) for (int i = (a), _b = (b); i < _b; ++i)
#define FORD(i, b, a) for (int i = (b), _a = (a); --i >= _a; )
#define FORE(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define FORDE(i, b, a) for (int i = (b), _a = (a); i >= _a; --i)
#define scan_op(...) istream & operator >> (istream &in, __VA_ARGS__ &u)
#define print_op(...) ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#ifdef LOCAL
#include "debug.h"
#else
#define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
#define DB(...) 23
#define db(...) 23
#define debug(...) 23
#endif
template <class U, class V> scan_op(pair <U, V>) { return in >> u.first >> u.second; }
template <class T> scan_op(vector <T>) { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class U, class V> print_op(pair <U, V>) { return out << '(' << u.first << ", " << u.second << ')'; }
template <size_t i, class T> ostream & print_tuple_utils(ostream &out, const T &tup) { if constexpr(i == tuple_size<T>::value) return out << ")"; else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); }
template <class ...U> print_op(tuple<U...>) { return print_tuple_utils<0, tuple<U...>>(out, u); }
template <class Con, class = decltype(begin(declval<Con>()))> typename enable_if <!is_same<Con, string>::value, ostream&>::type operator << (ostream &out, const Con &con) { out << '{'; for (__typeof(con.begin()) it = con.begin(); it != con.end(); ++it) out << (it == con.begin() ? "" : ", ") << *it; return out << '}'; }
// end of template
const int LOG = 20;
vector <vector <int>> adj;
vector <bool> can_connect;
vector <int> weights, anc[20], depth;
void init(int n, int m, vector <int> U, vector <int> V, vector <int> W) {
vector <tuple <int, int, int>> edges;
REP(i, m) edges.emplace_back(W[i], U[i], V[i]);
sort(ALL(edges));
vector <int> par(n + m);
iota(ALL(par), 0);
vector <int> deg(n);
adj.resize(n + m);
can_connect.resize(n + m);
weights.resize(n + m);
function <int(int)> find = [&] (int u) {
return par[u] == u ? u : par[u] = find(par[u]);
};
auto join = [&] (int u, int v) {
int pu = find(u), pv = find(v);
par[pu] = par[pv] = n;
adj[n].push_back(pu);
can_connect[n] = can_connect[pu] || can_connect[pv];
if (pu == pv) {
can_connect[n] = true;
} else {
adj[n].push_back(pv);
if (max(++deg[u], ++deg[v]) > 2) can_connect[n] = true;
}
++n;
};
for (auto [w, u, v]: edges) {
weights[n] = w;
join(u, v);
}
REP(i, LOG) anc[i].resize(n);
depth.resize(n);
function<void(int)> dfs = [&] (int u) {
FOR(i, 1, LOG) anc[i][u] = anc[i - 1][anc[i - 1][u]];
for (int v: adj[u]) if (v != anc[0][u]) {
depth[v] = depth[u] + 1;
anc[0][v] = u;
dfs(v);
}
};
anc[0][n - 1] = n - 1;
dfs(n - 1);
}
int getMinimumFuelCapacity(int u, int v) {
if (depth[u] < depth[v]) swap(u, v);
REPD(i, LOG) if (depth[anc[i][u]] >= depth[v]) u = anc[i][u];
if (u != v) {
REPD(i, LOG) if (anc[i][u] != anc[i][v]) u = anc[i][u], v = anc[i][v];
u = anc[0][u];
}
if (can_connect[u]) return weights[u];
REPD(i, LOG) if (!can_connect[anc[i][u]]) u = anc[i][u];
return anc[0][u] == u ? -1 : weights[anc[0][u]];
}
