#include "swap.h"
#include <bits/stdc++.h>
using namespace std;
int n, m;
const int N = (int)2e5 + 5;
vector<pair<int, int>> adj[N];
int mx[18][N], dp[18][N], dep[N], dis[N], dis2[N];
pair<int, int> kth(int v, int k) {
int ret = 0;
for (int j = 0; j < 18; j++) {
if ((1 << j) & k) {
ret = max(ret, mx[j][v]);
v = dp[j][v];
}
}
return make_pair(v, ret);
}
pair<int, int> Lca(int u, int v) {
if (dep[u] > dep[v]) swap(u, v);
int ret = 0;
tie(v, ret) = kth(v, dep[v] - dep[u]);
for (int j = 17; j >= 0; j--) {
if (dp[j][v] != dp[j][u]) {
ret = max({ret, mx[j][u], mx[j][v]});
v = dp[j][v], u = dp[j][u];
}
}
if (u == v) return make_pair(u, ret);
else return make_pair(dp[0][u], max({ret, mx[0][u], mx[0][v]}));
}
void dfs(int v, int par) {
dep[v] = dep[par] + 1;
for (auto [u, w]: adj[v]) {
if (u == par) continue;
mx[0][u] = w;
dp[0][u] = v;
for (int j = 1; j < 18; j++) {
mx[j][u] = max(mx[j - 1][u], mx[j - 1][dp[j - 1][u]]);
dp[j][u] = dp[j - 1][dp[j - 1][u]];
}
dfs(u, v);
}
}
void init(int N2, int M, vector<int> U, vector<int> V, vector<int> W) {
n = N2, m = M;
vector<tuple<int, int, int>> se2;
for (int i = 0; i < m; i++) {
auto [u, v, w] = make_tuple(U[i] + 1, V[i] + 1, W[i]);
se2.push_back({w, u, v});
}
vector<vector<int>> nodes(n + 1);
for (int i = 1; i <= n; i++) {
nodes[i].push_back(i);
}
sort(se2.begin(), se2.end());
vector<int> par(n + 1, -1);
function<int(int)> getpar = [&](int x) {
return (par[x] < 0 ? x : getpar(par[x]));
};
auto mrg = [&](int x, int y, int w) {
x = getpar(x), y = getpar(y);
if (x == y) {
if (dis2[x] > w) {
for (int u: nodes[x]) {
dis2[u] = w;
}
}
return 0;
}
if (par[x] > par[y]) swap(x, y);
par[x] += par[y];
par[y] = x;
if (dis2[y] != INT_MAX && dis2[x] == INT_MAX) {
for (int u: nodes[x]) {
dis2[u] = w;
}
}
if (dis2[y] == INT_MAX && dis2[x] != INT_MAX) {
for (int u: nodes[y]) {
dis2[u] = w;
}
}
for (int u: nodes[y]) {
nodes[x].push_back(u);
}
nodes[y].clear();
return 1;
};
for (int i = 1; i <= n; i++) {
dis2[i] = INT_MAX;
}
for (auto [w, u, v]: se2) {
if (mrg(u, v, w)) {
adj[u].push_back({v, w}), adj[v].push_back({u, w});
}
}
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> se;
for (int i = 1; i <= n; i++) {
sort(adj[i].begin(), adj[i].end(), [&](pair<int, int> a, pair<int, int> b) {
return a.second < b.second;
});
}
for (int i = 1; i <= n; i++) {
if ((int)adj[i].size() > 2) {
dis[i] = adj[i][2].second;
se.push({dis[i], i});
} else dis[i] = INT_MAX;
}
while (!se.empty()) {
auto [ds, v] = se.top();
se.pop();
if (ds != dis[v]) continue;
for (auto [u, w]: adj[v]) {
if (dis[u] > max(dis[v], w)) {
dis[u] = max(dis[v], w);
se.push({dis[u], u});
}
}
}
dfs(1, 0);
for (int i = 1; i <= n; i++) {
dis[i] = min(dis[i], dis2[i]);
}
}
int getMinimumFuelCapacity(int X, int Y) {
auto [u, v] = make_tuple(X + 1, Y + 1);
if (dis[u] == INT_MAX) return -1;
return max(Lca(u, v).second, min(dis[u], dis[v]));
}
