#include "swap.h"
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
#define ff first
#define ss second
#define pb push_back
#define mp make_pair
#define END "\n"
#define rall(v) (v).rbegin(), (v).rend()
#define all(v) (v).begin(), (v).end()
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template <typename T>
using ordered_set =
tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
vector<int> parent, sz;
void make_set(int n) {
parent.resize(n);
iota(all(parent), 0);
sz.assign(n, 1);
}
int find_parent(int a) {
if (a == parent[a]) return a;
else return parent[a] = find_parent(parent[a]);
}
vector<vector<int>> adj;
vector<int> good, weight;
struct LCA {
int n, d;
vector<vector<int>> parent;
vector<int> depth;
LCA () {}
LCA (const vector<vector<int>>& adj, int r) {
n = adj.size();
assert(r < adj.size());
d = 0;
while ((1 << d) <= n) d++;
depth.resize(n);
parent.resize(d, vector<int>(n));
parent[0][r] = r;
dfs(adj, r, -1);
pre_calc();
}
void dfs(const vector<vector<int>>& adj, int v, int p) {
// cout << "VISITING: " << v << " " << p << endl;
for (auto u: adj[v]) {
if (u != p)
parent[0][u] = v, depth[u] = depth[v] + 1, dfs(adj, u, v);
}
}
void pre_calc() {
for (int i = 1; i < d; ++i) {
for (int j = 0; j < n; ++j) {
parent[i][j] = parent[i - 1][parent[i - 1][j]];
}
}
}
int walk(int v, int x) {
for (int i = d - 1; i >= 0; --i) {
if (x & (1 << i)) v = parent[i][v];
}
return v;
}
int lca(int u, int v) {
if (depth[u] < depth[v]) swap(u, v);
int x = depth[u] - depth[v];
u = walk(u, x);
if (u == v) return u;
for (int i = d - 1; i >= 0; --i) {
if (parent[i][u] != parent[i][v]) u = parent[i][u], v = parent[i][v];
}
return parent[0][u];
}
};
LCA lca;
int root;
void init(int N, int M, std::vector<int> U, std::vector<int> V, std::vector<int> W) {
make_set(N + M);
adj.clear();
adj.resize(N + M);
vector<int> idxes(M);
iota(all(idxes), 0);
sort(all(idxes), [&] (int a, int b) {
return W[a] < W[b];
});
int counter = N;
good.resize(N + M), weight.resize(N + M);
vector<int> degree(N);
for (int i = 0; i < M; ++i) {
int idx = idxes[i];
int a = find_parent(U[idx]), b = find_parent(V[idx]), w = W[idx];
++degree[U[idx]];
++degree[V[idx]];
int v = counter++;
// cout << "ADDING EDGE: " << v << " " << a << " " << b << endl;
adj[v].push_back(a);
if (a != b) adj[v].push_back(b);
if (a == b || good[a] || good[b] || degree[U[idx]] > 2 || degree[V[idx]] > 2) {
good[v] = 1;
}
weight[v] = w;
parent[a] = v;
parent[b] = v;
}
assert(counter == N + M);
lca = LCA(adj, counter - 1);
// for (int i = 0; i < N + M; ++i) cout << i << ": " << lca.parent[0][i] << endl;
root = counter - 1;
}
int getMinimumFuelCapacity(int X, int Y) {
int V = lca.lca(X, Y);
// cout << X << " " << Y << ": " << V << endl;
if (good[V]) return weight[V];
for (int i = lca.d - 1; i >= 0; --i) {
if (!good[lca.parent[i][V]]) V = lca.parent[i][V];
}
// cout << "FINAL: " << X << " " << Y << ": " << V << endl;
if (V == root) return -1;
return weight[lca.parent[0][V]];
return 0;
}
