#include <bits/stdc++.h>
#include "swap.h"
using namespace std;
const int MAX_N = 2e5 + 5;
const int INF = 1e9 + 7;
int N, M;
int parent[MAX_N];
int degree[MAX_N];
int min_weight[MAX_N];
vector <int> graph[MAX_N];
int depth[MAX_N], par[MAX_N][20];
int find_parent(int u) {
if(u == parent[u]) {
return u;
}
return parent[u] = find_parent(parent[u]);
}
void merge(int u, int v, int w) {
bool valid = (degree[u] > 1 or degree[v] > 1);
degree[u]++, degree[v]++;
u = find_parent(u), v = find_parent(v);
if(u == v) {
min_weight[u] = min(min_weight[u], w);
return;
}
N++;
parent[v] = parent[u] = N;
graph[N].push_back(u);
graph[N].push_back(v);
if(valid == true or min_weight[u] != INF or min_weight[v] != INF) {
min_weight[N] = w;
}
}
void dfs(int u) {
for(int i = 1; i < 20; i++) {
par[u][i] = par[par[u][i - 1]][i - 1];
}
for(auto v : graph[u]) {
par[v][0] = u;
depth[v] = depth[u] + 1;
min_weight[v] = min(min_weight[v], min_weight[u]);
dfs(v);
}
}
int find_lca(int u, int v) {
if(depth[u] < depth[v]) {
swap(u, v);
}
for(int i = 19; i >= 0; i--) {
if(depth[par[u][i]] >= depth[v]) {
u = par[u][i];
}
}
for(int i = 19; i >= 0; i--) {
if(par[u][i] != par[v][i]) {
u = par[u][i], v = par[v][i];
}
}
return (u == v ? u : par[u][0]);
}
void init(int n, int m, vector <int> U, vector <int> V, vector <int> W) {
N = n, M = m;
vector <tuple <int, int, int>> edges;
for(int i = 0; i < m; i++) {
edges.emplace_back(W[i], U[i] + 1, V[i] + 1);
}
sort(edges.begin(), edges.end());
fill(min_weight, min_weight + MAX_N, INF);
iota(parent, parent + MAX_N, 0);
for(auto [w, u, v] : edges) {
merge(u, v, w);
}
depth[0] = -1;
dfs(N);
for(int i = 1; i <= N; i++) {
if(min_weight[i] == INF) {
min_weight[i] = -1;
}
}
}
int getMinimumFuelCapacity(int X, int Y) {
return min_weight[find_lca(X + 1, Y + 1)];
}
