#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
//#include "temp.cpp"
#include <cstdio>
using namespace std;
#ifndef ONLINE_JUDGE
#define dbg(x) cerr << #x <<" "; print(x); cerr << endl;
#else
#define dbg(x)
#endif
#define sz(x) (int)x.size()
#define len(x) (int)x.length()
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define clr(x) (x).clear()
#define uniq(x) x.resize(unique(all(x)) - x.begin());
#define blt __builtin_popcount
#define pb push_back
#define popf pop_front
#define popb pop_back
#define ld long double
void print(long long t) {cerr << t;}
void print(int t) {cerr << t;}
void print(string t) {cerr << t;}
void print(char t) {cerr << t;}
void print(double t) {cerr << t;}
void print(long double t) {cerr << t;}
void print(unsigned long long t) {cerr << t;}
template <class T, class V> void print(pair <T, V> p);
template <class T> void print(vector <T> v);
template <class T> void print(set <T> v);
template <class T, class V> void print(map <T, V> v);
template <class T> void print(multiset <T> v);
template <class T, class V> void print(T v[],V n) {cerr << "["; for(int i = 0; i < n; i++) {print(v[i]); cerr << " "; } cerr << "]";}
template <class T, class V> void print(pair <T, V> p) {cerr << "{"; print(p.first); cerr << ","; print(p.second); cerr << "}";}
template <class T> void print(vector <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(set <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(multiset <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T, class V> void print(map <T, V> v) {cerr << "[ "; for (auto i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(deque <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
#define nl '\n'
// for random generations
// mt19937 myrand(chrono::steady_clock::now().time_since_epoch().count());
mt19937 myrand(373);
// for grid problems
int dx[8] = {-1,0,1,0,1,-1,1,-1};
int dy[8] = {0,1,0,-1,1,1,-1,-1};
// lowest / (1 << 17) >= 1e5 / (1 << 18) >= 2e5 / (1 << 21) >= 1e6
void fastIO() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr); cout.tie(nullptr);
}
// file in/out
void setIO(string str = "") {
fastIO();
if(str == "input") {
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
} else {
// freopen("skis.in", "r", stdin);
// freopen("skis.out", "w", stdout);
}
}
// Indexed Set
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
const int N = 5e5 + 10, LOG = 22;
int a[N], n, mx, m, sz[N], p[N], deg[N], mx_edge[N], new_node;
vector<int> adj[N];
int up[N][LOG], in[N], depths[N];
bool exist[N];
set<pair<int, int>> st;
bool flag1 = true;
// dsu
int find(int a) {
// dbg(a)
if(a != p[a]) {
p[a] = find(p[a]);
}
return p[a];
}
int same(int a, int b) {
if(find(a) == find(b)) {
return 1;
}
return 0;
}
int merge(int a, int b, int curr) {
deg[a]++, deg[b]++;
bool is_possible = false;
if(deg[a] >= 3 || deg[b] >= 3) is_possible = true;
a = find(a), b = find(b);
if(a == b) {
if(!exist[a]) {
mx_edge[a] = curr;
exist[a] = true;
}
return 0;
}
if(sz[b] > sz[a]) {
swap(a, b);
}
sz[new_node] = sz[a] + sz[b];
p[b] = new_node, p[a] = new_node;
//
adj[new_node].push_back(a);
adj[new_node].push_back(b);
in[a]++, in[b]++;
up[b][0] = new_node, up[a][0] = new_node;
mx_edge[new_node] = curr;
exist[new_node] = (exist[a] || exist[b] || is_possible);
new_node++;
return 1;
}
void dfs(int node, int parent) {
depths[node] = depths[parent] + 1;
for(auto i: adj[node]) {
dfs(i, node);
}
}
int lca(int a, int b) {
if(a == b) {
return a;
}
if(depths[a] > depths[b]) {
swap(a, b);
}
int delta = depths[b] - depths[a];
for(int i = 0; i < LOG; i++) {
if(delta & (1 << i)) {
b = up[b][i];
}
}
if(a == b) {
return a;
}
for(int i = LOG - 1; i >= 0; i--) {
if(up[a][i] != up[b][i]) {
a = up[a][i], b = up[b][i];
}
}
return up[a][0];
}
void init(int N, int M, vector<int> U, vector<int> V, vector<int> W) {
n = N, m = M;
vector<pair<int, pair<int, int>>> edges;
for(int i = 0; i < M; i++) {
U[i]++, V[i]++;
edges.push_back({W[i], {U[i], V[i]}});
}
new_node = n + 1;
sort(all(edges));
for(int i = 0; i < ::N; i++) {
p[i] = i, sz[i] = 1;
}
for(int i = 0; i < M; i++) {
merge(edges[i].second.first, edges[i].second.second, edges[i].first);
}
for(int i = 1; i < LOG; i++) {
for(int j = 1; j < new_node; j++) {
up[j][i] = up[up[j][i - 1]][i - 1];
}
}
for(int i = 1; i < new_node; i++) {
if(!in[i]) {
dfs(i, 0);
}
}
}
int getMinimumFuelCapacity(int X, int Y) {
X++,Y++;
int lc = lca(X, Y);
int ina = 0, inb = N - 10, answ = -1;
while(ina <= inb) {
int mid = (ina + inb) / 2;
int curr = lc;
for(int i = 0; i < LOG; i++) {
if(mid & (1 << i)) {
curr = up[curr][i];
}
}
if(!curr) {
inb = mid - 1;
continue;
}
if(exist[curr]) {
answ = mid;
inb = mid - 1;
} else {
ina = mid + 1;
}
}
if(answ == -1) {
return answ;
}
int curr = lc;
for(int i = 0; i < LOG; i++) {
if(answ & (1 << i)) {
curr = up[curr][i];
}
}
return mx_edge[curr];
}
