//#define NDEBUG
#include "swap.h"
#include <bits/stdc++.h>
#include <bits/extc++.h>
#define StarBurstStream ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define iter(a) a.begin(), a.end()
#define riter(a) a.rbegin(), a.rend()
#define lsort(a) sort(iter(a))
#define gsort(a) sort(riter(a))
#define pb(a) push_back(a)
#define eb(a) emplace_back(a)
#define pf(a) push_front(a)
#define pob pop_back()
#define pof pop_front()
#define mp(a, b) make_pair(a, b)
#define F first
#define S second
#define mt make_tuple
#define gt(t, i) get<i>(t)
#define iceil(a, b) ((a + b - 1) / b)
#define tomax(a, b) (a = max(a, b))
#define printv(a, b) {bool pvaspace=false; \
for(auto pva : a){ \
if(pvaspace) b << " "; pvaspace=true;\
b << pva;\
}\
b << "\n";}
//#define TEST
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
using tiii = tuple<int, int, int>;
const ll MOD = 1000000007;
const ll MAX = 2147483647;
template<typename A, typename B>
ostream& operator<<(ostream& o, pair<A, B> p){
return o << '(' << p.F << ',' << p.S << ')';
}
vector<int> dsu, one, three;
vector<vector<int>> anc, g;
vector<int> ans, in, out;
int findDSU(int a){
if(dsu[a] != a) dsu[a] = findDSU(dsu[a]);
return dsu[a];
}
void unionDSU(int a, int b){
a = findDSU(a); b = findDSU(b);
if(a == b) return;
dsu[b] = a;
one[a] += one[b];
three[a] += three[b];
}
int dfsts = 0;
void dfs(int now, int p){
in[now] = dfsts++;
if(ans[now] == -1) ans[now] = ans[p];
for(int i : g[now]) dfs(i, now);
out[now] = dfsts++;
}
bool isAnc(int a, int b){
return in[a] <= in[b] && out[a] >= out[b];
}
int lca(int a, int b){
if(isAnc(a, b)) return a;
for(int i = 19; i >= 0; i--){
if(!isAnc(anc[a][i], b)) a = anc[a][i];
}
return anc[a][0];
}
void init(int N, int M,
std::vector<int> U, std::vector<int> V, std::vector<int> W) {
vector<pair<int, pii>> e(M);
for(int i = 0; i < M; i++){
e[i] = mp(W[i], mp(U[i], V[i]));
}
lsort(e);
dsu.resize(N + M);
for(int i = 0; i < N + M; i++) dsu[i] = i;
one.resize(N + M); three.resize(N + M);
int ts = N;
anc.resize(N + M, vector<int>(20));
for(int i = 0; i < N + M; i++) anc[i][0] = i;
ans.resize(N + M, -1);
g.resize(N + M);
in.resize(N + M);
out.resize(N + M);
vector<int> deg(N);
for(auto i : e){
int w = i.F, u = i.S.F, v = i.S.S;
if(deg[u] == 1) one[findDSU(u)]--;
if(deg[v] == 1) one[findDSU(v)]--;
deg[u]++; deg[v]++;
if(deg[u] == 1) one[findDSU(u)]++;
else if(deg[u] == 3) three[findDSU(u)]++;
if(deg[v] == 1) one[findDSU(v)]++;
else if(deg[v] == 3) three[findDSU(v)]++;
u = findDSU(u);
v = findDSU(v);
int dv = ts++;
if(u == v){
unionDSU(dv, u);
anc[u][0] = dv;
g[dv].eb(u);
}
else{
unionDSU(dv, u);
unionDSU(dv, v);
anc[u][0] = anc[v][0] = dv;
g[dv].eb(u); g[dv].eb(v);
}
if(!one[dv] || three[dv]) ans[dv] = w;
}
// for(int i = 0; i < N + M; i++) cerr << anc[i][0] << " ";
// cerr << "\n";
for(int i = 0; i < N + M; i++){
if(anc[i][0] == i) dfs(i, i);
}
for(int i = 1; i < 20; i++){
for(int j = 0; j < N + M; j++){
anc[j][i] = anc[anc[j][i - 1]][i - 1];
}
}
}
int getMinimumFuelCapacity(int X, int Y) {
if(findDSU(X) != findDSU(Y)) return -1;
return ans[lca(X, Y)];
}
