// #pragma GCC optimize("Ofast,no-stack-protector")
// #pragma GCC optimize("O3,unroll-loops")
// #pragma GCC target("avx,avx2,bmi,bmi2,lzcnt,popcnt")
#include <bits/stdc++.h>
#define lowbit(x) ((x) & -(x))
#define ml(a, b) ((1ll * (a) * (b)) % M)
#define tml(a, b) (a) = ((1ll * (a) * (b)) % M)
#define ad(a, b) ((0ll + (a) + (b)) % M)
#define tad(a, b) (a) = ((0ll + (a) + (b)) % M)
#define mi(a, b) ((0ll + M + (a) - (b)) % M)
#define tmi(a, b) (a) = ((0ll + M + (a) - (b)) % M)
#define tmin(a, b) (a) = min((a), (b))
#define tmax(a, b) (a) = max((a), (b))
#define iter(a) (a).begin(), (a).end()
#define riter(a) (a).rbegin(), (a).rend()
#define inin(a, b) memset((a), (b), sizeof(a))
#define cpy(a, b) memcpy((a), (b), sizeof(a))
#define uni(a) a.resize(unique(iter(a)) - a.begin())
#define size(x) (int)x.size()
#define pb emplace_back
#define mpr make_pair
#define ls(i) ((i) << 1)
#define rs(i) ((i) << 1 | 1)
#define INF 0x3f3f3f3f
#define NIF 0xc0c0c0c0
#define eps 1e-9
#define F first
#define S second
#define AC cin.tie(0)->sync_with_stdio(0)
using namespace std;
typedef long long llt;
typedef __int128_t lll;
typedef pair<int, int> pii;
typedef pair<double, double> pdd;
typedef pair<llt, llt> pll;
typedef complex<double> cd;
// const int M = 998244353;
// random_device rm;
// mt19937 rg(rm());
// default_random_engine rg(rm());
// uniform_int_distribution<int> rd(INT_MIN, INT_MAX);
// uniform_real_distribution<double> rd(0, M_PI);
void db() { cerr << "\n"; }
template <class T, class... U>
void db(T a, U... b) { cerr << a << " ", db(b...); }
inline char gc()
{
const static int SZ = 1 << 16;
static char buf[SZ], *p1, *p2;
if (p1 == p2 && (p2 = buf + fread(p1 = buf, 1, SZ, stdin), p1 == p2))
return -1;
return *p1++;
}
void rd() {}
template <typename T, typename... U>
void rd(T &x, U &...y)
{
x = 0;
bool f = 0;
char c = gc();
while (!isdigit(c))
f ^= !(c ^ 45), c = gc();
while (isdigit(c))
x = (x << 1) + (x << 3) + (c ^ 48), c = gc();
f && (x = -x), rd(y...);
}
template <typename T>
void prt(T x)
{
if (x < 0)
putchar('-'), x = -x;
if (x > 9)
prt(x / 10);
putchar((x % 10) ^ 48);
}
const int N = 2e5 + 5;
int ds[N], vl[N], p1[N], p2[N], ac[20][N], in[N], ou[N], ctt, n, m, ct;
bool ok[N];
vector<int> pt[N], eg[N];
int f(int x)
{
return ds[x] < 0 ? x : ds[x] = f(ds[x]);
}
inline void mg(int i, int j)
{
i = f(i), j = f(j);
if (i != j)
{
if (size(pt[i]) < size(pt[j]))
swap(i, j);
for (int p : pt[j])
pt[i].pb(p);
ds[i] += ds[j], ds[j] = i;
}
}
void dfs(int u)
{
in[u] = ++ctt;
for (int v : eg[u])
{
ac[0][v] = u;
for (int i = 1; i < 20; i++)
ac[i][v] = ac[i - 1][ac[i - 1][v]];
dfs(v);
}
ou[u] = ctt;
}
inline bool isa(int a, int p)
{
return in[a] <= in[p] && ou[p] <= ou[a];
}
int lca(int u, int v)
{
if (f(u) != f(v) || !ok[f(v)])
return -1;
if (isa(u, v))
assert(0);
for (int i = 19; i >= 0; i--)
if (ac[i][u] && !isa(ac[i][u], v))
u = ac[i][u];
return vl[ac[0][u]];
}
void init(int _n, int _m, vector<int> U, vector<int> V, vector<int> W)
{
n = ct = _n, m = _m, inin(ds, -1);
for (int i = 1; i <= n; i++)
pt[i].pb(i), p1[i] = p2[i] = i;
vector<int> od(m);
iota(iter(od), 0);
sort(iter(od), [&](int a, int b)
{ return W[a] < W[b]; });
for (int i : od)
{
int u = f(++U[i]), v = f(++V[i]);
if (u == v)
{
if (ok[u])
continue;
vl[++ct] = W[i];
for (int j : pt[v])
eg[ct].pb(j);
pt[v].clear();
pt[ct].pb(ct);
mg(ct, u);
ok[f(ct)] = 1;
}
else
{
if (ok[u] || ok[v] || (U[i] != p1[u] && U[i] != p2[u]) ||
(V[i] != p1[v] && V[i] != p2[v]))
{
vl[++ct] = W[i];
for (int j : pt[v])
eg[ct].pb(j);
pt[v].clear();
for (int j : pt[u])
eg[ct].pb(j);
pt[u].clear();
pt[ct].pb(ct);
mg(ct, u), mg(ct, v);
ok[f(ct)] = 1;
}
else
{
int a = U[i] == p1[u] ? p2[u] : p1[u];
int b = V[i] == p2[v] ? p1[v] : p2[v];
mg(u, v);
p1[f(u)] = a, p2[f(v)] = b;
}
}
}
for (int i = n + 1; i <= ct; i++)
if (!pt[i].empty())
dfs(i);
}
int getMinimumFuelCapacity(int X, int Y)
{
return lca(++X, ++Y);
}
