#include "swap.h"
#include <bits/stdc++.h>
using namespace std;
struct DSU {
vector<int> f;
// vector<int> siz;
vector<int> deg;
vector<bool> ok;
DSU(int n) : f(n), deg(n, 0), ok(n, false) { iota(f.begin(), f.end(), 0); }
int leader(int u) {
while (u != f[u]) u = f[u] = f[f[u]];
return u;
}
bool unionize(int u0, int v0) {
int u = leader(u0);
int v = leader(v0);
if (u == v) {
ok[u] = true;
return false;
}
// if (siz[u] > siz[v]) swap(u, v);
// siz[v] += siz[u];
if (++deg[u0] >= 3 || ++deg[v0] >= 3) ok[v] = true;
ok[v] = ok[v] | ok[u];
f[u] = v;
return true;
}
bool same(int u, int v) {
return leader(u) == leader(v);
}
bool isOk(int u) {
return ok[leader(u)];
}
};
struct LiteDSU {
vector<int> f;
vector<int> siz;
vector<bool> ok;
LiteDSU(int n) : f(n), siz(n, 1), ok(n, false) { iota(f.begin(), f.end(), 0); }
int leader(int u) {
while (u != f[u]) u = f[u] = f[f[u]];
return u;
}
bool unionize(int u, int v) {
u = leader(u);
v = leader(v);
if (u == v) return false;
if (siz[u] > siz[v]) swap(u, v);
siz[v] += siz[u];
ok[v] = ok[v] | ok[u];
f[u] = v;
return true;
}
bool same(int u, int v) {
return leader(u) == leader(v);
}
bool isOk(int u) {
return ok[leader(u)];
}
};
int n, m;
vector<array<int, 3>> edges;
const int B = 300;
vector<DSU> dsus;
int b;
vector<int> mp;
void init(int N, int M, vector<int> U, vector<int> V, vector<int> W) {
n = N;
m = M;
edges.resize(m);
for (int i = 0; i < m; i++) {
edges[i] = {U[i], V[i], W[i]};
}
sort(edges.begin(), edges.end(), [&](array<int, 3> e0, array<int, 3> e1) { return e0[2] < e1[2]; });
dsus.emplace_back(n);
for (b = 0; B * b < m; b++) {
dsus.push_back(dsus.back());
for (int i = B * b; i < min(m, B * b + B); i++) {
dsus.back().unionize(edges[i][0], edges[i][1]);
}
for (int u = 0; u < n; u++) dsus.back().leader(u);
}
b++;
mp.resize(n, -1);
}
int getMinimumFuelCapacity(int X, int Y) {
if (!dsus.back().same(X, Y) || !dsus.back().isOk(X)) return -1;
int b0 = [&]() -> int {
int l = 0, r = b - 2;
while (l < r) {
int m = (l + r + 1) >> 1;
if (!dsus[m].same(X, Y) || !dsus[m].isOk(X)) {
l = m;
} else {
r = m - 1;
}
}
return l;
}();
vector<int> dom;
for (int i = B * b0; i < min(m, B * b0 + B); i++) {
if (dsus[b0 + 1].same(X, edges[i][0]) || dsus[b0 + 1].same(X, edges[i][1])) {
int u = dsus[b0].leader(edges[i][0]);
int v = dsus[b0].leader(edges[i][1]);
if (mp[u] == -1) mp[u] = 0, dom.push_back(u);
if (mp[v] == -1) mp[v] = 0, dom.push_back(v);
}
}
int c = dom.size();
int label = 0;
for (int u : dom) mp[u] = label++;
int x = mp[dsus[b0].leader(X)];
int y = mp[dsus[b0].leader(Y)];
LiteDSU dsu(c);
int res = -2;
vector<int> defer;
for (int u : dom) if (dsus[b0].isOk(u)) dsu.ok[mp[u]] = true;
for (int i = B * b0; i < min(m, B * b0 + B); i++) {
if (dsus[b0 + 1].same(X, edges[i][0]) || dsus[b0 + 1].same(X, edges[i][1])) {
int u = mp[dsus[b0].leader(edges[i][0])];
int v = mp[dsus[b0].leader(edges[i][1])];
if (dsu.same(u, v)) {
dsu.ok[dsu.leader(u)] = true;
} else {
defer.push_back(edges[i][0]);
defer.push_back(edges[i][1]);
if (++dsus[b0].deg[edges[i][0]] >= 3) dsu.ok[dsu.leader(u)] = true;
if (++dsus[b0].deg[edges[i][1]] >= 3) dsu.ok[dsu.leader(v)] = true;
dsu.unionize(u, v);
}
if (dsu.same(x, y) && dsu.isOk(x)) {
res = edges[i][2];
break;
}
}
}
for (int u : defer) dsus[b0].deg[u]--;
for (int u : dom) mp[u] = -1;
return res;
}
