#include "swap.h"
#include <bits/stdc++.h>
#define pii pair<int, int>
using namespace std;
const int MAX = 200007;
int N, M, D[MAX];
bool isLine;
vector<tuple<int, int, int>> E;
vector<pii> R[MAX], T[MAX], C[MAX];
void Clear() {
for (int i = 0; i < MAX; ++i) {
R[i].clear();
T[i].clear();
C[i].clear();
R[i].emplace_back(-1, i);
T[i].emplace_back(-1, 0);
C[i].emplace_back(-1, 0);
}
memset(D, 0, sizeof(D));
}
int Find(int n, int t) {
int tr = R[n].back().second;
if (T[n].back().second && !T[tr].back().second) T[tr].emplace_back(t, 1);
if (C[n].back().second && !C[tr].back().second) C[tr].emplace_back(t, 1);
if (n == tr) return n;
int r = Find(tr, t);
if (R[n].back().second != r) R[n].emplace_back(r, t);
return R[n].back().second;
}
void Union(int a, int b, int t) {
if (++D[a] == 3 && !T[a].back().second) T[a].emplace_back(t, 1);
if (++D[b] == 3 && !T[b].back().second) T[b].emplace_back(t, 1);
a = Find(a, t), b = Find(b, t);
if (a == b) {
if (!C[a].back().second) C[a].emplace_back(t, 1);
return;
}
R[a].emplace_back(t, b);
if (T[a].back().second && !T[b].back().second) T[b].emplace_back(t, 1);
if (C[a].back().second && !C[b].back().second) C[b].emplace_back(t, 1);
}
int TFind(vector<pii>& S, int t) {
auto it = upper_bound(S.begin(), S.end(), pii{t, 1 << 30});
return (*--it).second;
}
int getMinimumFuelCapacity(int x, int y) {
if (isLine) return -1;
int l = -1, r = M - 1;
while (l + 1 < r) {
int mid = (l + r) >> 1;
int rx = x, ry = y;
while (1) {
int t = TFind(R[rx], mid);
if (rx == t) break;
rx = t;
}
while (1) {
int t = TFind(R[ry], mid);
if (ry == t) break;
ry = t;
}
bool ok = (rx == ry && (TFind(T[rx], mid) || TFind(C[rx], mid)));
(ok ? r : l) = mid;
}
auto [ans, a, b] = E[r];
return ans;
}
void init(int _N, int _M, vector<int> U, vector<int> V, vector<int> W) {
N = _N, M = _M;
for (int i = 0; i < M; ++i) {
E.emplace_back(W[i], U[i], V[i]);
D[U[i]]++;
D[V[i]]++;
}
if (N == M + 1 && *max_element(D, D + MAX) <= 2) isLine = 1;
sort(E.begin(), E.end());
Clear();
for (int i = 0; i < M; ++i) {
auto [_, a, b] = E[i];
Union(a, b, i);
}
}
