#include "swap.h"
#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <bitset>
#include <math.h>
#include <iomanip>
#define rep(i, s, e) for (ll i = s; i < e; i++)
#define upmax(a, b) a = max(a, b)
#define upmin(a, b) a = min(a, b)
using namespace std;
using ll = long long;
using vll = vector<ll>;
using vvll = vector<vll>;
using pll = pair<ll, ll>;
using vpll = vector<pll>;
using vvpll = vector<vpll>;
const ll INF = 2e18;
const ll MOD = 1e9 + 7;
ll n, m;
vvpll g;
vvll dp;
vll deg;
vector<pair<ll, pll>> edges;
struct DSU {
vll papa, sz, swappable;
DSU(ll n) {
papa.resize(n), sz.resize(n, 1);
swappable.resize(n, 0);
for (ll i = 0; i < n; i++) papa[i] = i;
}
ll find(ll i) {
if (papa[i] == i) return i;
papa[i] = find(papa[i]);
return papa[i];
}
bool unite(ll a, ll b) {
bool is_swappable = false;
a = find(a);
b = find(b);
is_swappable = (swappable[a] || swappable[b]);
if (a == b) {
swappable[a] = true;
return false;
}
if (sz[a] < sz[b]) swap(a, b);
sz[a] += sz[b];
papa[b] = a;
if (deg[a] == 3 || deg[b] == 3) {
is_swappable = true;
}
swappable[a] = is_swappable;
return true;
}
};
void dijkstra(ll x, ll y) {
dp.clear();
dp.resize(n, vll(n, INF));
dp[x][y] = 0;
priority_queue<pair<ll, pll>, vector<pair<ll, pll>>, greater<pair<ll, pll>>> pq;
pq.push({ 0, {x, y} });
while (!pq.empty()) {
ll cur_x = pq.top().second.first;
ll cur_y = pq.top().second.second;
ll max_edge = pq.top().first;
pq.pop();
for (auto& it : g[cur_x]) {
ll next_x = it.first;
ll w = it.second;
if (next_x == cur_y) continue;
if (max(w, max_edge) < dp[next_x][cur_y]) {
dp[next_x][cur_y] = max(w, max_edge);
pq.push({ dp[next_x][cur_y], {next_x, cur_y} });
}
}
for (auto& it : g[cur_y]) {
ll next_y = it.first;
ll w = it.second;
if (next_y == cur_x) continue;
if (max(w, max_edge) < dp[cur_x][next_y]) {
dp[cur_x][next_y] = max(w, max_edge);
pq.push({ dp[cur_x][next_y], {cur_x, next_y} });
}
}
}
}
void init(int N, int M, vector<int> U, vector<int> V, vector<int> W) {
n = N, m = M;
g.clear(), g.resize(n);
deg.clear(), deg.resize(n);
edges.clear();
rep(i, 0, m) {
g[U[i]].push_back({ V[i], W[i] });
g[V[i]].push_back({ U[i], W[i] });
edges.push_back({ W[i], {U[i], V[i]} });
}
sort(edges.begin(), edges.end());
}
int getMinimumFuelCapacity(int X, int Y) {
ll x = X, y = Y;
DSU dsu(n);
rep(i, 0, m) {
ll w = edges[i].first;
ll a = edges[i].second.first;
ll b = edges[i].second.second;
dsu.unite(a, b);
ll root_x = dsu.find(x);
ll root_y = dsu.find(y);
if (root_x == root_y && dsu.swappable[root_x]) {
return w;
}
}
return -1;
dijkstra(x, y);
if (dp[y][x] == INF) return -1;
return dp[y][x];
}
/*
5 4
0 1 3
0 2 10
0 3 5
0 4 4
8
0 1
0 2
0 3
0 4
1 2
1 3
1 4
2 3
3 3
0 1 1
1 2 2
2 0 3
3
0 1
0 2
1 2
4 3
0 1 1
1 2 2
2 3 1
3
0 1
0 2
1 2
5 6
0 1 4
0 2 4
1 2 1
1 3 2
1 4 10
2 3 3
3
1 2
2 4
0 1
*/
