#include "swap.h"
#include <bits/stdc++.h>
using namespace std;
int p[100001], pweight[100001][20], st[100001], en[100001], lineWeight[100001][20], twok[100001][20];
void init(int N){
iota(p, p+N, 0);
iota(st, st+N, 0);
iota(en, en+N, 0);
for (int i = 0; i < N; i++) lineWeight[i][0] = 2e9;
memset(twok, -1, sizeof twok);
memset(pweight, -1, sizeof pweight);
}
int fs(int x){
if (p[x] == x) return x;
return p[x] = fs(p[x]);
}
void ms(int x, int y, int w){
int px = fs(x), py = fs(y);
if (px == py){
st[px] = en[px] = -1;
lineWeight[px][0] = min(lineWeight[px][0], w);
return;
}
p[py] = px; // px -> py
//cout << px << ' ' << py << ' ' << w << endl;
twok[py][0] = px;
pweight[py][0] = w;
if (st[px] != -1 && st[py] != -1){
if ((st[px] == x || en[px] == x) && (st[py] == y || en[py] == y)){
st[px] = (st[px] == x ? en[px] : st[px]);
en[px] = (st[py] == y ? en[py] : st[py]);
} else {
st[px] = en[px] = -1;
lineWeight[px][0] = min(lineWeight[px][0], w);
}
} else if (st[px] != -1){
st[px] = en[px] = -1;
lineWeight[px][0] = w;
} else {
lineWeight[px][0] = min(lineWeight[px][0], lineWeight[py][0]);
}
}
void init(int N, int M,
std::vector<int> U, std::vector<int> V, std::vector<int> W) {
init(N);
vector<tuple<int, int, int>> edges;
for (int i = 0; i < M; i++){
edges.push_back({W[i], U[i], V[i]});
}
sort(edges.begin(), edges.end());
for (auto [w, a, b] : edges){
ms(a, b, w);
}
for (int i = 1; i <= 19; i++){
for (int j = 0; j < N; j++){
if (twok[j][i-1] != -1){
twok[j][i] = twok[twok[j][i-1]][i-1];
pweight[j][i] = max(pweight[j][i-1], pweight[twok[j][i-1]][i-1]);
lineWeight[j][i] = max(lineWeight[j][i-1], lineWeight[twok[j][i-1]][i-1]);
}
}
}
}
bool isOkay(int mid, int X, int Y){
int w = 0;
for (int i = 19; i >= 0; i--){
if (twok[X][i] != -1 && pweight[X][i] <= mid) {w = max(w, lineWeight[X][i]); X = twok[X][i];}
if (twok[Y][i] != -1 && pweight[Y][i] <= mid) {w = max(w, lineWeight[Y][i]); Y = twok[Y][i];}
}
if (X != Y) return false;
//cout << mid << ' ' << min(lineWeight[X][0], w) << endl;
return max(lineWeight[X][0], w) <= mid;
}
int getMinimumFuelCapacity(int X, int Y) {
int mini = 0, maxi = 1e9+10;
while (maxi - mini > 1){
int mid = (maxi + mini) / 2;
if (isOkay(mid, X, Y)) maxi = mid;
else mini = mid;
}
return (maxi==1e9+10?-1:maxi);
}
