#include "swap.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ii pair<ll,ll>
#define iii pair<ll,ii>
#define fi first
#define se second
#define rep(x,s,e) for (auto x=s-(s>e);x!=e-(s>e);(s<e?x++:x--))
#define sz(x) (int)(x).size()
#define all(x) (x).begin(),(x).end()
const int INF=1e9+100;
int n,m;
vector<ii> al[100005];
vector<iii> edges,loop;
int p[200005]; //ufds
int find(int i){
if (i==p[i]) return i;
else return p[i]=find(p[i]);
}
ll w[200005]; //weight of kruskal tree
ll extra[200005]; //extra stuff (fork, loop)
int pa[200005][20]; //2k decomp on kruskal tree
int d[200005]; //depth for lca query
vector<int> child[200005]; //stupid al
int IDX;
int mov(int i,int k){
rep(x,0,20) if (k&(1<<x)) {
i=pa[i][x];
}
return i;
}
int lca(int i,int j){
if (d[i]<d[j]) swap(i,j);
i=mov(i,d[i]-d[j]);
if (i==j) return i;
rep(x,20,0){
if (pa[i][x]!=pa[j][x]){
i=pa[i][x];
j=pa[j][x];
}
}
return pa[i][0];
}
void init(int N, int M,
std::vector<int> U, std::vector<int> V, std::vector<int> W) {
rep(x,0,200005) p[x]=x;
memset(pa,-1,sizeof(pa));
memset(extra,63,sizeof(extra));
n=N,m=M;
rep(x,0,m){
al[U[x]].push_back(ii(V[x],W[x]));
al[V[x]].push_back(ii(U[x],W[x]));
edges.push_back(iii(W[x],ii(V[x],U[x])));
}
rep(x,0,n){
vector<int> temp;
for (auto &it:al[x]) temp.push_back(it.se);
sort(all(temp));
if (sz(temp)>=3) extra[x]=temp[2];
}
IDX=n;
sort(all(edges));
for (auto &it:edges){
int u=find(it.se.fi),v=find(it.se.se);
if (u==v){
loop.push_back(it);
continue;
}
w[IDX]=it.fi;
p[u]=p[v]=IDX;
child[IDX].push_back(u);
child[IDX].push_back(v);
IDX++;
}
rep(node,IDX,0){
for (auto &it:child[node]){
d[it]=d[node]+1;
int curr=pa[it][0]=node;
rep(x,0,20){
if (curr==-1) break;
curr=pa[it][x+1]=pa[curr][x];
}
}
}
for (auto &it:loop){
int temp=lca(it.se.se,it.se.se);
extra[temp]=min(extra[temp],it.fi);
}
rep(x,0,IDX){
for (auto &it:child[x]){
extra[x]=min(extra[x],extra[it]);
}
w[x]=max(w[x],extra[x]);
}
rep(x,IDX,0){
for (auto &it:child[x]){
w[it]=min(w[it],w[x]);
}
}
}
int getMinimumFuelCapacity(int u, int v) {
if (w[IDX-1]>=INF) return -1;
u=lca(u,v);
if (w[u]!=INF) return w[u];
return w[pa[u][0]];
}
