#include "swap.h"
#include "bits/stdc++.h"
#define MAXN 300009
#define INF 1000000007
#define mp(x,y) make_pair(x,y)
#define all(v) v.begin(),v.end()
#define pb(x) push_back(x)
#define wr cout<<"----------------"<<endl;
#define ppb() pop_back()
#define tr(ii,c) for(__typeof((c).begin()) ii=(c).begin();ii!=(c).end();ii++)
#define ff first
#define ss second
#define my_little_dodge 46
#define debug(x) cerr<< #x <<" = "<< x<<endl;
using namespace std;
typedef long long ll;
typedef pair<int,int> PII;
template<class T>bool umin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
template<class T>bool umax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
vector<int>u,v,w,ind;
int m,n;
int ata[MAXN],bad[MAXN],deg[MAXN];
int tap(int x){
if(ata[x]==x)return x;
return ata[x]=tap(ata[x]);
}
bool cmp(int x,int y){
return (w[x]<w[y]);
}
const int LOG=19;
int lvl[MAXN],P[MAXN][LOG];
vector<int>adj[MAXN];
PII arr[MAXN];
void add(int x,int y){
P[y][0]=x;adj[x].pb(y);
//cerr<<x<<"->"<<y<<endl;
}
void merge(int x,int y,int val){
deg[x]++;deg[y]++;
int so=(max(deg[x],deg[y])>=3);
//printf("HI %d %d %d\n",x,y,val);
x=tap(x);y=tap(y);
if(x==y)
bad[n]=1,ata[x]=n,add(n,x);
else{
add(n,x);add(n,y);
ata[y]=ata[x]=n;
bad[n]=bad[x]|bad[y]|so;
}
//printf("%d %d\n",val,bad[n]);
arr[n++]=mp(val,bad[n]);
}
void dfs(int nd){tr(it,adj[nd])lvl[*it]=lvl[nd]+1,dfs(*it);}
void init(int N, int M,vector<int>U,vector<int> V,vector<int> W) {
u=U;v=V;w=W;m=M;n=N;
for(int i=0;i<m;i++)ind.pb(i);
sort(all(ind),cmp);
for(int i=0;i<m+n;i++)ata[i]=i;
for(int i=0;i<m;i++)
merge(u[ind[i]],v[ind[i]],w[ind[i]]);
for(int j=1;j<LOG;j++)
for(int i=0;i<n;i++)
if(P[i][j-1])
P[i][j]=P[P[i][j-1]][j-1];
dfs(n-1);
}
int getMinimumFuelCapacity(int x, int y){
if(lvl[x]<lvl[y])swap(x,y);
for(int j=LOG-1;j>=0;j--)
if(P[x][j] and lvl[P[x][j]]>=lvl[y])
x=P[x][j];
for(int j=LOG-1;j>=0;j--)
if(P[x][j] and P[x][j]!=P[y][j])
x=P[x][j],y=P[y][j];
x=P[x][0];
if(arr[x].ss)return arr[x].ff;
for(int j=LOG-1;j>=0;j--)
if(P[x][j] and !arr[P[x][j]].ss)
x=P[x][j];
x=P[x][0];
if(!x)return -1;
return arr[x].ff;
}
