#include "swap.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vii;
typedef pair<int,int> pi;
typedef vector<pi> pii;
typedef tuple<int,int,int> ti;
typedef vector<ll> li;
typedef vector<li> lii;
#define REP(i,a,b) for(int i=a;i<b;i++)
#define F first
#define S second
#define PB push_back
#define LSOne(s) ((s)&(-s))
ll INF=1000000000000000010;
int inf=1e9+10;
ll M=1e9+7;
int n,k,v1=1,v2=1,pos;
vii p,X,q;
vector<vector<pi>> a;
vi low,num,par,sw,cnt,d,Y;
bool flag=0;
void dfs(int x){
num[x]=v1++;
for(auto u:a[x])if(p[x][0]!=u.F){
p[u.F][0]=x;
X[u.F][0]=u.S;
dfs(u.F);
}
low[x]=v2++;
}
int parent(int x){
if(par[x]==x)return x;
else return par[x]=parent(par[x]);
}
bool merge(int x,int y,int w){
int xt=x,yt=y;
x=parent(x);
y=parent(y);
if(x==y){
par[x]=pos;
sw[pos]=1;
q[x][0]=pos;
Y[pos]=w;
pos++;
return 0;
}
par[x]=pos;par[y]=pos;
cnt[xt]++;cnt[yt]++;
q[x][0]=pos;q[y][0]=pos;
Y[pos]=w;
if(cnt[xt]>=3||cnt[yt]>=3||sw[x]||sw[y])sw[pos]=1;
pos++;
return 1;
}
void init(int N, int M,std::vector<int> U, std::vector<int> V, std::vector<int> W) {
n=N;
k=log2(n+M)+1;
low.resize(n,0);num.resize(n,0);
p.resize(n,vi(k,-1));
X.resize(n,vi(k,0));
a.resize(n);
sw.resize(N+M,0);d.resize(n+M,0);
par.resize(N+M);q.resize(N+M,vi(k,-1));Y.resize(N+M,inf);
REP(i,0,N+M)par[i]=i;
cnt.resize(n,0);
priority_queue<ti,vector<ti>,greater<ti>> pq;
REP(i,0,M)pq.push({W[i],U[i],V[i]});
pos=n;
while(!pq.empty()){
int x=get<0>(pq.top());
int y=get<1>(pq.top());
int z=get<2>(pq.top());
pq.pop();
if(merge(y,z,x)){
a[y].PB({z,x});
a[z].PB({y,x});
}
}
dfs(0);
REP(j,1,k)REP(i,0,n)if(p[i][j-1]!=-1){
p[i][j]=p[p[i][j-1]][j-1];
X[i][j]=max(X[i][j-1],X[p[i][j-1]][j-1]);
}
REP(j,1,k)REP(i,0,n+M)if(q[i][j-1]!=-1)q[i][j]=q[q[i][j-1]][j-1];
if(sw[n+M-1]==0)flag=1;
for(int i=n+M-2;i>=0;i--)d[i]=d[q[i][0]]+1;
}
bool ances(int x,int y){
if(y==-1)return 1;
if(x==-1)return 0;
return (num[y]<=num[x]&&low[y]>=low[x]);
}
int solve(int x,int y){
if(d[x]<d[y])swap(x,y);
for(int i=k-1;i>=0;i--)if(q[x][i]!=-1&&d[q[x][i]]>=d[y])x=q[x][i];
for(int i=k-1;i>=0;i--)if(q[x][i]!=q[y][i]){
x=q[x][i];
y=q[y][i];
}
x=q[x][0];
y=q[y][0];
if(sw[x])return Y[x];
for(int i=k-1;i>=0;i--)if(q[x][i]!=-1&&sw[q[x][i]]==0)x=q[x][i];
x=q[x][0];
return Y[x];
}
int getMinimumFuelCapacity(int x, int y) {
if(flag)return -1;
int ans=0,ans2=solve(x,y);
for(int i=k-1;i>=0;i--)if(!ances(y,p[x][i])){
ans=max(ans,X[x][i]);
x=p[x][i];
}
for(int i=k-1;i>=0;i--)if(!ances(x,p[y][i])){
ans=max(ans,X[y][i]);
y=p[y][i];
}
if(ances(y,x))swap(x,y);
ans=max(ans,X[x][0]);
if(!ances(x,y))ans=max(ans,X[y][0]);
return max(ans,ans2);
}
