#include "dreaming.h"
#include <bits/stdc++.h>
using namespace std;
typedef pair<int,int> P;
#define PB push_back
#define F first
#define S second
#define INF 1000000001
int n,m,dp[100005];
vector<P>g[100005];
bool vis[100005];
void dfs1(int v,int p){
vis[v]=true;
dp[v]=0;
for(int i=0;i<g[v].size();i++){
int u=g[v][i].F,c=g[v][i].S;
if(u==p)continue;
dfs1(u,v);
dp[v]=max(dp[v],dp[u]+c);
}
}
int dfs2(int v,int p,int x){
int l[g[v].size()],r[g[v].size()];
for(int i=0;i<g[v].size();i++)l[i]=0,r[i]=0;
for(int i=0;i<g[v].size();i++){
int u=g[v][i].F,c=g[v][i].S;
if(u==p){
dp[v]=max(dp[v],x+c);
l[i]=x+c,r[i]=x+c;
}else l[i]=dp[u]+c,r[i]=dp[u]+c;
}
int res=dp[v];
for(int i=1;i<g[v].size();i++)l[i]=max(l[i],l[i-1]);
for(int i=g[v].size()-1;i>0;i--)r[i-1]=max(r[i-1],r[i]);
for(int i=0;i<g[v].size();i++){
int u=g[v][i].F;
if(u==p)continue;
int c=0;
if(i>0)c=max(c,l[i-1]);
if(i+1<g[v].size())c=max(c,r[i+1]);
res=min(res,dfs2(u,v,c));
}
return res;
}
int travelTime(int N, int M, int L, int A[], int B[], int T[]) {
n=N,m=M;
for(int i=0;i<m;i++){
g[A[i]].PB(P(B[i],T[i]));
g[B[i]].PB(P(A[i],T[i]));
}
vector<int>p;
for(int i=n-1;i>=0;i--){
if(!vis[i]){
dfs1(i,-1);
p.PB(dfs2(i,-1,0));
}
}
sort(p.begin(),p.end(),greater<int>());
for(int i=1;i<p.size();i++)p[i]+=L;
p.PB(0);
sort(p.begin(),p.end(),greater<int>());
return p[0]+p[1];
}
