#include "dreaming.h"
#include <bits/stdc++.h>
using namespace std;
#define name "dreaming"
#define MAXN 100005
#define pb push_back
#define pf push_front
#define ll long long
#define ii pair<int, int>
#define fs first
#define sc second
#define ill pair<int, ll>
#define lli pair<ll, int>
#define llll pair<ll, ll>
#define all(v) v.begin(),v.end()
#define uni(v) v.erase(unique(all(v)),v.end())
#define bit(n,i) (((n)>>(i))&1)
#define FOR(i,a,b) for (int i=(a),_b=(b); i<=_b; i++)
#define FORD(i,a,b) for (int i=(a),_b=(b); i>=_b; i--)
#define MASK(i) (1LL<<(i))
const int INF=1e9;
const int MOD=1e9+7;
void add(int &u, int v){
u+=v;
if (u>=MOD) u-=MOD;
}
void sub(int &u, int v){
u-=v;
if (u<0) u+=MOD;
}
void minimize(int &u, int v){
u=min(u,v);
}
void maximize(ll &u, ll v){
u=max(u,v);
}
long long Rand(long long l, long long r){
ll tmp=0;
FOR(i,1,4) tmp=((tmp<<15)^(((1<<15)-1)&rand()));
return l+tmp%(r-l+1);
}
llll Max[MAXN],res[MAXN];
vector<ii> adj[MAXN];
ll depth[MAXN],high[MAXN];
bool visited[MAXN];
vector<ii> vec;
void dfs0(int u, int p){
visited[u]=1;
Max[u]={0LL,0LL};
for (ii pairs:adj[u]){
int v=pairs.fs;
int w=pairs.sc;
if (v==p) continue;
dfs0(v,u);
maximize(high[u],high[v]+1LL*w);
if (high[v]+1LL*w>=Max[u].fs){
Max[u].sc=Max[u].fs;
Max[u].fs=high[v]+1LL*w;
}
else maximize(Max[u].sc,high[v]+1LL*w);
}
}
ll diam;
void dfs1(int u, int p){
res[u]=Max[u];
if (depth[u]>res[u].fs){
res[u].sc=res[u].fs;
res[u].fs=depth[u];
}
if (res[u].fs+res[u].sc>diam){
diam=res[u].fs+res[u].sc;
vec.back()=res[u];
}
else if (res[u].fs+res[u].sc==diam){
if (vec.back().fs>res[u].fs) vec.back()=res[u];
}
else maximize(res[u].sc,depth[u]);
for (ii pairs:adj[u]){
int v=pairs.fs;
int w=pairs.sc;
if (v==p) continue;
if (Max[u].fs==Max[v].fs+1LL*w){
depth[v]=max(depth[u],Max[u].sc)+1LL*w;
}
else{
depth[v]=max(depth[u],Max[u].fs)+1LL*w;
}
dfs1(v,u);
}
}
int travelTime(int N, int M, int L, int A[], int B[], int T[]){
FOR(i,1,M){
int x=A[i-1],y=B[i-1],w=T[i-1];
++x;
++y;
adj[x].pb({y,w});
adj[y].pb({x,w});
}
FOR(i,1,N) if (!visited[i]){
dfs0(i,0);
diam=0;
vec.emplace_back();
dfs1(i,0);
}
llll cur=vec.back();
vec.pop_back();
while (vec.size()){
llll tmp=vec.back();
vec.pop_back();
if (cur.fs+tmp.fs+1LL*L>max(cur.fs+cur.sc,tmp.fs+tmp.sc)){
if (cur.fs<tmp.fs){
cur.fs+=1LL*L;
cur.sc=tmp.fs;
}
else cur.sc=tmp.fs+1LL*L;
if (cur.fs<cur.sc) swap(cur.fs,cur.sc);
}
else{
if (cur.fs+cur.sc<tmp.fs+tmp.sc){
cur=tmp;
}
}
}
return cur.fs+cur.sc;
}
