#include <bits/stdc++.h>
#include "dreaming.h"
using namespace std;
#define ll long long
#define fastIO cin.tie(0); ios::sync_with_stdio(false)
unordered_map<int, vector<pair<int, int>>> adjList;
bool vis[100005];
int d1[100005];
int d2[100005];
int r11[100005];
int r12[100005];
int r2[100005];
int farthest[100005];
void dp1(vector<int> &comp, int v, int p = -1) {
comp.push_back(v);
d1[v] = 0;
int mxp1 = -1, mxp2 = -1;
for(auto i : adjList[v]) if(i.first != p) {
dp1(comp, i.first, v);
int pl = d1[i.first] + i.second;
d1[v] = max(d1[v], pl);
if(mxp1 < pl) {
mxp2 = mxp1;
mxp1 = pl;
} else if (mxp2 < pl) mxp2 = pl;
}
if(mxp2 != -1) {
d2[v] = mxp1+mxp2;
}
}
void dp2(int v, int p = -1) {
r11[v] = 0;
r12[v] = 0;
for(auto i : adjList[v]) if (i.first != p) {
dp2(i.first, v);
int pl = r11[i.first] + i.second;
if(pl > r11[v]) {
r12[v] = r11[v];
r11[v] = pl;
} else if (pl > r12[v]) r12[v] = pl;
}
}
void dp3(int v, int p = -1) {
for(auto i : adjList[v]) if (i.first != p) {
r2[i.first] = max(r11[i.first]+i.second==r11[v]?r12[v]:r11[v], r2[v]) + i.second;
dp3(i.first, v);
}
}
pair<int, int> solve(int r) {
vector<int> connComp;
dp1(connComp, r);
dp2(r);
dp3(r);
int d = 0;
int rad = INT_MAX;
for(auto i : connComp) {d = max(d, max(d1[i], d2[i])); rad = min(rad, max(r11[i], i==r?r11[i]:r2[i])); vis[i] = true;}
return make_pair(d, rad);
}
int travelTime(int N, int M, int L, int A[], int B[], int T[]) {
for(int i = 0; i < N; i++) {
vis[i] = false;
d1[i] = -1;
d2[i] = -1;
r2[i] = 0;
}
for(int i = 0; i < M; i++) {
adjList[A[i]].push_back({B[i], T[i]});
adjList[B[i]].push_back({A[i], T[i]});
}
vector<int> radii;
vector<int> diams;
int comps = 0;
for(int i = 0; i < N; i++) {
if(!vis[i]) {
pair<int, int> ans = solve(i);
diams.push_back(ans.first);
radii.push_back(ans.second);
comps++;
}
}
sort(radii.begin(), radii.end(), greater<int>());
sort(diams.begin(), diams.end(), greater<int>());
if(comps == 1) {
return diams[0];
} else if (comps == 2) {
return max(diams[0], radii[0] + radii[1] + L);
} else {
return max({diams[0], radii[0] + radii[1] + L, radii[1] + radii[2] + L + L});
}
}
