#include "dreaming.h"
#include <bits/stdc++.h>
using namespace std;
#define FOR(i, a, b) for(int i = a; i <= b; i++)
inline bool maximize(int &u, int v){
return v > u ? u = v, true : false;
}
inline bool minimize(int &u, int v){
return v < u ? u = v, true : false;
}
const int maxN = 1e5 + 5;
int n, m, l;
vector<pair<int, int>> adj[maxN];
int cnt;
bool visited[maxN];
int mx1[maxN], out[maxN], mx2[maxN];
int root[maxN], sz[maxN];
int maxBranch[maxN];
int find_root(int v){
return root[v] = root[v] == v ? v : find_root(root[v]);
}
bool union_set(int u, int v){
u = find_root(u);
v = find_root(v);
if(u == v) return false;
if(sz[u] < sz[v])swap(u, v);
sz[u] += sz[v];
root[v] = u;
return true;
}
void dfs(int u){
visited[u] = true;
// cout << u << "\n";
for(auto[v, w] : adj[u]){
if(visited[v])continue;
dfs(v);
if(mx1[v] + w > mx1[u]){
mx2[u] = mx1[u];
mx1[u] = mx1[v] + w;
}else maximize(mx2[u], mx1[v] + w);
}
}
void dfs2(int u){
visited[u] = true;
for(auto[v, w] : adj[u]){
if(visited[v])continue;
out[v] = out[u] + w;
if(mx1[v] + w == mx1[u])maximize(out[v], mx2[u] + w);
else maximize(out[v], mx1[u] + w);
dfs2(v);
}
}
int travelTime(int N, int M, int L, int A[], int B[], int T[]){
n = N;
m = M;
l = L;
FOR(i, 0, n - 1)root[i] = i, sz[i] = 1;
FOR(i, 0, m - 1){
int u = A[i];
int v = B[i];
int w = T[i];
adj[u].emplace_back(v, w);
adj[v].emplace_back(u, w);
union_set(u, v);
}
FOR(i, 0, n - 1){
if(!visited[i]){
dfs(i);
}
}
FOR(i, 0, n - 1)visited[i] = false;
FOR(i, 0, n - 1){
if(!visited[i]){
dfs2(i);
}
}
int ans = 0;
FOR(i, 0, n - 1){
maximize(ans, max(mx1[i] + mx2[i], mx1[i] + out[i]));
}
vector<int> res;
FOR(i, 0, n - 1)maxBranch[i] = 1e9;
FOR(i, 0, n - 1)minimize(maxBranch[find_root(i)], max(mx1[i], out[i]));
FOR(i, 0, n - 1)if(i == find_root(i))res.emplace_back(maxBranch[i]);
sort(res.begin(), res.end());
reverse(res.begin(), res.end());
if(res.size() == 1){
return ans;
}else if(res.size() == 2){
return max(ans, res[0] + res[1] + l);
}else{
ans = max(ans, res[0] + res[1] + l);
ans = max(ans, res[1] + res[2] + 2 * l);
return ans;
}
}
