#include "dreaming.h"
#include <bits/stdc++.h>
using namespace std;
const int INF = 0x3f3f3f3f;
int cur_cc = 0;
vector< vector< pair<int, int> > > g;
vector<int> cc, d, mn, mx, diameter;
void dfs1(int u, int p) {
cc[u] = cur_cc;
for (auto& v : g[u]) {
if (v.first != p) {
d[v.first] = d[u] + v.second;
dfs1(v.first, u);
}
}
mx[u] = d[u];
vector<int> tmp = {0, 0};
for (auto& v : g[u]) {
mx[u] = max(mx[u], mx[v.first]);
tmp.push_back(mx[v.first]);
}
sort(tmp.rbegin(), tmp.rend());
diameter[cc[u]] = max(diameter[cc[u]], tmp[0] + tmp[1] - 2 * d[u]);
}
void dfs2(int u, int p, int len) {
multiset<int> st;
for (auto& v : g[u]) {
if (v.first != p) {
st.insert(mx[v.first]);
}
}
for (auto& v : g[u]) {
if (v.first != p) {
st.erase(mx[v.first]);
dfs2(v.first, u, max(len, (st.empty() ? 0 : *st.rbegin() - d[u])) + v.second);
st.insert(mx[v.first]);
}
}
mn[cc[u]] = min(mn[cc[u]], max(len, mx[u] - d[u]));
}
int travelTime(int N, int M, int L, int A[], int B[], int T[]) {
g.resize(N);
for (int i = 0; i < M; i++) g[A[i]].push_back({B[i], T[i]});
for (int i = 0; i < M; i++) g[B[i]].push_back({A[i], T[i]});
d.assign(N, 0);
cc.assign(N, -1);
mx.resize(N);
for (int i = 0; i < N; i++) {
if (cc[i] == -1) {
diameter.push_back(0);
dfs1(i, -1);
cur_cc++;
}
}
mn.assign(cur_cc, INF);
for (int i = 0; i < N; i++) {
if (mn[cc[i]] == INF) dfs2(i, -1, 0);
}
sort(mn.begin(), mn.end());
int tmp = *max_element(diameter.begin(), diameter.end());
if (cur_cc == 1) return tmp;
if (cur_cc == 2) return max(tmp, mn[0] + mn[1] + L);
return max({tmp, mn[cur_cc - 2] + mn[cur_cc - 3] + 2 * L, mn[cur_cc - 1] + mn[cur_cc - 2] + L});
}
