#include "factories.h"
#include <iostream>
#include <queue>
#include <cassert>
#include <set>
#include <vector>
#include <algorithm>
#include <stack>
using namespace std;
typedef pair<int, int> P;
typedef pair<long long, int> P2;
#define rep(i, n) for (int i=0; i<(n); i++)
#define all(x) x.begin(), x.end()
#define uniq(x) x.erase(unique(all(x)), x.end())
#define index(x, y) (int)(lower_bound(all(x), y) - x.begin())
#define pb push_back
#define _1 first
#define _2 second
#define INF (1LL<<60)
int N;
vector<P> G[500000];
int U[19][500000];
int R[500000];
long long W[500000];
int IN[500000], OUT[500000];
int rev[500000];
vector<int> T;
vector<int> T2;
int pos[500000];
int sparseL[19][1000000], sparseR[19][1000000];
void dfs(int x, int p, int r, long long w) {
IN[x] = T.size();
rev[IN[x]] = x;
T.pb(x);
pos[x] = T2.size();
T2.pb(IN[x]);
R[x] = r, W[x] = w;
U[0][x] = p;
for (P pp : G[x]) if (pp._1 != p) {
dfs(pp._1, x, r+1, w+pp._2);
T2.pb(IN[x]);
}
OUT[x] = (int)T.size()-1;
}
inline int rmq_min(int l, int r) {
//int m = 1145141919;
//for (int i=l; i<=r; i++) m = min(m, T2[i]);
//return m;
int k = 31-__builtin_clz(r-l+1);
return min(sparseL[k][l], sparseR[k][r]);
}
int lca_orgi(int x, int y) {
if (R[x] < R[y]) swap(x, y);
for (int k=18; k>=0; k--) if ((R[x]-R[y])>>k) x = U[k][x];
if (x == y) return x;
for (int k=18; k>=0; k--) if (U[k][x] != U[k][y]) x = U[k][x], y = U[k][y];
return U[0][x];
}
inline int lca(int x, int y) {
if (x == y) return x;
if (pos[x] > pos[y]) swap(x, y);
assert(rev[rmq_min(pos[x], pos[y])] == lca_orgi(x, y));
return rev[rmq_min(pos[x], pos[y])];
}
void Init(int NN, int A[], int B[], int D[]) {
N = NN;
rep(i, N-1) {
G[A[i]].pb(P(B[i], D[i]));
G[B[i]].pb(P(A[i], D[i]));
}
dfs(0, -1, 0, 0);
rep(k, 18) rep(x, N) {
if (U[k][x] == -1) U[k+1][x] = -1;
U[k+1][x] = U[k][U[k][x]];
}
rep(i, T2.size()) sparseL[0][i] = sparseR[0][i] = T2[i];
rep(k, 18) rep(i, T2.size()) {
sparseL[k+1][i] = sparseL[k][i];
sparseR[k+1][i] = sparseR[k][i];
if (i+(1<<k) < T2.size()) sparseL[k+1][i] = min(sparseL[k+1][i], sparseL[k][i+(1<<k)]);
if (i-(1<<k) >= 0) sparseR[k+1][i] = min(sparseR[k+1][i], sparseR[k][i-(1<<k)]);
}
}
long long D[500000];
bool isT[500000];
vector<int> G2[500000];
long long sum = 0;
long long Query(int S, int X[], int T, int Y[]) {
vector<int> ps;
rep(i, S) ps.pb(IN[X[i]]);
rep(i, T) ps.pb(IN[Y[i]]);
sort(all(ps)); uniq(ps);
vector<int> new_ps(ps);
rep(i, (int)ps.size()-1) {
int v = lca(rev[ps[i]], rev[ps[i+1]]);
if (v != rev[ps[i]] && v != rev[ps[i+1]]) new_ps.pb(IN[v]);
}
sum += ps.size();
swap(new_ps, ps);
sort(all(ps)); uniq(ps);
stack<int> st;
for (int &p : ps) p = rev[p];
for (int v : ps) {
D[v] = INF;
while (!st.empty() && !(IN[st.top()] <= IN[v] && IN[v] <= OUT[st.top()])) st.pop();
if (!st.empty()) {
int p = st.top();
G2[p].pb(v);
G2[v].pb(p);
}
st.push(v);
}
rep(i, T) isT[Y[i]] = true;
priority_queue<P2, vector<P2>, greater<P2> > q;
rep(i, S) q.push(P(0, X[i])), D[X[i]] = 0;
long long ans = INF;
while (!q.empty()) {
long long r = q.top()._1;
int x = q.top()._2;
q.pop();
if (D[x] < r) continue;
if (isT[x]) {
ans = r;
break;
}
for (int t : G2[x]) {
long long len = abs(W[t]-W[x]);
if (D[t] > r+len) {
D[t] = r+len;
q.push(P2(D[t], t));
}
}
}
for (int v : ps) G2[v].clear(), G2[v].shrink_to_fit();
rep(i, T) isT[Y[i]] = false;
return ans;
}
