#include "factories.h"
#include<bits/stdc++.h>
using namespace std;
#define task "a"
#define se second
#define fi first
#define ll long long
#define ii pair<ll, ll>
const long mxN = 5e5 + 7;
int par[mxN][25], par_Cen[mxN], h[mxN], child[mxN];
bool del[mxN];
ll dis[mxN][25], mn[mxN];
vector<ii> w[mxN];
void Buildlog(int j)
{
for (int i = 1; i < __lg(h[j]); i++)
{
par[j][i] = par[par[j][i - 1]][i - 1];
dis[j][i] = dis[j][i - 1] + dis[par[j][i - 1]][i - 1];
}
}
void Build_LCA(int j)
{
Buildlog(j);
for (ii i : w[j])
{
if (h[i.fi])
continue;
par[i.fi][0] = j;
dis[i.fi][0] = i.se;
h[i.fi] = h[j] + 1;
Build_LCA(i.fi);
}
}
void Pre(int j, int par)
{
child[j] = 1;
for (ii i : w[j])
{
if (del[i.fi] || i.fi == par)
continue;
Pre(i.fi, j);
child[j] += child[i.fi];
}
}
int Find(int j, int sz)
{
for (ii i : w[j])
{
if (del[i.fi] || child[i.fi] > child[j])
continue;
if (child[i.fi] * 2 > sz)
return Find(i.fi, sz);
}
return j;
}
const ll inf = 1e18;
void Centroid(int j)
{
Pre(j, 0);
j = Find(j, child[j]);
mn[j] = inf;
del[j] = 1;
for (ii i : w[j])
{
if (del[i.fi])
continue;
par_Cen[i.fi] = j;
Centroid(i.fi);
}
}
void Init(int N, int A[], int B[], int D[])
{
for (int i = 0; i < N - 1; i++)
{
w[A[i]].push_back({B[i], D[i]});
w[B[i]].push_back({A[i], D[i]});
}
h[1] = 1;
Build_LCA(1);
Centroid(1);
}
ll LCA(int u, int v)
{
if (h[u] < h[v])
swap(u, v);
ll res = 0;
for (int i = 19; i >= 0; i--)
{
if (h[u] - (1 << i) >= h[v])
{
res += dis[u][i];
u = par[u][i];
}
}
if (u == v)
return res;
for (int i = 19; i >= 0; i--)
{
if (par[u][i] != par[v][i])
{
res += dis[u][i] + dis[v][i];
u = par[u][i];
v = par[v][i];
}
}
return res + dis[u][0] + dis[v][0];
}
long long Query(int S, int X[], int T, int Y[])
{
vector<int> ver;
for (int i = 0; i < S; i++)
{
int cur = X[i];
while (cur)
{
ver.push_back(cur);
mn[cur] = min(mn[cur], LCA(X[i], cur));
cur = par_Cen[cur];
}
}
ll ans = inf;
for (int i = 0; i < T; i++)
{
int cur = Y[i];
while (cur)
{
ans = min(ans, mn[cur] + LCA(Y[i], cur));
cur = par_Cen[cur];
}
}
for (int i : ver)
mn[i] = inf;
return ans;
}
//
//#include <stdlib.h>
//
//#define MAX_N 500000
//#define MAX_Q 100000
//#define MAX_SUM_ST 1000000
//#define MAX_VALUE 1000000000
//
//static int N, Q;
//static int A[MAX_N], B[MAX_N], D[MAX_N];
//static int S[MAX_N];
//static int T[MAX_N];
//static int X[MAX_SUM_ST];
//static int Y[MAX_SUM_ST];
//
//static int Qx[MAX_N];
//static int Qy[MAX_N];
//
//int main() {
// freopen("sample-in-01.txt","r",stdin);
//
// int i, j, k;
// int STop, TTop;
//
// if (2 != scanf("%d%d", &N, &Q)) {
// fprintf(stderr, "error: cannot read N and Q.\n");
// exit(1);
// }
// if (!(2 <= N && N <= MAX_N)) {
// fprintf(stderr, "error: N is out of bounds.\n");
// exit(1);
// }
// if (!(1 <= Q && Q <= MAX_Q)) {
// fprintf(stderr, "error: Q is out of bounds.\n");
// exit(1);
// }
// for (i = 0; i < N - 1; ++i) {
// if (1 != scanf("%d", &A[i])) {
// fprintf(stderr, "error: cannot read A[%d].\n", i);
// exit(1);
// }
// if (!(0 <= A[i] && A[i] <= N - 1)) {
// fprintf(stderr, "error: A[%d] is out of bounds.\n", i);
// exit(1);
// }
// if (1 != scanf("%d", &B[i])) {
// fprintf(stderr, "error: cannot read B[%d].\n", i);
// exit(1);
// }
// if (!(0 <= B[i] && B[i] <= N - 1)) {
// fprintf(stderr, "error: B[%d] is out of bounds.\n", i);
// exit(1);
// }
// if (A[i] == B[i]) {
// fprintf(stderr, "error: B[%d] is equal to A[%d].\n", i, i);
// exit(1);
// }
// if (1 != scanf("%d", &D[i])) {
// fprintf(stderr, "error: cannot read D[%d].\n", i);
// exit(1);
// }
// if (!(1 <= D[i] && D[i] <= MAX_VALUE)) {
// fprintf(stderr, "error: D[%d] is out of bounds.\n", i);
// exit(1);
// }
// }
//
// STop = 0;
// TTop = 0;
//
// for (j = 0; j < Q; ++j) {
// if (2 != scanf("%d%d", &S[j], &T[j])) {
// fprintf(stderr, "error: cannot read L[%d] and R[%d].\n", j, j);
// exit(1);
// }
//
// if(STop + S[j] > MAX_SUM_ST) {
// fprintf(stderr, "error: S[0] + S[1] + ... + S[%d] is out of bounds.\n", j);
// exit(1);
// }
//
// if(TTop + T[j] > MAX_SUM_ST) {
// fprintf(stderr, "error: T[0] + T[1] + ... + T[%d] is out of bounds.\n", j);
// exit(1);
// }
//
// for (k = 0; k < S[j]; ++k, ++STop) {
// if (1 != scanf("%d", &X[STop])) {
// fprintf(stderr, "error: cannot read X[%d][%d].\n", j, k);
// exit(1);
// }
//
// if (!(0 <= X[STop] && X[STop] <= N - 1)) {
// fprintf(stderr, "error: cannot read X[%d][%d].\n", j, k);
// exit(1);
// }
// }
//
// for (k = 0; k < T[j]; ++k, ++TTop) {
// if (1 != scanf("%d", &Y[TTop])) {
// fprintf(stderr, "error: cannot read Y[%d][%d].\n", j, k);
// exit(1);
// }
//
// if (!(0 <= Y[TTop] && Y[TTop] <= N - 1)) {
// fprintf(stderr, "error: cannot read Y[%d][%d].\n", j, k);
// exit(1);
// }
// }
// }
//
// STop = 0;
// TTop = 0;
// Init(N, A, B, D);
//
// for (j = 0; j < Q; ++j) {
// for (k = 0; k < S[j]; k++) {
// Qx[k] = X[STop++];
// }
// for (k = 0; k < T[j]; k++) {
// Qy[k] = Y[TTop++];
// }
//
// printf("%lld\n", Query(S[j], Qx, T[j], Qy));
// }
//
//
// return 0;
//}
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