#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, int p)
{
Pre(j, -1);
j = Find(j, child[j]);
par_Cen[j] = p;
mn[j] = inf;
del[j] = 1;
for (ii i : w[j])
{
if (del[i.fi])
continue;
Centroid(i.fi, j);
}
}
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[0] = 1;
Build_LCA(0);
Centroid(0, -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 >= 0)
{
//cerr << X[i] << " " << cur << " " << LCA(X[i], cur) << '\n';
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 >= 0)
{
ans = min(ans, mn[cur] + LCA(Y[i], cur));
cur = par_Cen[cur];
}
}
for (int i : ver)
mn[i] = inf;
return ans;
}
