#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
#define pb push_back
#define el "\n"
#define f first
#define s second
#pragma GCC optimize("O3")
#pragma GCC target("sse4")
typedef long long ll;
const ll MM=5e5+5, MOD=1e9+7, LOG=20, INF=1e18;
int dep[MM], sz[MM], nxt[MM], in[MM], ot[MM], head[2*MM], ct=1, chn; ll dst[MM], spc[MM], pcl[LOG][MM];
pair<int,int> st[LOG][4*MM];
bool blk[MM];
struct E {int nxt; pair<int,int> v; } e[2*MM];
void add(int u, int v, int w){
e[chn].v={v,w}; e[chn].nxt=head[u]; head[u]=chn++; }
int lg2(int x) {
return 32-__builtin_clz(x)-1; }
void df1(int u, int pa) {
dep[u]=dep[pa]+1; st[0][ct]=make_pair(dep[u], u); in[u]=ct++;
for(int i=head[u]; i!=-1; i=e[i].nxt) {
int v=e[i].v.f, w=e[i].v.s; if(v==pa) continue;
dst[v]=dst[u]+w; df1(v, u); sz[u]+=sz[v];
st[0][ct++]=make_pair(dep[u], u); }
ot[u]=ct; }
inline int qry(int l, int r) {
int lg=lg2(r-l+1);
return min(st[lg][l], st[lg][r-(1<<lg)+1]).s; }
inline int lca(int u, int v) {
if(in[u]>in[v]) return qry(in[v], in[u]);
return qry(in[u], in[v]); }
void gsz(int u, int pa) {
sz[u]=1;
for(int i=head[u]; i!=-1; i=e[i].nxt) {
int v=e[i].v.f; if(blk[v]||v==pa) continue;
gsz(v, u); sz[u]+=sz[v]; } }
int ctr(int u, int pa, int nd) {
for(int i=head[u]; i!=-1; i=e[i].nxt) {
int v=e[i].v.f; if(blk[v]||v==pa) continue;
if(sz[v]*2>nd) return ctr(v, u, nd); }
return u; }
inline ll dist(int u, int c, int id) {
if(pcl[id][u]) return pcl[id][u];
return pcl[id][u]=dst[u]+dst[c]-2LL*dst[lca(u, c)]; }
void slv(int u, int pa) {
gsz(u, -1); u=ctr(u, -1, sz[u]); blk[u]=1; nxt[u]=pa;
for(int i=head[u]; i!=-1; i=e[i].nxt) {
int v=e[i].v.f; if(!blk[v]) slv(v, u); } }
void Init(int N, int A[], int B[], int D[]) {
memset(head, -1, sizeof(head));
for(int i=0; i<N; ++i) spc[i]=INF;
for(int i=0; i<N-1; ++i) {
add(A[i], B[i], D[i]); add(B[i], A[i], D[i]); }
df1(0, 0); slv(0, -1);
for(int i=1; i<LOG; ++i)
for(int j=1; j+(1<<i)-1<=ct; ++j)
st[i][j]=min(st[i-1][j], st[i-1][j+(1<<(i-1))]); }
long long Query(int S, int X[], int T, int Y[]) {
for(int i=0, c, l=0; i<S; ++i, l=0) {
c=X[i];
while(c!=-1)
spc[c]=min(spc[c], dist(X[i], c, l)), c=nxt[c], ++l; }
long long ans=INF;
for(int i=0, c, l=0; i<T; ++i, l=0) {
c=Y[i];
while(c!=-1)
ans=min(ans, dist(Y[i], c, l)+spc[c]), c=nxt[c], ++l; }
for(int i=0, c; i<S; ++i) {
c=X[i];
while(c!=-1)
spc[c]=INF, c=nxt[c]; }
return ans;
}
