#include "factories.h"
#include <bits/stdc++.h>
using namespace std;
#define name "code"
#define MAXN 1000006
#define pb push_back
#define pf push_front
#define ll long long
#define ii pair<int, int>
#define fs first
#define sc second
#define ill pair<int, ll>
#define lli pair<ll, int>
#define llll pair<ll, ll>
#define all(v) v.begin(),v.end()
#define uni(v) v.erase(unique(all(v)),v.end())
#define bit(n,i) (((n)>>(i))&1)
#define FOR(i,a,b) for (int i=(a),_b=(b); i<=_b; i++)
#define FORD(i,a,b) for (int i=(a),_b=(b); i>=_b; i--)
#define MASK(i) (1LL<<(i))
const ll INF=1e18;
const int MOD=1e9+7;
void add(int &u, int v){
u+=v;
if (u>=MOD) u-=MOD;
}
void sub(int &u, int v){
u-=v;
if (u<0) u+=MOD;
}
void minimize(ll &u, ll v){
u=min(u,v);
}
void maximize(int &u, int v){
u=max(u,v);
}
long long Rand(long long l, long long r){
ll tmp=0;
FOR(i,1,4) tmp=((tmp<<15)^(((1<<15)-1)&rand()));
return l+tmp%(r-l+1);
}
vector<ii> adj[MAXN];
int times,timesDFS;
ii cnt[MAXN];
int in[MAXN],depth[MAXN];
int order[MAXN];
ll d[MAXN];
bool check_ancestor(int u, int v){
return cnt[u].fs<=cnt[v].fs&&cnt[v].fs<=cnt[u].sc;
}
int MIN(int u, int v){
return (depth[u]<depth[v]?u:v);
}
void dfs0(int u, int p){
cnt[u].fs=++times;
order[++timesDFS]=u;
in[u]=timesDFS;
for (ii pairs:adj[u]){
int v=pairs.fs,w=pairs.sc;
if (v==p) continue;
d[v]=d[u]+1LL*w;
depth[v]=depth[u]+1;
dfs0(v,u);
order[++timesDFS]=u;
}
cnt[u].sc=times;
}
const int LOG=19;
int rmq[LOG+1][MAXN],lg[MAXN];
int get_min(int u, int v){
int x=lg[v-u+1];
return MIN(rmq[x][u],rmq[x][v-MASK(x)+1]);
}
int lca(int u, int v){
if (in[u]>in[v]) swap(u,v);
return get_min(in[u],in[v]);
}
void Init(int n, int a[], int b[], int c[]){
FOR(i,1,n) adj[i].clear();
FOR(i,0,n-2){
int x=a[i];
int y=b[i];
int z=c[i];
++x;
++y;
adj[x].pb({y,z});
adj[y].pb({x,z});
}
times=0,timesDFS=0;
dfs0(1,0);
FOR(i,1,timesDFS) rmq[0][i]=order[i];
FOR(j,1,LOG) FOR(i,1,timesDFS-MASK(j)+1) rmq[j][i]=MIN(rmq[j-1][i],rmq[j-1][i+MASK(j-1)]);
FOR(i,2,timesDFS) lg[i]=lg[(int)i/2]+1;
}
bool cmp(int x, int y){
return cnt[x].fs<cnt[y].fs;
}
vector<ill> g[MAXN];
int color[MAXN];
ll h[2][MAXN];
ll k[2][MAXN];
ll f[2][MAXN][3];
void dfs(int u, int p, int c){
if (bit(color[u],c)) h[c][u]=0;
else h[c][u]=INF;
FOR(j,0,1) f[c][u][j]=INF;
for (ill pairs:g[u]){
int v=pairs.fs;
ll w=pairs.sc;
if (v==p) continue;
dfs(v,u,c);
minimize(h[c][u],h[c][v]+w);
int j=2;
f[c][u][j]=h[c][v]+w;
while (j>=1&&f[c][u][j]<f[c][u][j-1]){
swap(f[c][u][j],f[c][u][j-1]);
--j;
}
}
}
void dfs_dp(int u, int p, int c){
k[c][u]=INF;
for (ill pairs:g[u]){
int v=pairs.fs;
ll w=pairs.sc;
if (v==p) continue;
minimize(k[c][v],k[c][u]+w);
if (f[c][u][0]==h[c][v]+w){
minimize(k[c][v],f[c][u][1]+w);
}
else minimize(k[c][v],f[c][u][0]+w);
dfs_dp(v,u,c);
}
}
long long query(int s, int x[], int t, int y[]){
vector<int> nodes;
FOR(i,0,s-1){
int u=x[i];
nodes.pb(++u);
color[u]|=MASK(0);
}
FOR(i,0,t-1){
int u=y[i];
nodes.pb(++u);
color[u]|=MASK(1);
}
sort(all(nodes),cmp);
uni(nodes);
FOR(i,0,(int)nodes.size()-2) nodes.pb(lca(nodes[i],nodes[i+1]));
sort(all(nodes),cmp);
uni(nodes);
stack<int> st;
st.push(nodes[0]);
FOR(i,1,(int)nodes.size()-1){
while (!check_ancestor(st.top(),nodes[i])) st.pop();
ll dist=d[nodes[i]]-d[st.top()];
g[st.top()].pb({nodes[i],dist});
g[nodes[i]].pb({st.top(),dist});
st.push(nodes[i]);
}
FOR(j,0,1) dfs(nodes[0],-1,j);
FOR(j,0,1) dfs_dp(nodes[0],-1,j);
ll res=INF;
for (int u:nodes) minimize(res,min(h[0][u],k[0][u])+min(h[1][u],k[1][u]));
for (int u:nodes){
g[u].clear();
color[u]=0;
}
return res;
}
