template<int SZ> struct centroidDecomp {
    int N;
    bool done[SZ];
    int sub[SZ], par[SZ], cen[SZ];
    ll ans[SZ];
    ll dist[SZ][20], tmp[SZ];
    vpi adj[SZ];

    // INITIALIZE

    void addEdge(int a, int b, int d) { adj[a].pb({b,d}), adj[b].pb({a,d}); }

    void dfs (int no) {
        sub[no] = 1;
        for (pi i: adj[no]) if (!done[i.f] && i.f != par[no]) {
            par[i.f] = no;
            dfs(i.f);
            sub[no] += sub[i.f];
        }
    }

    void genDist(int par, int no, int t, ll dis) {
        dist[no][tmp[no]++] = dis;
        for (pi i: adj[no]) if (!done[i.f] && i.f != par) {
            cen[i.f] = t;
            genDist(no,i.f,t,dis+i.s);
        }
    }

    int getCentroid(int x) {
        par[x] = -1; dfs(x);
        int sz = sub[x];
        while (1) {
            pi mx = {0,0};
            for (pi i: adj[x]) if (!done[i.f] && i.f != par[x]) mx = max(mx,{sub[i.f],i.f});
            if (mx.f*2 > sz) x = mx.s;
            else return x;
        }
    }

    void solve (int x) {
        x = getCentroid(x); done[x] = 1;
        genDist(-1,x,x,0);
        for (pi i: adj[x]) if (!done[i.f]) solve(i.f);
    }

    void init() {
        F0R(i,N) cen[i] = -1, ans[i] = INF;
        solve(0);
    }

    // QUERY

    void upd(int v, int x = 1) {
        for (int V = v, ind = tmp[v]-1; V >= 0; V = cen[V], ind --) {
            // cout << "OH " << v << " " << V << " " << x << "\n";
            if (x == 1) ans[V] = min(ans[V],dist[v][ind]);
            else ans[V] = INF;
        }
    }

    ll query(int v) {
        ll ret = INF;
        for (int V = v, ind = tmp[v]-1; V >= 0; V = cen[V], ind --) {
            // cout << "AH " << V << " " << v << "\n";
            ret = min(ret,ans[V]+dist[v][ind]);
        }
        return ret;
    }
};

centroidDecomp<MX> C;

void Init(int N, int A[], int B[], int D[]) {
    C.N = N;
    F0R(i,N-1) C.addEdge(A[i],B[i],D[i]);
    C.init();
}

long long Query(int S, int X[], int T, int Y[]) {
    ll ans = INF;
    if (S > T) {
        swap(S,T);
        swap(X,Y);
    }
    F0R(i,S) C.upd(X[i]);
    F0R(i,T) ans = min(ans,C.query(Y[i]));
    F0R(i,S) C.upd(X[i],-1);
    return ans;
}