#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <complex>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <unordered_map>
#include <vector>
using namespace std;
// BEGIN NO SAD
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define trav(a, x) for(auto& a : x)
#define all(x) x.begin(), x.end()
#define sz(x) (int)(x).size()
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
typedef vector<int> vi;
#define f first
#define s second
#define derr if(0) cerr
void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ", "; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? ", " : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#define debug(x...) cerr << "\e[91m"<<__func__<<":"<<__LINE__<<" [" << #x << "] = ["; _print(x); cerr << "\e[39m" << flush;
// END NO SAD
template<class Fun>
class y_combinator_result {
Fun fun_;
public:
template<class T>
explicit y_combinator_result(T &&fun): fun_(std::forward<T>(fun)) {}
template<class ...Args>
decltype(auto) operator()(Args &&...args) {
return fun_(std::ref(*this), std::forward<Args>(args)...);
}
};
template<class Fun>
decltype(auto) y_combinator(Fun &&fun) {
return y_combinator_result<std::decay_t<Fun>>(std::forward<Fun>(fun));
}
template<class T>
bool updmin(T& a, T b) {
if(b < a) {
a = b;
return true;
}
return false;
}
template<class T>
bool updmax(T& a, T b) {
if(b > a) {
a = b;
return true;
}
return false;
}
typedef int64_t ll;
typedef pair<int, int> pii;
mt19937 g1(0x48);
ll get_random_int(ll a, ll b) {
return uniform_int_distribution<ll>(a, b)(g1);
}
struct koosaga {
vector<vector<ll>> centroidtovertexdist; // <id, depth>
vector<vector<int>> centroidtochildidx; // <id, depth>
vector<vector<int>> centroidtochildcentroid;
int n;
int rootcentroid;
ll qry(int currcentroid, int depth, vector<int>& lhs, vector<int>& rhs) {
if(sz(lhs) == 0 || sz(rhs) == 0) return 1e18;
ll ret = 1e18;
ll lv = 1e18;
ll rv = 1e18;
{
sort(all(lhs), [&](int a, int b) -> bool {
return centroidtochildidx[a][depth] < centroidtochildidx[b][depth];
});
sort(all(rhs), [&](int a, int b) -> bool {
return centroidtochildidx[a][depth] < centroidtochildidx[b][depth];
});
}
int li = 0, ri = 0;
if(lhs[li] == currcentroid) lv = 0, li++;
if(rhs[ri] == currcentroid) rv = 0, ri++;
while(li < sz(lhs) || ri < sz(rhs)) {
int choice = 1e9;
if(li < sz(lhs)) updmin(choice, centroidtochildidx[lhs[li]][depth]);
if(ri < sz(rhs)) updmin(choice, centroidtochildidx[rhs[ri]][depth]);
assert(choice >= 0);
int nli = li;
vector<int> nlv, nrv;
while(nli < sz(lhs) && centroidtochildidx[lhs[nli]][depth] == choice) {
nlv.pb(lhs[nli]);
updmin(lv, centroidtovertexdist[lhs[nli++]][depth]);
}
int nri = ri;
while(nri < sz(rhs) && centroidtochildidx[rhs[nri]][depth] == choice) {
nrv.pb(rhs[nri]);
updmin(rv, centroidtovertexdist[rhs[nri++]][depth]);
}
updmin(ret, qry(centroidtochildcentroid[currcentroid][choice], depth+1, nlv, nrv));
li = nli;
ri = nri;
}
return min(lv+rv, ret);
}
koosaga(){}
koosaga(vector<array<int, 3>>& e) {
n = sz(e) + 1;
vector<int> nxtid(2*n-2, -1);
vector<int> startid(n, -1);
vector<int> to(2*n-2, -1);
vector<int> weights(2*n-2);
for(int i = 0; i < sz(e); i++) {
auto [a, b, w] = e[i];
to[2*i] = b;
weights[2*i] = w;
nxtid[2*i] = startid[a];
startid[a] = 2*i;
to[2*i+1] = a;
weights[2*i+1] = w;
nxtid[2*i+1] = startid[b];
startid[b] = 2*i+1;
}
centroidtovertexdist.resize(n);
centroidtochildidx.resize(n);
centroidtochildcentroid.resize(n);
rootcentroid = -1;
vector<int> seen(n);
vector<int> par(n);
vector<int> treesz(n);
vector<bool> processed(n);
int centroiditer = 0;
vector<int> postorder(n);
vector<array<ll, 3>> q(n);
auto init = y_combinator([&](auto initself, const int srcv) -> int {
assert(!processed[srcv]);
auto getcentroid = [&]() -> int {
seen[srcv] = centroiditer++;
int ql = 0;
int qr = 0;
postorder[qr++] = srcv;
while(ql < qr) {
int curr = postorder[ql++];
treesz[curr] = 1;
for(int id = startid[curr]; id >= 0; id = nxtid[id]) {
int nv = to[id];
if(!processed[nv] && seen[nv] != centroiditer) {
seen[nv] = centroiditer;
par[nv] = curr;
postorder[qr++] = nv;
}
}
}
int totnodes = qr;
for(int i = qr-1; i > 0; i--) {
treesz[par[postorder[i]]] += treesz[postorder[i]];
if(2*treesz[postorder[i]] >= totnodes) return postorder[i];
}
return srcv;
};
int centroid = getcentroid();
centroidtochildidx[centroid].pb(-1);
int childidx = 0;
{
int ql = 0;
int qr = 0;
q[qr++] = {centroid, 0, -1};
while(ql < qr) {
auto [v, w, p] = q[ql++];
centroidtovertexdist[v].pb(w);
if(p == centroid) centroidtochildidx[v].pb(childidx++);
else if(p >= 0) centroidtochildidx[v].pb(centroidtochildidx[p].back());
for(int id = startid[v]; id >= 0; id = nxtid[id]) {
int nv = to[id];
int nw = weights[id];
if(processed[nv] || nv == p) continue;
q[qr++] = {nv, w+nw, v};
}
}
}
processed[centroid] = true;
for(int id = startid[centroid]; id >= 0; id = nxtid[id]) {
int nv = to[id];
if(processed[nv]) continue;
centroidtochildcentroid[centroid].pb(initself(nv));
}
return centroid;
});
rootcentroid = init(get_random_int(0, n-1));
}
};
koosaga koo;
void Init(int N, int A[], int B[], int D[]){
vector<array<int, 3>> edges(N-1);
for(int i = 0; i < N-1; i++) edges[i] = {A[i], B[i], D[i]};
koo = koosaga(edges);
}
long long Query(int S, int X[], int T, int Y[]){
vector<int> lhs(S), rhs(T);
for(int i = 0; i < S; i++) lhs[i] = X[i];
for(int i = 0; i < T; i++) rhs[i] = Y[i];
return koo.qry(koo.rootcentroid, 0, lhs, rhs);
}
/*
void solve() {
int n, q;
cin >> n >> q;
int *A = (int*)malloc(sizeof(int) * (n - 1));
int *B = (int*)malloc(sizeof(int) * (n - 1));
int *D = (int*)malloc(sizeof(int) * (n - 1));
for(int a = 0; a < n - 1; a++){
cin >> A[a] >> B[a] >> D[a];
}
Init(n, A, B, D);
while(q--) {
int S, T;
cin >> S >> T;
int *X = (int*)malloc(sizeof(int) * S);
int *Y = (int*)malloc(sizeof(int) * T);
for(int b = 0; b < S; b++) cin >> X[b];
for(int b = 0; b < T; b++) cin >> Y[b];
cout << Query(S, X, T, Y) << "\n";
}
}
// what would chika do
// are there edge cases (N=1?)
// are array sizes proper (scaled by proper constant, for example 2* for koosaga tree)
// integer overflow?
// DS reset properly between test cases
// are you doing geometry in floating points
// are you not using modint when you should
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
solve();
}
*/
