#include <bits/stdc++.h>
#include "factories.h"
#define fi first
#define se second
#define pb push_back
#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 FORLL(i, a, b) for (ll i = a, _b = b; i <= _b; ++i)
#define FORDLL(i, a, b) for (ll i = a, _b = b; i >= _b; --i)
#define all(x) x.begin(), x.end()
#define uni(x) sort(all(x)), x.erase(unique(all(x)), x.end())
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define dbg(...) debug(#__VA_ARGS__, __VA_ARGS__)
template<typename T>
void __print_one(const char *&s, const T &x)
{
while (*s == ' ') ++s;
const char *p = s;
int bal = 0;
while (*s)
{
if (*s == '(') ++bal;
else if (*s == ')') --bal;
else if (*s == ',' && bal == 0) break;
++s;
}
cerr.write(p, s - p) << " = " << x;
if (*s == ',')
{
++s;
cerr << " , ";
}
}
template<typename... Args>
void debug(const char *s, Args... args)
{
cerr << "[ ";
int dummy[] = { 0 , ( __print_one(s, args) , 0 )... };
(void)dummy;
cerr << " ]\n\n";
}
template<class X>
bool maximize(X &a, X b)
{
if (a < b)
{
a = b;
return true;
}
return false;
}
template<class X>
bool minimize(X &a, X b)
{
if (a > b)
{
a = b;
return true;
}
return false;
}
// --------------------------------------------------------------------------------------------
const int maxn = 5e5 + 3;
int n, q, h[maxn], tin[maxn], tout[maxn], tour[maxn << 1][20], lg[maxn << 1], tdfs;
ll D[maxn], dist[maxn], dp_down[maxn], dp_up[maxn];
vector<pii> g[maxn];
vector<pair<int, ll>> tree[maxn];
bool has[maxn];
// --------------------------------------------------------------------------------------------
void dfs_pre(int u, int p)
{
tin[u] = ++tdfs;
tour[tdfs][0] = u;
for (const auto &e : g[u])
{
if (e.fi == p) continue;
D[e.fi] = D[u] + e.se;
h[e.fi] = h[u] + 1;
dfs_pre(e.fi, u);
tour[++tdfs][0] = u;
}
tout[u] = tdfs;
}
#define MIN_H(x, y) (h[x] < h[y] ? x : y)
int lca(int u, int v)
{
u = tin[u]; v = tin[v];
if (u > v) swap(u, v);
int k = lg[v - u + 1];
return MIN_H(tour[u][k], tour[v - (1 << k) + 1][k]);
}
ll get_dist(int u, int v)
{
return D[u] + D[v] - 2 * D[lca(u, v)];
}
void dfs_down(int u, int p)
{
if (has[u])
dp_down[u] = 0ll;
for (const auto &e : tree[u])
{
if (e.fi == p) continue;
dfs_down(e.fi, u);
minimize(dp_down[u], dp_down[e.fi] + e.se);
}
}
void dfs_up(int u, int p)
{
if (has[u])
dp_up[u] = 0ll;
vector<pair<int, ll>> nodes;
for (const auto &e : tree[u])
{
if (e.fi == p) continue;
nodes.push_back(e);
}
vector<ll> SUFF(int(nodes.size()) + 3, ll(1e18));
FORD(i, int(nodes.size()) - 1, 0)
{
auto &e = nodes[i];
SUFF[i] = dp_down[e.fi] + e.se;
minimize(SUFF[i], SUFF[i + 1]);
}
ll PRE = ll(1e18);
FOR(i, 0, int(nodes.size()) - 1)
{
auto &e = nodes[i];
ll dpu = dp_up[u];
minimize(dpu, SUFF[i + 1]);
minimize(dpu, PRE);
dp_up[e.fi] = dpu + e.se;
minimize(PRE, dp_down[e.fi] + e.se);
}
for (const auto &e : nodes)
dfs_up(e.fi, u);
}
ll Query(int S, int X[], int T, int Y[])
{
int nA = S, nB = T;
vector<int> vers, vecA, vecB;
FOR(i, 0, nA - 1)
{
vecA.push_back(X[i]);
vers.push_back(X[i]);
}
FOR(i, 0, nB - 1)
{
vecB.push_back(Y[i]);
vers.push_back(Y[i]);
has[Y[i]] = 1;
}
sort(all(vers), [&](const int &x, const int &y) {
return tin[x] < tin[y];
});
FOR(i, 0, int(vers.size()) - 2)
{
vers.push_back(lca(vers[i], vers[i + 1]));
}
sort(all(vers), [&](const int &x, const int &y) {
return tin[x] < tin[y];
});
vers.erase(unique(all(vers)), vers.end());
for (int x : vers)
{
dp_down[x] = dp_up[x] = ll(1e18);
}
vector<int> st;
st.push_back(vers[0]);
FOR(i, 1, int(vers.size()) - 1)
{
int u = vers[i];
while (st.size() && tin[u] > tout[st.back()]) st.pop_back();
tree[st.back()].push_back({u, get_dist(st.back(), u)});
st.push_back(u);
}
dfs_down(vers[0], -1);
dfs_up(vers[0], -1);
ll res = 1e18;
for (int x : vecA)
{
minimize(res, dp_down[x]);
minimize(res, dp_up[x]);
}
for (int x : vers)
{
tree[x].clear();
}
for (int x : vecB)
has[x] = 0;
return res;
}
void Init(int N, int A[], int B[], int D[])
{
n = N;
FOR(i, 0, n - 1)
{
g[i].clear();
}
FOR(i, 0, n - 2)
{
int u = A[i], v = B[i], w = D[i];
if (u > v) swap(u, v);
g[u].push_back({v, w});
g[v].push_back({u, w});
}
tdfs = 0;
dfs_pre(0, -1);
FOR(i, 2, tdfs)
lg[i] = lg[i >> 1] + 1;
FOR(j, 1, 19)
FOR(i, 1, tdfs - (1 << j) + 1)
tour[i][j] = MIN_H(tour[i][j - 1], tour[i + (1 << j - 1)][j - 1]);
}
//signed main()
//{
// ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
// #define TASK "TEST"
// if (fopen(TASK".INP", "r"))
// {
// freopen(TASK".INP", "r", stdin);
// freopen(TASK".OUT", "w", stdout);
// }
// solve();
// return 0;
//}
