//Power Of Ninja Go
#include <bits/stdc++.h>
#ifdef atom
#include "grader.cpp"
#else
#include "factories.h"
#endif
using namespace std;
typedef long long ll; typedef pair<int, int> ii; typedef vector<int> vi; typedef vector< ii > vii;
#define X first
#define Y second
#define pb push_back
const int maxn = 5e5+5;
vii adj[maxn];
int dp[22][maxn];
int h[maxn];
int par[maxn];
ll sweep[maxn];
int cnt[maxn];
bool use[maxn];
ll bst[maxn];
void trv(int u, int p)
{
for(auto edge : adj[u])
{
int v = edge.X, w = edge.Y;
if(v != p)
{
h[v] = h[u]+1;
dp[0][v] = u;
sweep[v] = sweep[u]+w;
trv(v, u);
}
}
}
void dfs(int u, int p)
{
cnt[u] = 1;
for(auto edge : adj[u])
{
int v = edge.X;
if(use[v] or v == p) continue;
dfs(v, u);
cnt[u] += cnt[v];
}
}
int find_centroid(int u, int p, int full)
{
for(auto edge : adj[u])
{
int v = edge.X;
if(use[v] or v == p) continue;
if(cnt[v]*2> full) return find_centroid(v, u, full);
}
return u;
}
void maketree(int top, int p)
{
dfs(top, p);
int c = find_centroid(top, p, cnt[top]);
use[c] = true;
par[c] = p;
//printf("centroid %d\n", c);
for(auto edge : adj[c])
{
int v = edge.X;
if(use[v] or v == p) continue;
maketree(v, c);
}
}
int LCA(int u, int v)
{
if(h[u]< h[v]) swap(u, v);
for(int i = 20; i>= 0; i--)
{
int x = dp[i][u];
if(h[x]>= h[v]) u = x;
}
if(u == v) return u;
for(int i = 20; i>= 0; i--)
{
int x = dp[i][u], y = dp[i][v];
if(x == y) continue;
u = x; v = y;
}
return dp[0][u];
}
ll dist(int u, int v)
{
int x = LCA(u, v);
return sweep[u]+sweep[v]-2LL*sweep[x];
}
void Init(int N, int A[], int B[], int D[])
{
for(int i = 0; i< N-1; i++)
{
int u, v; u = A[i]+1; v = B[i]+1;
int w = D[i];
adj[u].pb(ii(v, w));
adj[v].pb(ii(u, w));
}
h[1] = 1; trv(1, 0);
//for(int i = 1; i<= N; i++) printf("sweep[i] = %lld\n", sweep[i]);
return;
maketree(1, 0);
for(int i = 1; i<= 20; i++)
for(int j = 1; j<= N; j++)
dp[i][j] = dp[i-1][dp[i-1][j]];
for(int i = 1; i<= N; i++) bst[i] = 4e18;
}
long long Query(int S, int X[], int T, int Y[])
{
set<int> vec;
for(int i = 0; i< S; i++)
{
int u = X[i]+1;
//printf("updating %d\n", u);
while(u)
{
bst[u] = min(bst[u], dist(u, X[i]+1));
//printf("bst[%d] is now %lld\n", u, bst[u]);
vec.insert(u);
u = par[u];
}
}
ll best = 4e18;
for(int i = 0; i< T; i++)
{
int u = Y[i]+1;
while(u)
{
best = min(best, dist(u, Y[i]+1)+bst[u]);
u = par[u];
}
}
for(auto x : vec) bst[x] = 4e18;
return best;
}
