//chockolateman
#include<bits/stdc++.h>
// #include "factories.h"
using namespace std;
const long long INF = 1e15;
int s[500005],col[500005][21],anc[500005][21],par_c[500005],my_d[500005],timer;
long long ans[500005];
vector<pair<int,int>> adj[500005];
bool is_removed[500005];
vector<long long> dist[500005];
void dfs1(int v,int p,int d)
{
s[v] = 1;
col[v][d] = ++timer;
for(auto e : adj[v])
{
int u = e.first;
if(!is_removed[u] && u != p)
{
dfs1(u,v,d);
s[v] += s[u];
}
}
}
int centroid(int v,int p, int n)
{
for(auto e : adj[v])
{
int u = e.first;
if(!is_removed[u] && u != p && 2*s[u] > n)
return centroid(u,v,n);
}
return v;
}
void dfs2(int v,int p,int root)
{
anc[v][my_d[root]] = root;
for(auto e : adj[v])
{
int u = e.first;
int w = e.second;
if(!is_removed[u] && u != p)
{
dist[root][col[u][my_d[root]]] = dist[root][col[v][my_d[root]]] + w;
dfs2(u,v,root);
}
}
}
void build(int v,int p,int d)
{
timer = 0;
dfs1(v,v,d);
int n = s[v];
int c = centroid(v,v,n);
vector<int> temp;
for(int i = 0 ; i <= timer ; i++)
dist[c].push_back(0ll);
dfs2(c,c,c);
ans[c] = INF;
if(p == -1)
p = c;
par_c[c] = p;
my_d[c] = d;
is_removed[c] = true;
for(auto e : adj[c])
{
int u = e.first;
if(!is_removed[u])
build(u,c,d+1);
}
}
void update(int v)
{
ans[v] = 0;
int pos = v;
while(par_c[pos] != pos)
{
pos = par_c[pos];
ans[pos] = min(ans[pos],dist[pos][col[v][my_d[pos]]]);
}
}
void undo(int v)
{
ans[v] = INF;
int pos = v;
while(par_c[pos] != pos)
{
pos = par_c[pos];
ans[pos] = INF;
}
}
void Init(int N, int A[], int B[], int D[]) {
for(int a,b,w,i = 0 ; i < N-1 ; i++)
{
a = A[i]+1;
b = B[i]+1;
w = D[i];
adj[a].push_back({b,w});
adj[b].push_back({a,w});
}
}
long long Query(int S, int X[], int T, int Y[]) {
return 0;
}
