/*Author: KawakiMeido*/
#include <bits/stdc++.h>
#define pb push_back
#define endl "\n"
#define ll long long
#define int long long
#define ld long double
#define all(x) (x).begin(),(x).end()
#define pii pair<int,int>
#define fi first
#define se second
using namespace std;
/*Constants*/
const int N = 1e5+10;
const int INF = 1e9+7;
const long long LLINF = 1e18+3;
/*TestCases*/
int test=1;
void solve();
void TestCases(bool v){
if (v) cin >> test;
while(test--) solve();
}
struct Line{
int m,n;
Line(int _m, int _n): m(_m), n(_n) {};
ll operator()(ll x){ return m*x+n;}
friend ld intersect(Line a, Line b){ return (ld)(b.n-a.n)/(ld)(a.m-b.m);}
};
/*Global Variables*/
int n,m;
stack<Line> tmpline[N];
int dist[N],dp[N];
vector<pii> adj[N];
int s[N],v[N];
deque<Line> dq;
void AddLine (Line u, int pos){
while (dq.size() > 1 && intersect(dq[dq.size()-1],dq[dq.size()-2])>intersect(dq[dq.size()-1],u)){
tmpline[pos].push(dq.back());
dq.pop_back();
}
dq.push_back(u);
}
void DeleteLine(int pos){
dq.pop_back();
while (!tmpline[pos].empty()){
dq.push_back(tmpline[pos].top());
tmpline[pos].pop();
}
}
int Query(int x){
int ans = 0;
int l = 1, r = dq.size()-1;
while (l<=r){
int mid = (l+r)/2;
if (intersect(dq[mid-1],dq[mid])<x){
ans = mid;
l = mid+1;
}
else{
r = mid-1;
}
}
return ans;
}
void DFS(int u, int p=0){
if (u!=1){
int pos = Query(v[u]);
dp[u] = v[u]*dq[pos].m + dq[pos].n + s[u] + dist[u]*v[u];
}
AddLine(Line(-dist[u],dp[u]),u);
for (auto in:adj[u]){
int v = in.fi;
int w = in.se;
if (v==p) continue;
dist[v] = dist[u] + w;
DFS(v,u);
}
DeleteLine(u);
}
/*Solution*/
void solve(){
cin >> n;
for (int i=1; i<n; i++){
int u,v,w; cin >> u >> v >> w;
adj[u].push_back({v,w});
adj[v].push_back({u,w});
}
for (int i=2; i<=n; i++){
cin >> s[i] >> v[i];
}
// DFS(1);
for (int i=2; i<=n; i++){
cout << dp[i] << " ";
}
}
/*Driver Code*/
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
TestCases(0);
return 0;
}
