#include <bits/stdc++.h>
using namespace std;
#define int long long
const int N = 3e5+5;
struct Line{
int a,b;
int operator()(int x) {return a * x + b;};
}lines[N];
vector<pair<int,int> > A[N];
int dis[N],prep[N],v[N],dp[N];
int sz=1;
int inter(Line x,Line y) {
return (x.b - y.b) / (y.a - x.a);
}
stack<tuple<int,int,Line> > his;
void add(Line nw) {
int pos = sz, l = 1, r = sz-1;
while(l<=r){
int mid = (l+r)/2;
if(inter(lines[mid-1],nw) >= inter(lines[mid],nw)){
pos=mid;
r=mid-1;
}else l=mid+1;
}
his.emplace(sz,pos,lines[pos]);
lines[pos]=nw;
sz=pos+1;
}
int query(int x) {
int pos = 0, l = 1, r = sz-1;
while(l<=r){
int mid=(l+r)/2;
if(inter(lines[mid],lines[mid-1])<x){
pos=mid;
l=mid+1;
}r=mid-1;
}
return lines[pos](x);
}
void rollback() {
auto [a,b,c] = his.top();
his.pop();
lines[b]=c;
sz=a;
}
void dfs(int u,int par = -1) {
if(par!=-1){
dp[u] = prep[u] + v[u] * dis[u] + query(v[u]);
add({-dis[u],dp[u]});
}
for(auto [nxt,w] : A[u])if(nxt!=par){
dis[nxt] = dis[u] + w;
dfs(nxt,u);
}
if(par!=-1)rollback();
}
int32_t main() {
cin.tie(0)->sync_with_stdio(0);
int a,b,w,n;
cin >> n;
for(int i = 0;i<n-1;i++) {
cin >> a >> b >> w;
A[a].push_back({b,w});
A[b].push_back({a,w});
}
for(int i = 2;i<=n;i++)cin>>prep[i]>>v[i];
// get dis values + do lichao
dfs(1);
for(int i = 2;i<=n;i++) cout << dp[i] << " ";
}
