#include <bits/stdc++.h>
//#define cin in
//#define cout out
#define ll long long int
#define pii pair<ll, ll>
#define fi first
#define se second
using namespace std;
const ll inf=2e18;
ll dis=0;
struct line{
ll m, b;
bool ex=false;
ll eval(ll x){
return (dis+m)*x+b;
}
bool operator==(line a)const{
return m==a.m && b==a.b && ex==a.ex;
}
};
struct lichao{
lichao *left, *right;
int l, r, mid;
line act;
lichao(int x, int y){
l=x;
r=y;
mid=(l+r)/2;
}
void insert(line nw){
if(act.ex){
if(act.eval(mid)>nw.eval(mid)){
swap(act,nw);
}
if(l==r || nw.m==act.m) return;
if(act.m<nw.m){
if(!left) left=new lichao(l,mid);
left->insert(nw);
}else{
if(!right) right=new lichao(mid+1,r);
right->insert(nw);
}
return;
}
act=nw;
}
void erase(line nw){
if(act==nw){
act.ex=false;
return;
}
if(act.m<nw.m && left) left->erase(nw);
else if(right) right->erase(nw);
}
ll query(ll x){
if(r<x || x<l) return inf;
if(l==r){
if(act.ex) return act.eval(x);
else return inf;
}
ll ans=inf;
if(act.ex) ans=act.eval(x);
if(left) ans=min(ans,left->query(x));
if(right) ans=min(ans,right->query(x));
return ans;
}
};
int n;
const int lim=1e5+5;
vector<pii> ady[lim];
pii harb[lim];
bool vis[lim]{};
ll dp[lim]{};
lichao cht(0,lim);
void dfs(int u, ll h=0){
line act;
vis[u]=true;
if(u>1){
dis=h;
dp[u]=harb[u].fi+cht.query(harb[u].se);
}
act={-h,dp[u],true};
cht.insert(act);
for(pii v:ady[u]){
if(!vis[v.fi]){
dfs(v.fi,h+v.se);
}
}
cht.erase(act);
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
ifstream in;
ofstream out;
in.open("harbingers.in");
out.open("harbingers.out");
int u, v;
ll w;
int n;
cin>>n;
for(int i=1; i<n; i++){
cin>>u>>v>>w;
ady[u].push_back({v,w});
ady[v].push_back({u,w});
}
for(int i=2; i<=n; i++){
cin>>harb[i].fi>>harb[i].se;
}
dfs(1);
for(int i=2; i<=n; i++) cout<<dp[i]<<" ";
}
