///breaker
///every second counts
#pragma GCC optimize("O2")
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define fi first
#define se second
#define ii pair<ll,ll>
#define mp make_pair
#define in(x) freopen(x,"r",stdin)
#define out(x) freopen(x,"w",stdout)
#define bit(x,i) ((x>>i)&1)
#define lc (id<<1)
#define rc ((id<<1)^1)
const int maxn=1e5+7;
int n;
vector<ii>adj[maxn];
ll f[maxn];
ii chiso[maxn];
int maxst=0;
struct line
{
ll m,b;
line(ll m=0,ll b=0):m(m),b(b){}
ll operator()(ll x){return 1ll*m*x+b;}
friend double slope(const line &a,const line &b)
{
return (double)-(a.b-b.b)/(a.m-b.m);
}
}st[maxn];
ll getmin(ll x)
{
int l=0,r=maxst-1;
while(l<r){
int m=(l+r)/2;
if(slope(st[m],st[m+1])<x){
l=m+1;
}
else r=m;
}
return st[l](x);
}
int removeline(line x)
{
if(maxst<2||slope(st[maxst-2],st[maxst-1])<=slope(st[maxst-1],x))return maxst;
int l=1,r=maxst-1;
while(l<r){
int m=(l+r)/2;
if(slope(st[m-1],st[m])>slope(st[m],x)){
r=m;
}
else l=m+1;
}
return l;
}
void dfs(int u,int par,ll h)
{
int premax,prepos;
line preline;
if(u!=1){
f[u]=getmin(chiso[u].se)+chiso[u].fi+1ll*chiso[u].se*h;
line l={-h,f[u]};
premax=maxst;
prepos=maxst=removeline(l);
preline=st[maxst];
st[maxst++]=l;
}
else{
f[u]=0;
st[maxst++]={0,0};
}
for(ii x:adj[u]){
int v=x.fi;
int w=x.se;
if(v==par)continue;
dfs(v,u,h+w);
}
if(u!=1){
maxst=premax;
st[prepos]=preline;
}
}
void sol(void){
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>>chiso[i].fi>>chiso[i].se;
}
dfs(1,0,0);
for(int i=2;i<=n;i++)cout<<f[i]<<" ";
}
signed main(){
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
int t=1;
while(t--){
sol();
}
// you should actually read the stuff at the bottom
return 0;
}
/* stuff you should look for
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
* DON'T GET STUCK ON ONE APPROACH
*/
