#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int N=1e5+10;
int cnt=0;
ll dp[N],d[N],vl[N],s[N];
vector<pair<int,ll>> adj[N];
struct line{
ll m,c;
double cut(line b){return (double)(b.c-c)/(double)(m-b.m);}
double val(ll x){return m*x+c;}
}st[N];
bool bad(line a,line b,line c){return c.cut(a)>=c.cut(b);}
ll query(ll x){
int l=0,r=cnt-1;
while(l<r){
int mid=(l+r+1)/2;
if(st[mid].cut(st[mid-1])<=x) l=mid;
else r=mid-1;
}
return st[l].val(x);
}
int ins(line li){
int l=0,r=cnt-1;
if(cnt<2 || !bad(st[cnt-2],st[cnt-1],li)) return cnt;
while(l<r){
int mid=(l+r)/2;
if(bad(st[mid-1],st[mid],li)) r=mid;
else l=mid+1;
}
return l;
}
void dfs(int u,int p){
int pi,pcnt;
line pl;
dp[u]=s[u]+d[u]*vl[u]+query(vl[u]);
line l={-d[u],dp[u]};
pi=ins(l);
pl=st[pi];
pcnt=cnt;
st[pi]=l;
cnt=pi+1;
//cout<<u <<"\n";
//for(int i=0;i<cnt;i++) cout<<st[i].m <<" " <<st[i].c <<"\n";
for(auto [v,w]:adj[u]){
if(v==p) continue;
d[v]=d[u]+w;
dfs(v,u);
}
cnt=pcnt;
st[pi]=pl;
}
int main(){
int n;
cin>>n;
for(int i=0;i<n-1;i++){
int u,v;
ll 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] >>vl[i];
dfs(1,1);
for(int i=2;i<=n;i++) cout<<dp[i] <<" ";
}
