#include<bits/stdc++.h>
#define fi first
#define se second
#define ll long long
using namespace std;
ll dp[100005],f[100005],s[100005],v[100005];pair<ll,ll> line[100005];
vector<pair<ll,ll>> g[100005];
int sz;
struct Node{
ll fi,se;pair<ll,ll> ba;
};
deque<Node> tra;
ll get(pair<ll,ll> u1,ll z){
return u1.fi*z+u1.se;
}
ll get_min(ll z){
ll l=1,r=sz,ans=get(line[1],z);
while (l<r){
int mid=(l+r)/2;
ll z1=get(line[mid],z),z2=get(line[mid+1],z);
if (z1>=z2) l=mid+1;else r=mid;
ans=min(ans,min(z1,z2));
}
return ans;
}
bool check(pair<ll,ll> x,pair<ll,ll> y,pair<ll,ll> z){
return (z.se-x.se)*(x.fi-y.fi)<=(y.se-x.se)*(x.fi-z.fi);
}
void bodyfix(pair<ll,ll> x){
int l=2,r=sz,ans=sz+1;
while (l<=r){
int mid=(l+r)/2;
if (check(line[mid-1],line[mid],x)) ans=mid,r=mid-1;
else l=mid+1;
}
// cout<<ans<<" "<<line[ans].fi<<" "<<line[ans].se<<endl;
tra.push_back({sz,ans,line[ans]});
sz=ans;
line[ans]=x;
}
void dfs(int u,int pa){
if (u!=1){
ll z=get_min(v[u]);
dp[u]=z+s[u]+f[u]*v[u];
bodyfix({-f[u],dp[u]});
}
else{
sz=1;line[1]={0,0};
}
for (auto j:g[u]){
if (j.fi==pa) continue;
f[j.fi]=f[u]+j.se;
dfs(j.fi,u);
}
if (u==1) return ;
Node z=tra.back();tra.pop_back();
sz=z.fi;line[z.se]=z.ba;
}
int main(){
if (fopen("CHT4.inp","r")){
freopen("CHT4.inp","r",stdin);
freopen("CHT4.out","w",stdout);
}
ios_base::sync_with_stdio(0);
cin.tie(0);cout.tie(0);
int n;cin>>n;
for (int i=1;i<n;i++){
ll u,j,w;cin>>u>>j>>w;
g[u].push_back({j,w});
g[j].push_back({u,w});
}
for (int i=2;i<=n;i++) cin>>s[i]>>v[i];
dfs(1,1);
for (int i=2;i<=n;i++)cout<<dp[i]<<" ";
}
