#include<bits/stdc++.h>
#define int long long
using namespace std;
#define II signed
struct {
struct line{
II K;
int B;
line(int k,int b){
K=k,B=b;
}
line(){
K=0;
B=1e18;
}
inline int operator()(int x){
return K*x+B;
}
} T[100100];
II lc[100100],rc[100100],rt,CCC;
stack<pair<II,line>> oppss;
void update(II &i,int l,int r,line s){
if(!i)i=++CCC;
if(T[i].B==1e18) return T[i]=s,oppss.push({i,s});
if(l==r-1){
if(s(l)<T[i](l))
swap(s,T[i]),
oppss.push({i,s});
return;
}
if(s.K<T[i].K)
swap(s,T[i]),
oppss.push({i,s});
int mid=l+r>>1;
if(s(mid) < T[i](mid)) swap(s,T[i]),
oppss.push({i,s}),update(rc[i],mid,r,s);
else update(lc[i],l,mid,s);
}
int query(int i,int l,int r,int p){
if(!i)return 1e18;
if(T[i].B==1e18)
return 1e18;
if(l==r-1)
return T[i](p);
if(p<l+r>>1)
return min(T[i](p),query(lc[i],l,l+r>>1,p));
else return min(T[i](p),query(rc[i],l+r>>1,r,p));
}
inline int pointintime(){
return oppss.size();
}
void add_line(int k,int b){
update(rt,-1,1e9+1,line(k,b));
}
int calc_best(int pos){
return query(rt,-1,1e9+1,pos);
}
void rewind(int x){
while(oppss.size()>x){
auto[a,b]=oppss.top();
oppss.pop();
T[a]=b;
}
}
} lichao;
II S[100100],V[100100],res[100100];
vector<pair<II,II>>adj[100100];
void dfs(II n,II p,II d){
int X = lichao.pointintime();
if(n==1){
lichao.add_line(0,0);
} else {
res[n] = lichao.calc_best(V[n])+S[n]+d*V[n];
lichao.add_line(-d,res[n]);
}
for(auto[i,j]:adj[n])
if(i-p)dfs(i,n,j+d);
lichao.rewind(X);
}
II main(){
cin.tie(0)->sync_with_stdio(0);
int n;
cin>>n;
for(int i=1;i<n;i++){
int a,b,c;
cin>>a>>b>>c;
adj[a].push_back({b,c});
adj[b].push_back({a,c});
}
for(int i=2;i<=n;i++)
cin>>S[i]>>V[i];
dfs(1,0,0);
for(int i=2;i<=n;i++)
cout<<res[i]<<' ';
}
