#include <bits/stdc++.h>
using namespace std;
#define int long long
const int inf = 3e18;
const int mxn=1e5+5;
int siz=0;
vector<array<int,2>>cht(mxn);
int div2(int a, int b){
if(b==0){
return inf;
}
return (a/b) - ((a%b)&&((a^b)<0));
}
void dfs(int st, vector<array<int,2>>g[], int dep, int p, long long dp[], int t[], int v[]){
if(st){
///for v[st] find minima
int lo = 0;
int hi = siz-1;
while(lo<hi){
int mid = (lo+hi)/2;
int x = div2(cht[mid][1]-cht[mid+1][1],cht[mid+1][0]-cht[mid][0]);
if(x<v[st]){
lo=mid+1;
}
else{
hi=mid;
}
}
dp[st]=t[st]+v[st]*dep+(cht[lo][0]*v[st]+cht[lo][1]);
}
else{
dp[st]=0;
siz++;
}
int m = -dep;
int c = dp[st];
int lo = 0;
int hi = siz;
while(lo<hi){
int mid = (lo+hi)/2;
int x = div2(cht[mid][1]-c,m-cht[mid][0]);
int x2 = -inf;
if(mid){
x2=(div2(cht[mid][1]-cht[mid-1][1],cht[mid-1][0]-cht[mid][0]));
}
if(x>x2){
lo=mid+1;
}
else{
hi=mid;
}
}
int osiz = siz;
int om = cht[lo][0];
int oc = cht[lo][1];
siz=lo+1;
cht[lo][0]=m;
cht[lo][1]=c;
for(array<int,2>e:g[st]){
if(e[0]==p)
continue;
dfs(e[0],g,dep+e[1],st,dp,t,v);
}
siz=osiz;
cht[lo][0]=om;
cht[lo][1]=oc;
}
signed main(){
ios::sync_with_stdio(0);
cin.tie(0);
int n;
cin >> n;
vector<array<int,2>>g[n];
for(int i = 0;i<n-1;i++){
int u,v,d;
cin >> u >> v >> d;
u--;v--;
g[u].push_back({v,d});
g[v].push_back({u,d});
}
int t[n];
int v[n];
t[0]=0;
v[0]=0;
for(int i = 1;i<n;i++){
cin >> t[i];
cin >> v[i];
}
long long dp[n];
dfs(0,g,0,-1,dp,t,v);
for(int i = 1;i<n;i++){
cout << dp[i] << " ";
}
return 0;
}
