#include <bits/stdc++.h>
using namespace std;
#define int long long
struct line{
mutable long long m,c,p;
bool operator<(const line &o) const {return m>o.m;}
bool operator<(long long x) const {return p<x;}
};
///persistant lineContainer
struct lineContainer : multiset<line,less<>>{
vector<vector<array<int,2>>>roll;
const long long inf = 3e18;
long long div(long long a, long long b){
return (a/b)-((a%b)&&((a^b)<0));
}
bool isect(iterator x, iterator y){
if(y==end()){
x->p=inf;
return 0;
}
if(x->m==y->m){
x->p = (x->c<=y->c) ? inf : -inf;
}
else{
x->p = div(x->c-y->c,y->m-x->m);
}
return x->p>=y->p;
}
void add(long long m, long long c, bool r=1){
auto z = insert({m,c,-inf});
vector<array<int,2>>arr;
arr.push_back({m,c});
int cnt = 1;
auto y = z++;
auto x = y;
bool rel=1;
while(isect(y,z)){
if(r){
arr.push_back({z->m,z->c});
cnt++;
}
else{
assert(0);
}
z=erase(z);
}
if(x!=begin() && isect(--x,y)){
if(r){
///this must have deleted the initial which means this line doesnt matter
rel=0;
arr.push_back({y->m,y->c});
cnt++;
}
else{
assert(0);
}
isect(x,y=erase(y));
}
while((y=x)!=begin()&&(--x)->p>=y->p){
if(r){
arr.push_back({y->m,y->c});
cnt++;
}
else{
assert(0);
}
isect(x,erase(y));
}
if(r){
if(rel){
roll.push_back(arr);
}
else{
arr.clear();
roll.push_back(arr);
}
}
}
long long query(long long x){
line l = *lower_bound(x);
return l.m*x+l.c;
}
void rollback(){
vector<array<int,2>>arr = roll.back();
roll.pop_back();
if(arr.size()==0){
return;
}
auto l = lower_bound({arr[0][0],arr[0][1]});
l=erase(l);
if(l!=begin()){
auto lef = l;
lef--;
isect(lef,l);
}
for(int i = 1;i<arr.size();i++){
add(arr[i][0],arr[i][1],0);
}
}
};
void dfs(int st, vector<array<int,2>>g[], int dep, int p, long long dp[], int t[], int v[], lineContainer &lc){
if(st){
dp[st]=t[st]+v[st]*dep+lc.query(v[st]);
}
else{
dp[st]=0;
}
lc.add(-dep,dp[st]);
for(array<int,2>e:g[st]){
if(e[0]==p)
continue;
dfs(e[0],g,dep+e[1],st,dp,t,v,lc);
}
lc.rollback();
}
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];
lineContainer lc;
dfs(0,g,0,-1,dp,t,v,lc);
for(int i = 1;i<n;i++){
cout << dp[i] << " ";
}
return 0;
}
