#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define pll pair<ll, ll>
#define pii pair<int, int>
#define point complex<ll>
const short OP_RESIZE = 0;
const short OP_SET = 1;
const ll MAX_SZ = 100001;
struct PStack{
array<point, MAX_SZ> elems;
int sz= 0;
vector<short> ops;
vector<int> resizes;
vector<pair<int, point>> sets;
void resize(ll new_sz){
ops.push_back(OP_RESIZE);
resizes.push_back(sz);
sz = new_sz;
}
void set(int pos, point elem){
ops.push_back(OP_SET);
sets.push_back({pos, elems[pos]});
elems[pos] = elem;
}
void push_back(point p){
set(sz, p);
resize(sz+1);
}
void undo(){
short tp = ops.back();
ops.pop_back();
if(tp == OP_RESIZE){
sz = resizes.back();
resizes.pop_back();
}
else{
elems[sets.back().first] = sets.back().second;
sets.pop_back();
}
}
void go_back(ll target_sz){
while(ops.size()>target_sz){
undo();
}
}
};
ll cross(point a, point b){
return (a*conj(b)).imag();
}
ll dot(point a, point b){
return (a*conj(b)).real();
}
bool ok(point a, point b, point c){
return cross(b-a, c-b)>0;
}
struct Hull{
PStack pts;
void push_back(point e){
if(pts.sz>1){
ll cur = -1;
for(ll step = (1<<20); step>=1; step/=2){
if(cur+step+1<pts.sz){
if(ok(pts.elems[cur+step], pts.elems[cur+step+1], e)){
cur+=step;
}
}
}
pts.resize(cur+2);
}
pts.push_back(e);
}
ll get_min(point normal){
/*cout<<"getting at "<<normal.real()<<" "<<normal.imag()<<endl;
for(ll i = 0; i<pts.sz; i++){
cout<<pts.elems[i].real()<<" "<<pts.elems[i].imag()<<endl;
}
cout<<"done "<<endl;*/
if(pts.elems.size() == 0){
return 0;
}
ll cur = 0;
for(ll step = (1<<20); step>=1; step/=2){
if(cur+step<pts.sz){
if(dot(normal, pts.elems[cur+step])<dot(normal, pts.elems[cur+step-1])){
cur+=step;
}
}
}
return dot(pts.elems[cur], normal);
}
};
vector<pii> params;
vector<ll> dp_res;
array<vector<pii>, MAX_SZ> adj;
void dfs(int u,int anc, ll depth, Hull& h){
int ops_sz = h.pts.ops.size();
ll dp_cur = h.get_min({params[u].first, 1LL})-(ll)(params[u].first)*depth + (ll)(params[u].second);
//cout<<u<<" "<<dp_cur<<endl;
h.push_back({depth, dp_cur});
dp_res[u] = dp_cur;
for(auto e: adj[u]){
if(e.first!=anc){
dfs(e.first,u, depth-e.second, h);
}
}
h.pts.go_back(ops_sz);
}
void dfs0(int u, int a){
for(int i = 0; i<adj[u].size(); i++){
auto e= adj[u][i];
if(e.first!=a){
dfs0(e.first, u);
}
else{
swap(adj[u][i], adj[u].back());
adj[u].pop_back();
i--;
}
}
}
signed main(){
int n;
cin>>n;
for(int i = 0; i<n-1; i++){
ll u, v, d;
cin>>u>>v>>d;
u--;v--;
adj[u].push_back({v, d});
adj[v].push_back({u, d});
}
dfs0(0, -1);
for(int i = 0; i<n; i++){
adj[i].shrink_to_fit();
}
params.resize(n);
for(int i = 1; i<n; i++){
cin>>params[i].second>>params[i].first;
}
Hull h;
dp_res.resize(n);
dfs(0, -1, 0, h);
for(int i =1; i<n; i++){
cout<<dp_res[i]<<" ";
}
cout<<endl;
}
