#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pb push_back
#define sz(x) ((int)x.size())
#define all(x) x.begin(), x.end()
#define F first
#define S second
#define ins insert
#define pii pair<int, int>
const int N = 1e5 + 100, K = 5, mod = 998244353, inf = 1e18;
vector<pii>g[N];
int dp[N], d[N], a[N], b[N];
struct line{
int k, b;
line(int x, int y){
k = x, b = y;
}
line(){
}
double find(line x){
return double(x.b - b) / double(k - x.k);
}
int get(int x){
return k * x + b;
}
};
bool check(line nw, line lst, line prv){
return nw.find(prv) >= lst.find(prv);
}
struct convex{
vector<line>l;
vector<vector<line>>st;
vector<bool>st2;
convex(){
l.clear();
}
void add(line x){
vector<line>V;
while(sz(l) && l.back().k == x.k && l.back().b > x.b){
V.pb(l.back());
l.pop_back();
}
if(sz(l) && l.back().k == x.k && l.back().b <= x.b){
st.pb(V);
st2.pb(false);
return;
}
while(sz(l) > 1 && check(x, l.back(), l[sz(l) - 2])){
V.pb(l.back());
l.pop_back();
}
st.pb(V);
l.pb(x);
st2.pb(true);
}
int get(int x){
if(!sz(l)) return inf;
if(sz(l) == 1) return l[0].get(x);
int L = 0, R = sz(l) - 2, res = inf;
while(L <= R){
int m = (L + R) / 2;
int vl = l[m].get(x), vl2 = l[m + 1].get(x);
res = min(res, vl);
res = min(res, vl2);
if(vl <= vl2){
R = m - 1;
}
else{
L = m + 1;
}
}
return res;
}
void otkat(){
if(st2.back()) l.pop_back();
for(auto it : st.back()) l.pb(it);
st.pop_back();
st2.pop_back();
}
};
convex T;
void dfs(int v, int p){
dp[v] = inf;
if(v == 1){
dp[v] = 0;
}
else{
dp[v] = T.get(-b[v]) + a[v] + d[v] * b[v];
}
T.add({d[v], dp[v]});
for(auto it : g[v]){
int to = it.F, w = it.S;
if(to == p) continue;
d[to] = d[v] + w;
dfs(to, v);
}
T.otkat();
}
signed main(){
ios_base :: sync_with_stdio(false);
cin.tie(nullptr);
int n;
cin>>n;
for(int i = 1; i < n; i++){
int u, v, w;
cin>>u>>v>>w;
g[u].pb({v, w});
g[v].pb({u, w});
}
for(int i = 2; i <= n; i++){
cin>>a[i]>>b[i];
}
dfs(1, 1);
for(int i = 2; i <= n; i++){
cout<<dp[i]<<' ';
}
}
