#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef double ld;
vector<pair<ll, ll>> g[100000];
pair<ll, ll> ps[100000], all[100000];
ll oo = 1e14, re[100000];
ld xinter(pair<ll, ll> a, pair<ll, ll> b){
return ((ld) b.second - a.second) / ((ld) a.first - b.first);
}
ll vl(ll id, ll x){
ll l = 1, r = id;
while(l <= r){
ll m = (l + r) / 2;
if(m >= id - 1 || x <= xinter(ps[m], ps[m + 1])) r = m - 1;
else l = m + 1;
}
return ps[l].first * x + ps[l].second;
}
void dfs(ll p, ll at, ll del, ll id){
ll res = vl(id, all[at].second), c = all[at].first + all[at].second * del;
re[at] = res + c;
while(id > 2 && xinter(ps[id - 2], {-del, res + c}) <= xinter(ps[id - 2], ps[id - 1]))
--id;
pair<ll, ll> aux = ps[id];
ps[id] = {-del, res + c}; // inserindo no Convex Hull
for(auto [i, j] : g[at]) if(i != p)
dfs(at, i, del + j, id + 1);
ps[id] = aux;
}
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
ll n; cin >> n;
for(int i = 1, a, b, c; i < n; i++){
cin >> a >> b >> c; a--, b--;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
for(ll i = 1; i < n; i++)
cin >> all[i].first >> all[i].second;
ps[0] = {1, 0};
dfs(-1, 0, 0, 1);
for(ll i = 1; i < n; i++)
cout << to_string((ll) re[i]) << " ";
cout << "\n";
}
