#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef double ld;
vector<array<ll, 2>> g[100000];
array<ll, 2> ps[100000], all[100000];
ll oo = 1e14, re[100000];
ld xinter(array<ll, 2> a, array<ll, 2> b){
return ((ld) b[1] - a[1]) / ((ld) a[0] - b[0]);
}
ll chinter(ll id, ll i, ll x){
if(i >= id - 1) return 1; // oo é a interseção
return (x <= xinter(ps[i], ps[i + 1]));
}
ll vl(ll id, ll x){
ll l = 1, r = id;
while(l <= r){
ll m = (l + r) / 2;
if(chinter(id, m, x)) r = m - 1;
else l = m + 1;
}
return ps[l][0] * x + ps[l][1];
}
array<ll, 2> ins(ll &ind, array<ll, 2> at){
while(ind > 2 && xinter(ps[ind - 2], at) <= xinter(ps[ind - 2], ps[ind - 1]))
--ind;
auto ax = ps[ind];
ps[ind] = at;
return ax;
}
void dfs(ll p, ll at, ll del, ll ia){
ll res = vl(ia, all[at][1]), c = all[at][0] + all[at][1] * del;
re[at] = res + c;
auto aux = ins(ia, {-del, res + c});// o unico nó que editei
for(auto [i, j] : g[at]) if(i != p)
dfs(at, i, del + j, ia + 1);
ps[ia] = 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][0] >> all[i][1];
ps[0] = {1, 0};
dfs(-1, 0, 0, 1);
for(ll i = 1; i < n; i++)
cout << to_string((ll) re[i]) << " ";
cout << "\n";
}
