#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pll = pair<ll,ll>;
struct Frac {
// a/b
__int128 _a, _b;
Frac(ll a, ll b) {
if (b < 0) a *= -1, b *= -1;
_a = a, _b = b;
ll g = gcd(a, b);
_a /= g, _b /= g;
}
bool operator<=(Frac rhs) {
return _a*rhs._b <= rhs._a*_b;
}
string str() {
return to_string((ll)_a) + "/" + to_string((ll)_b);
}
};
struct F {
// ax+b
ll a, b;
Frac s;
F() : a(0), b(0), s(1,1) {}
F(ll a, ll b) : a(a), b(b), s((ll)1e18, 1) {}
F(ll a, ll b, Frac s) : a(a), b(b), s(s) {}
Frac intersect(F rhs) {
return Frac(rhs.b - b, a - rhs.a);
}
ll get(ll x){
return a*x+b;
}
};
ll S[101010], V[101010], P[101010], ans[101010], N;
vector<pll> T[101010];
F stk[101010];
int ei = 0;
void dfs(int v, int p) {
vector<pair<int,F>> log;
int befe = ei;
if (v != 1) {
int s = 0, e = ei, i = 0;
Frac x(V[v], 1);
while (s <= e) {
int m = s+e >> 1;
if (stk[m].s <= x) i = m, s = m+1;
else e = m-1;
}
ans[v] = stk[i].get(V[v]) + V[v]*P[v] + S[v];
F now(-P[v], ans[v]);
s = 0, e = ei, i = ei+1;
while (s <= e) {
int m = s+e >> 1;
if ((stk[m].a > now.a and now.intersect(stk[m]) <= stk[m].s) or (stk[m].a == now.a and stk[m].b >= now.b))
i = m, e = m-1;
else
s = m+1;
}
if (stk[i-1].a != now.a) {
ei = i;
log.emplace_back(i, stk[i]);
now.s = now.intersect(stk[i-1]);
stk[i] = now;
}
else {
ei = i-1;
log.emplace_back(-i+1, stk[i-1]);
}
}
for (auto[i,d] : T[v]){
if (i == p) continue;
P[i] = P[v] + d;
dfs(i, v);
}
while (log.size()) {
auto[x,f] = log.back();
log.pop_back();
if (x >= 0) stk[x] = f;
}
ei = befe;
}
int main() {
cin.tie(nullptr)->sync_with_stdio(0);
cin >> N;
for (int i = 1,u,v,c; i < N; i++) {
cin >> u >> v >> c;
T[u].emplace_back(v,c);
T[v].emplace_back(u,c);
}
for (int i = 2; i <= N; i++) cin >> S[i] >> V[i];
stk[0] = F(0,0,Frac(-(ll)1e18, 1LL));
dfs(1, -1);
for (int i = 2; i <= N; i++) cout << ans[i] << ' ';
}
