// perzistentni stak
// dfs od cvora 1
// radis CHT na perzistentnom staku
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
#define pb push_back
struct line {
ll k, c;
ll operator()(ll x) {
return k * x + c;
}
};
const int N = 1e5 + 5, LOG = 17;
vector<array<int, 2>> g[N];
int up[LOG][N], a[N], b[N], C = 0, d = 0;
ll dp[N];
line st[N];
ld intersect(line &A, line &B) {
return (ld)(A.c - B.c) / (B.k - A.k);
}
ll f(ll x) {
int u = d;
for (int i = LOG-1; i >= 0; --i) {
if (up[i][u] > 1 && intersect(st[up[i][u]], st[up[0][up[i][u]]]) >= x) {
u = up[i][u];
}
}
if (up[0][u] && intersect(st[u], st[up[0][u]]) >= x) u = up[0][u];
return min(st[u](x), st[1](x));
}
void dfs(int s, int e = -1, ll D = 0) {
if (s > 1) dp[s] = a[s] + b[s] * D + f(b[s]);
for (auto [u, w] : g[s]) {
if (u == e) continue;
st[++C] = {-D, dp[s]};
int d1 = d;
for (int i = LOG-1; i >= 0; --i) {
if (up[i][d] > 1 && intersect(st[up[i][d]], st[up[0][up[i][d]]]) >= intersect(st[C], st[up[0][up[i][d]]])) {
d = up[i][d];
}
}
if (up[0][d] && intersect(st[C], st[up[0][d]]) <= intersect(st[d], st[up[0][d]])) d = up[0][d];
up[0][C] = d;
for (int i = 1; i < LOG; ++i) up[i][C] = up[i-1][up[i-1][C]];
d = C;
dfs(u, s, D + w);
d = d1;
}
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
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);
for (int i = 2; i <= n; ++i) {
cout << dp[i] << ' ';
}
cout << '\n';
}
