/**
* author: chowgz
* created: 14/03/2021 21:31:52
**/
#include <bits/stdc++.h>
using namespace std;
constexpr int MAXN = 100'000;
int prep[MAXN], speed[MAXN], dist[MAXN], ints[MAXN + 1];
long long ans[MAXN];
bool visited[MAXN];
vector<pair<int, int>> v[MAXN];
struct Line {
int m;
long long c;
double operator^(const Line &rhs) {
return ((double)c - rhs.c) / ((double)rhs.m - m);
}
long long operator()(int x) {
return (long long)m * x + c;
}
};
struct ConvexHull {
Line lines[MAXN + 1];
void insert(Line line, int &r, Line &bak_line) {
r = lower_bound(ints + 1, ints + r, line, [&](const int &idx, const Line &line) {
return (lines[idx - 1] ^ lines[idx]) < (lines[idx] ^ line);
}) - ints;
bak_line = lines[r];
lines[r] = line;
}
long long query(int x, int r) {
return lines[lower_bound(ints, ints + r - 1, x, [&](const int &idx, const int& x){
return (lines[idx] ^ lines[idx + 1]) < x;
}) - ints](x);
}
void restore(int r, Line line) {
lines[r] = line;
}
} hull;
void dfs(int idx, int r) {
visited[idx] = true;
ans[idx] = (long long)speed[idx] * dist[idx] + prep[idx] + min(0LL, hull.query(speed[idx], r));
Line bak_line;
hull.insert(Line{-dist[idx], ans[idx]}, r, bak_line);
for (const auto &z : v[idx]) {
if (visited[z.first]) {
continue;
}
dist[z.first] = dist[idx] + z.second;
dfs(z.first, r + 1);
}
hull.restore(r, bak_line);
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
iota(ints, ints + MAXN + 1, 0);
int n;
cin >> n;
for (int i = 0, a, b, d; i < n - 1; i++) {
cin >> a >> b >> d;
a--;
b--;
v[a].emplace_back(b, d);
v[b].emplace_back(a, d);
}
for (int i = 1; i < n; i++) {
cin >> prep[i] >> speed[i];
}
Line bak_line;
int r = 0;
hull.insert(Line{0, 0}, r, bak_line);
dfs(0, 1);
cout << ans[1];
for (int i = 2; i < n; i++) {
cout << ' ' << ans[i];
}
cout << '\n';
return 0;
}
