#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using pint = pair<lint, lint>;
#define x first
#define y second
struct cht {
lint a[100004], b[100004];
int cnt = 0;
struct record {
int cnt, i;
lint a, b;
};
record r[100004];
int rcnt = 0;
void update(lint a0, lint b0) {
rcnt++;
r[rcnt].cnt = cnt;
while (cnt >= 2 and (b[cnt] - b[cnt - 1]) * (a0 - a[cnt]) <=
(b0 - b[cnt]) * (a[cnt] - a[cnt - 1]))
cnt--;
cnt++;
r[rcnt].i = cnt;
r[rcnt].a = a[cnt];
r[rcnt].b = b[cnt];
a[cnt] = a0;
b[cnt] = b0;
}
void undo() {
cnt = r[rcnt].cnt;
a[r[rcnt].i] = r[rcnt].a;
b[r[rcnt].i] = r[rcnt].b;
rcnt--;
}
lint f(int i, lint x) { return a[i] * x + b[i]; }
lint query(lint x) {
if (cnt == 0) return 0;
int l = 0, r = cnt;
while (l + 1 < r) {
int m = (l + r) / 2;
if (f(m, x) > f(m + 1, x))
l = m;
else
r = m;
}
return a[r] * x + b[r];
}
} t;
int N;
lint dep[100004], s[100004], v[100004], dp[100004];
vector<pint> g[100004];
void dfs0(int x, int p) {
for (auto [y, w] : g[x])
if (y != p) {
dep[y] = dep[x] + w;
dfs0(y, x);
}
}
void dfs(int x, int p) {
dp[x] = t.query(v[x]) + s[x] + dep[x] * v[x];
t.update(-dep[x], dp[x]);
for (auto [y, w] : g[x])
if (y != p) {
dfs(y, x);
}
t.undo();
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
cin >> N;
for (int i = 1; i < N; i++) {
int x, y, w;
cin >> x >> y >> w;
g[x].emplace_back(y, w);
g[y].emplace_back(x, w);
}
for (int i = 2; i <= N; i++) cin >> s[i] >> v[i];
dfs0(1, 1);
dfs(1, 1);
for (int i = 2; i <= N; i++) cout << dp[i] << ' ';
cout << '\n';
}
