#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include "debug.h"
#else
#define debug(...) 42
#endif
struct line {
long long a, b;
long long div(long long a, long long b) {
return a / b - ((a ^ b) < 0 && a % b);
}
long long slope(const line &o) {
return div(o.b - b, a - o.a);
}
long long eval(long long x) {
return a * x + b;
}
};
const int N = 1e5 + 5;
int n, top;
int S[N], V[N];
long long dp[N];
line st[N];
vector<pair<int, line>> his;
vector<array<int, 2>> g[N];
void add(line x) {
int l = 2, r = top, res = top + 1;
while (l <= r) {
int m = (l + r) / 2;
if (st[m - 1].slope(st[m]) >= st[m].slope(x)) {
res = m;
r = m - 1;
} else {
l = m + 1;
}
}
his.push_back({top, st[res]});
st[top = res] = x;
}
long long qry(long long x) {
int l = 2, r = top, p = 1;
while (l <= r) {
int m = (l + r) / 2;
if (st[m - 1].slope(st[m]) < x) {
p = m;
l = m + 1;
} else {
r = m - 1;
}
}
return st[p].eval(x);
}
void dfs(int u, int p = 0, long long dep = 0) {
if (u ^ 1) {
dp[u] = qry(V[u]) + dep * V[u] + S[u];
}
add({-dep, dp[u]});
for (auto [v, w] : g[u]) {
if (v ^ p) {
dfs(v, u, dep + w);
}
}
auto [x, l] = his.back(); his.pop_back();
st[top] = l;
top = x;
}
int main() {
ios::sync_with_stdio(false); cin.tie(nullptr);
cin >> n;
for (int i = 1; i < n; ++i) {
int u, v, d; cin >> u >> v >> d;
g[u].push_back({v, d});
g[v].push_back({u, d});
}
for (int i = 2; i <= n; ++i) {
cin >> S[i] >> V[i];
}
dfs(1);
for (int i = 2; i <= n; ++i) {
cout << dp[i] << " ";
}
return 0;
}
