#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using pll = pair<ll, ll>;
const int MAXN = 1e5 + 1;
struct Line {
ll m, b;
Line(ll m = 0, ll b = 0) : m(m), b(b) {}
ll operator()(ll x) { return m * x + b; }
friend ld intersect(Line l1, Line l2) {
return (ld)(l2.b - l1.b) / (ld)(l1.m - l2.m);
}
~Line() {}
};
int N;
ll S[MAXN], V[MAXN], dp[MAXN];
vector<pll> T[MAXN];
Line stk[MAXN];
int stk_max = 0;
ll line_min(ll x) {
int l = 0, r = stk_max - 1;
while (l < r) {
int m = (l + r) / 2;
if (intersect(stk[m], stk[m + 1]) < x)l = m + 1;
else r = m;
}
return stk[l](x);
}
ll remove_pos(Line line) {
if (stk_max < 2 || intersect(line, stk[stk_max - 1]) >= intersect(stk[stk_max - 1], stk[stk_max - 2])) return stk_max;
int l = 1, r = stk_max - 1;
while (l < r) {
int m = (l + r) / 2;
if (intersect(line, stk[m]) < intersect(stk[m], stk[m - 1])) r = m;
else l = m + 1;
}
return l;
}
void dfs(int u = 1, int p = 0, ll d = 0) {
int prev_max, prev_pos;
Line prev_line;
if (u == 1) {
dp[u] = 0;
stk[stk_max++] = {0, 0};
} else {
dp[u] = line_min(V[u]) + d * V[u] + S[u];
Line l(-d, dp[u]);
prev_max = stk_max;
prev_pos = stk_max = remove_pos(l);
prev_line = stk[stk_max];
stk[stk_max++] = l;
}
for (auto [v, w] : T[u]) if (v != p) dfs(v, u, d + w);
if (u != 1) {
stk_max = prev_max;
stk[prev_pos] = prev_line;
}
}
int main() {
cin >> N;
for (int i = 1; i < N; i++) {
int u, v, w;
cin >> u >> v >> w;
T[u].emplace_back(v, w);
T[v].emplace_back(u, w);
}
for (int i = 2; i <= N; i++) cin >> S[i] >> V[i];
dfs();
for (int i = 2; i <= N; i++) cout << dp[i] << ' ';
cout << '\n';
}
