#include <bits/stdc++.h>
using namespace std;
const long INF = 1e18;
int n, s[100100], t[100100];
vector<pair<int, int>> g[100100];
int sz[100100];
void dfs_sz(int u) {
sz[u] = 1;
for (auto &p : g[u]) {
int v = p.first;
g[v].erase(find_if(g[v].begin(), g[v].end(), [&](auto a) {
return a.first == u;
}));
dfs_sz(v);
if (sz[v] > sz[g[u][0].first]) swap(p, g[u][0]);
sz[u] += sz[v];
}
}
long dp[100100];
struct Line {
long m, c;
long operator()(long x) { return m * x + c; }
};
long intersect(Line a, Line b) {
long num = b.c - a.c, dem = a.m - b.m;
return num / dem - ((num ^ dem) < 0 && num % dem);
}
vector<pair<long, Line>> cht{{-INF, {0, 0}}};
vector<Line> st;
long query(long x) {
long ret = prev(lower_bound(cht.begin(), cht.end(), pair{x, Line{}}, [&](auto a, auto b) {
return a.first < b.first;
}))->second(x);
for (auto u : st) ret = max(ret, u(x));
return ret;
}
void dfs(int u, long cd, bool heavy) {
vector<Line> popped;
if (u != 1) {
dp[u] = -query(t[u]) + cd * t[u] + s[u];
auto l = Line{cd, -dp[u]};
if (heavy) {
while ((int) cht.size() >= 2) {
auto a = cht[cht.size() - 2].second;
auto b = cht[cht.size() - 1].second;
if (intersect(a, b) >= intersect(b, l)) {
popped.push_back(cht.back().second);
cht.pop_back();
} else break;
}
cht.emplace_back(intersect(cht.back().second, l), l);
} else {
st.push_back(l);
}
}
for (auto [v, d] : g[u]) {
dfs(v, cd + d, v == g[u][0].first);
}
if (u != 1) {
if (heavy) {
cht.pop_back();
while (!popped.empty()) {
cht.emplace_back(intersect(cht.back().second, popped.back()), popped.back());
popped.pop_back();
}
} else {
st.pop_back();
}
}
}
int main() {
scanf("%d", &n);
for (int i = 1, u, v, d; i <= n - 1; ++i) {
scanf("%d %d %d", &u, &v, &d);
g[u].emplace_back(v, d);
g[v].emplace_back(u, d);
}
for (int i = 2; i <= n; ++i) scanf("%d %d", s + i, t + i);
dfs_sz(1);
dfs(1, 0, 1);
for (int i = 2; i <= n; ++i) printf("%ld%c", dp[i], i == n ? '\n' : ' ');
}
// f_j(x) := -dp[j] + dep[j] * x
// dp[j] + (d - x) t_i + s_i
// = dp[j] - x * t_i + d * t_i + s_i
// = -f_j(t_i) + d * t_i + s_i
