/*
author : sh1ft
created : 08/07/2025 07:50
task : CEOI09_harbingers
*/
#include <bits/stdc++.h>
#define ll long long
using namespace std;
const int mxN = 1e5+5;
int n;
ll q[mxN], a[mxN], b[mxN], dp[mxN];
vector <pair <int, ll>> adj[mxN];
vector <int> iter;
int cht[mxN];
void build(int u, int p) { for (auto &[v, w] : adj[u]) if (v != p) q[v] = q[u] + w, build(v, u); }
ll calc(ll x, int j) { return -q[j]*x + dp[j]; }
long double m(int x, int y) { return (long double) (calc(0, x) - calc(0, y))/((-q[y])-(-q[x])); }
int sz = 0;
int qr(ll x) {
int l = 0, r = sz-2, idx = sz-1;
while (l <= r) {
int mid = l + (r-l)/2;
if (m(cht[mid], cht[mid+1]) <= x) l = mid+1;
else r = mid-1, idx = mid;
}
return cht[idx];
}
int add(int x) {
int l = 0, r = sz-2, idx = sz;
while (l <= r) {
int mid = l + (r-l)/2;
if (m(cht[mid+1], x) <= m(cht[mid], cht[mid+1])) r = mid-1, idx = mid+1;
else l = mid+1;
}
return idx;
}
void dfs(int u, int p) {
for (auto [v, w] : adj[u]) if (v != p) {
vector <int> del;
int idx = qr(a[v]);
dp[v] = calc(a[v], idx) + q[v]*a[v] + b[v];
int ida = add(v);
int tmp = cht[ida], tsz = sz;
cht[ida] = v;
sz = ida+1;
dfs(v, u);
cht[ida] = tmp;
sz = tsz;
}
}
int main() {
ios::sync_with_stdio(0), cin.tie(0);
cin >> n; iter.resize(n+10); iota(iter.begin(), iter.end(), 0);
for (int i = 1; i < n; i++) { int u, v; ll w; cin >> u >> v >> w; adj[u].emplace_back(v, w); adj[v].emplace_back(u, w); }
build(1, 1);
for (int i = 2; i <= n; i++) cin >> b[i] >> a[i];
cht[0] = 1; sz++;
dfs(1, 1);
for (int i = 2; i <= n; i++) cout << dp[i] << ' '; cout << '\n';
}
/*
dp[i] = min(dp[j] + (p[i] - p[j])*a[i] + b[i])
= min(dp[j] + p[i]*a[i] - p[j]*a[i] + b[i])
= p[i]*a[i] + b[i] + min(-p[j]*a[i] + dp[j])
*/
