#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
#define ff first
#define ss second
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define lb lower_bound
#define int ll
struct Line{
int m, c;
Line(int m = 0, int c = 0) : m(m), c(c) {}
int calc(int x) { return m * x + c; }
};
ld intX(Line A, Line B) {
return (ld)(B.c - A.c) / (ld)(A.m - B.m);
}
int N, S[100005], V[100005], DP[100005];
vector<array<int, 2>> adj[100005];
Line hull[100005]; int st = 0;
int query(int v) {
int lo = 0, hi = st - 1;
while(lo < hi) {
int md = (lo + hi) / 2;
if(intX(hull[md], hull[md + 1]) < v)
lo = md + 1;
else hi = md;
}
return hull[lo].calc(v);
}
int update(Line i) {
if(st < 2 || intX(i, hull[st - 1]) >= intX(hull[st - 1], hull[st - 2]))
return st;
int lo = 1, hi = st - 1;
while(lo < hi) {
int md = (lo + hi) / 2;
if(intX(i, hull[md]) < intX(hull[md], hull[md - 1]))
hi = md;
else lo = md + 1;
}
return lo;
}
void solve(int v, int p, int d) {
int prev_size, prev_pos;
Line prev_line;
if(v == 1) {
DP[v] = 0;
hull[st++] = {0, 0};
}
else {
DP[v] = query(S[v]) + d * S[v] + V[v];
Line i(-d, DP[v]);
prev_size = st;
prev_pos = st = update(i);
prev_line = hull[st];
hull[st++] = i;
}
for(auto u : adj[v]) {
if(u[0] == p) continue;
solve(u[0], v, d + u[1]);
}
if(v != 1) {
st = prev_size;
hull[prev_pos] = prev_line;
}
}
int32_t main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
cin >> N; memset(DP, -1, sizeof DP);
for(int l = 0; l < N - 1; l++) {
int U, V, C; cin >> U >> V >> C;
adj[U].push_back({V, C});
adj[V].push_back({U, C});
}
for(int l = 2; l <= N; l++)
cin >> V[l] >> S[l];
solve(1, 1, 0);
for(int l = 2; l <= N; l++)
cout << DP[l] << " ";
return 0;
}
