#include<iostream>
#include<cstdio>
#include<string>
#include<vector>
#include<cstring>
#include<algorithm>
#include<set>
using namespace std;
typedef long long ll;
const int MAXN = 100002;
const int MOD = 1000000007;
struct path {
int t;
ll d;
};
int n;
vector<path> adj[MAXN];
int si[MAXN], vi[MAXN];
ll ans[MAXN];
path anc[MAXN];
void dfs1(int x, int p) {
for (path v : adj[x]) {
if (v.t == p) {
anc[x] = v;
} else {
dfs1(v.t, x);
}
}
}
void dfs2(int x, int p) {
ll dist = anc[x].d;
int bi = p;
ll best = si[x]+dist*vi[x]+ans[bi];
do {
dist += anc[bi].d;
bi = anc[bi].t;
best = min(best, si[x]+dist*vi[x]+ans[bi]);
} while (bi != 1);
ans[x] = best;
for (path v : adj[x]) {
if (v.t != p) dfs2(v.t, x);
}
}
int main() {
ios_base::sync_with_stdio(0); cin.tie(0);
cin >> n;
for (int i = 0; i < n-1; i++) {
int u, v, d; cin >> u >> v >> d;
adj[u].push_back({v, d});
adj[v].push_back({u, d});
}
for (int i = 2; i <= n; i++) {
cin >> si[i] >> vi[i];
}
dfs1(1, 1);
anc[1] = {1, 0};
dfs2(1, 1);
for (int i = 2; i <= n; i++) cout << ans[i] << " ";
}
