#include <bits/stdc++.h>
#define ll long long
using namespace std;
const int NMAX = 1e5;
const ll INF = 1e18;
int n;
ll dp[NMAX + 1];
ll sp[NMAX + 1];
int st[NMAX + 1], v[NMAX + 1];
vector<pair<int, int>> g[NMAX + 1];
int parent[NMAX + 1];
ll get_dp(int node) {
ll mini = INF;
int dad = parent[node];
while(dad != 0) {
mini = min(mini, dp[dad] - sp[dad] * v[node]);
dad = parent[dad];
}
return st[node] + sp[node] * v[node] + mini;
}
void DFS(int node, int dad = 0) {
parent[node] = dad;
if(node != 1) {
dp[node] = get_dp(node);
}
for(auto [next_node, c] : g[node]) {
if(next_node != dad) {
sp[next_node] = sp[node] + c;
DFS(next_node, node);
}
}
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cin >> n;
for(int i = 1; i <= n - 1; i++) {
int a, b, c;
cin >> a >> b >> c;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
for(int i = 2; i <= n; i++) {
cin >> st[i] >> v[i];
}
DFS(1);
for(int i = 2; i <= n; i++) {
cout << dp[i] << ' ';
}
return 0;
}
