#include <bits/stdc++.h>
using namespace std;
#define F first
#define S second
typedef long long ll;
typedef pair<ll, ll> pii;
const ll N = 1e5 + 10;
ll n;
ll s[N], req[N], d[N], dp[N];
vector<pii> g[N];
vector<ll> path;
void dfs(ll v, ll p = -1){
path.push_back(v);
for (auto [w, u] : g[v]){
if (u == p) continue;
d[u] = d[v] + w;
dp[u] = 1e18;
for (ll x : path)
dp[u] = min(dp[u], dp[x] -s[u] * d[x] + s[u] * d[u] + req[u]);
dfs(u, v);
}
path.pop_back();
}
int main(){
cin >> n;
for (ll i = 0; i < n - 1; i ++){
ll u, v, w;
cin >> u >> v >> w;
g[u].push_back({w, v});
g[v].push_back({w, u});
}
for (ll i = 2; i <= n; i ++)
cin >> req[i] >> s[i];
dfs(1);
for (ll i = 2; i <= n; i ++)
cout << dp[i] << " ";
cout << endl;
}
