/// [_DukkSooCee3305_]
/// Date : 05/10/2021
#include <bits/stdc++.h>
using namespace std;
#define FOR(i, a, b) for(int i = (a); i <= (b); ++i)
#define FORD(i, a, b) for(int i = (a); i >= (b); --i)
#define ALL(i_) i_.begin(), i_.end()
#define Random(lf_, rt_) (lf_ + rand() % (rt_ - lf_ + 1))
#define PB push_back
#define sz(i_) ((int)(i_).size())
#define reset(i_, x_) memset(i_, x_, sizeof i_)
#define TASK "HARBINGERS"
typedef long long ll;
typedef long double ld;
typedef pair<int, ll> ii;
const int oo = 1000000099;
const int mod = 1000000007;
const int maxn = 100011;
int n;
vector<ii> ke[maxn];
ll s[maxn], v[maxn], dp[maxn], d[maxn];
bool vs[maxn];
namespace process{
void DFS(int u, int par){
if(u > 1){
dp[u] = oo;
FOR(p, 1, n){
if(!vs[p]) continue;
dp[u] = min(dp[u], dp[p] + s[u] + v[u] * (d[u] - d[p]));
}
}
vs[u] = 1;
for(auto x : ke[u]){
int v = x.first;
ll w = x.second;
if(v == par) continue;
d[v] = d[u] + w;
DFS(v, u);
}
vs[u] = 0;
}
void solve(){
dp[1] = 0;
d[1] = 0;
DFS(1, -1);
FOR(i, 2, n) cout << dp[i] << " ";
}
}
int main(){
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
cin >> n;
FOR(i, 1, n-1){
int u, v;
ll w;
cin >> u >> v >> w;
ke[u].PB({v, w});
ke[v].PB({u, w});
}
FOR(i, 2, n) cin >> s[i] >> v[i];
process::solve();
return 0;
}
