#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pii pair<int,int>
#define tt tuple<int,int,int>
#define NMAX 100005
#define INF 1e16
#define MOD 998244353
#define faster ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
vector<pii> g[NMAX];
int s[NMAX], t[NMAX], dist[NMAX], dp[NMAX];
int hull[NMAX];
int ptr;
double intersecx(int i, int j) {
return 1.0 * (dp[i] - dp[j]) / (dist[i] - dist[j]);
}
void DFS(int v, int pai) {
int aux = 0, sz = ptr;
if(v != 1) {
int l = 0, r = ptr-1;
while(l < r) {
int q = (r-l) / 3;
int m1 = l+q, m2 = r-q;
if(dp[hull[m1]] - dist[hull[m1]]*t[v] < dp[hull[m2]] - dist[hull[m2]]*t[v])
r = m2-1;
else l = m1+1;
}
dp[v] = dp[hull[r]] + (dist[v] - dist[hull[r]]) * t[v] + s[v];
l = 1, r = ptr;
while(l < r) {
int m = (l+r) / 2;
int j = hull[m], k = hull[m-1];
if(intersecx(v, j) < intersecx(j, k))
r = m;
else l = m+1;
}
aux = hull[r];
hull[r] = v;
ptr = r+1;
}
else {
hull[0] = 1;
ptr = 1;
}
for(auto [u, d] : g[v]) {
if(u == pai) continue;
dist[u] = dist[v] + d;
DFS(u, v);
}
hull[ptr-1] = aux;
ptr = sz;
}
int32_t main(){ faster
int n;
cin>>n;
for(int i = 1; i < n; 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>>s[i]>>t[i];
}
DFS(1, 0);
for(int i = 2; i <= n; i++) {
cout<<dp[i]<<" ";
}
cout<<"\n";
}
/*
*/
