#include <bits/stdc++.h>
using namespace std;
const int MAX = 1e5 + 5;
const long long inf = 1e18;
struct line{
long long a, b;
line() : a(0), b(0) {}
line(long long a, long long b) : a(a), b(b) {}
long long eval(long long x){ return a * x + b; }
};
long double isect(const line& d1, const line& d2){
return 1.0l * (d2.b - d1.b) / (d1.a - d2.a);
}
struct operation{
int top, pos;
line d;
operation(int top, int pos, line d) : top(top), pos(pos), d(d) {}
};
int top;
line v[MAX];
stack<operation> ops;
int N, S[MAX], V[MAX];
long long H[MAX], ans[MAX];
vector<pair<int, int>> adj[MAX];
void initial_dfs(int u, int p){
for(auto [v, w] : adj[u]) if(v != p){
H[v] = H[u] + w;
initial_dfs(v, u);
}
}
void insert(line d){
int l = 1, r = top - 1, change = top;
while(l <= r){
int mid = l + r >> 1;
if(isect(v[mid - 1], v[mid]) >= isect(v[mid - 1], d)){
change = mid;
r = mid - 1;
} else l = mid + 1;
}
ops.push(operation(top, change, v[change]));
top = change + 1;
v[change] = d;
}
void undo(){
assert(!ops.empty());
operation lst = ops.top(); ops.pop();
v[lst.pos] = lst.d;
top = lst.top;
}
long long query(long long x){
// long long ans = inf;
// cout << "query part : ";
// cout << " : " << "{\n";
// for(int i = 1; i <= top; ++i){
// cout << v[i].a << ' ' << v[i].b << '\n';
// }
// cout << "}\n";
// for(int i = 1; i <= top; ++i) ans = min(ans, v[i].eval(x));
// return ans;
int l = 0, r = top - 1;
while(l < r){
int mid = l + r >> 1;
if(v[mid].eval(x) >= v[mid + 1].eval(x)) l = mid + 1;
else r = mid;
}
return v[l].eval(x);
}
void solve(int u, int p){
if(u > 1){
ans[u] = S[u] + H[u] * V[u] + query(V[u]);
}
insert(line(-H[u], ans[u]));
// cout << u << " : " << "{\n";
// for(int i = 1; i <= top; ++i){
// cout << v[i].a << ' ' << v[i].b << '\n';
// }
// cout << "}\n";
for(auto [v, w] : adj[u]) if(v != p){
solve(v, u);
}
undo();
}
int main(){
ios_base::sync_with_stdio(0); cin.tie(0);
#ifdef LOCAL
freopen("task.inp", "r", stdin);
freopen("task.out", "w", stdout);
#endif //LOCAL
cin >> N;
for(int i = 1; i < N; ++i){
int u, v, w;
cin >> u >> v >> w;
adj[u].emplace_back(v, w);
adj[v].emplace_back(u, w);
}
for(int i = 2; i <= N; ++i) cin >> S[i] >> V[i];
initial_dfs(1, -1);
solve(1, -1);
for(int i = 2; i <= N; ++i) cout << ans[i] << ' ';
return 0;
}
