#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb push_back
#define sz(x) (int)x.size()
#define all(x) begin(x),end(x)
#define lb(x,y) lower_bound(all(x),y)-begin(x)
mt19937 rng;
struct Line {
mutable ll k, m, p;
bool operator<(const Line& o) const { return k < o.k; }
bool operator<(ll x) const { return p < x; }
};
struct LineContainer : multiset<Line, less<>> {
// (for doubles, use inf = 1/.0, div(a,b) = a/b)
static const ll inf = LLONG_MAX;
ll div(ll a, ll b) { // floored division
return a / b - ((a ^ b) < 0 && a % b); }
bool isect(iterator x, iterator y) {
if (y == end()) return x->p = inf, 0;
if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
else x->p = div(y->m - x->m, x->k - y->k);
return x->p >= y->p;
}
void add(ll k, ll m) {
auto z = insert({k, m, 0}), y = z++, x = y;
while (isect(y, z)) z = erase(z);
if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
while ((y = x) != begin() && (--x)->p >= y->p)
isect(x, erase(y));
}
ll query(ll x) {
assert(!empty());
auto l = *lower_bound(x);
return l.k * x + l.m;
}
};
vector<vector<pair<int, int>>> adj;
LineContainer lc;
vector<ll> res;
vector<int> s, v;
vector<bool> vis;
void dfs(int u, int p) {
vis[u] = true;
if (u > 0) {
res[u] = -lc.query(v[u]) + s[u] + (ll)v[u] * p;
lc.add(p, -res[u]);
}
for (auto &edge : adj[u]) {
int v = edge.first, k = edge.second;
if (vis[v]) continue;
//int t = lc.getTime();
dfs(v, p + k);
//lc.setTime(t);
}
}
void solve() {
int N; cin >> N;
adj = vector<vector<pair<int, int>>>(N);
for (int i = 0; i < N - 1; i++) {
int u, v, k; cin >> u >> v >> k; u--; v--;
adj[u].pb({v, k});
adj[v].pb({u, k});
}
s = vector<int>(N);
v = vector<int>(N);
for (int i = 1; i < sz(s); i++) cin >> s[i] >> v[i];
lc.add(0, 0);
res = vector<ll>(N);
vis = vector<bool>(N, 0);
dfs(0, 0);
for (int i = 1; i < sz(res); i++) {
cout << res[i] << (i == sz(res) - 1 ? "\n" : " ");
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
rng = mt19937(chrono::steady_clock::now().time_since_epoch().count());
solve();
/*int N = 200000;
cout << N << "\n";
for (int i = 1; i < N; i++) {
int p = rng() % i;
cout << (p + 1) << " " << (i + 1) << " " << (rng() % 1000000) << "\n";
}
for (int i = 0; i < N; i++) {
cout << (rng() % 1000000) << " " << (rng() % 1000000) << "\n";
}*/
return 0;
}
