#include <bits/stdc++.h>
using namespace std;
#define MOD1 1000000007
#define MOD2 998244353
#define fir first
#define sec second
#define pushf push_front
#define pushb push_back
#define popf pop_front
#define popb pop_back
#define mp make_pair
#define all(a) a.begin(), a.end()
#define lbound(v, x) lower_bound(all(v), x) - v.begin()
#define ubound(v, x) upper_bound(all(v), x) - v.begin()
#define chmax(a, b) a = max(a, b)
#define chmin(a, b) a = min(a, b)
#define FOR1(a) for (int _ = 0; _ < (a); ++_)
#define FOR2(i, a) for (int i = 0; i < (a); ++i)
#define FOR3(i, a, b) for (int i = (a); i < (b); ++i)
#define RFOR1(a) for (int _ = (a)-1; _ >= 0; --_)
#define RFOR2(i, a) for (int i = (a)-1; i >= 0; --i)
#define RFOR3(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define overload3(a, b, c, d, ...) d
// Always choose the fourth argument to call. Hence, which function to call is determined by the number of given arguments.
#define REP(...) overload3(__VA_ARGS__, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define RREP(...) overload3(__VA_ARGS__, RFOR3, RFOR2, RFOR1)(__VA_ARGS__)
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef pair<ll, ll> pll;
typedef vector<ll> vll;
typedef vector<bool> vb;
typedef vector<char> vc;
typedef vector<string> vs;
typedef vector<pii> vpii;
typedef vector<pll> vpll;
typedef vector<vi> vvi;
typedef vector<vll> vvll;
typedef vector<vb> vvb;
typedef vector<vc> vvc;
typedef vector<vpii> vvpii;
typedef vector<vpll> vvpll;
typedef queue<int> qi;
typedef queue<ll> qll;
typedef queue<pii> qpii;
typedef queue<pll> qpll;
typedef deque<int> dqi;
typedef deque<ll> dqll;
typedef deque<pii> dqpii;
typedef deque<pll> dqpll;
typedef priority_queue<int> pqi;
typedef priority_queue<ll> pqll;
typedef priority_queue<pii> pqpii;
typedef priority_queue<pll> pqpll;
typedef priority_queue<int, vi, greater<int> > r_pqi;
typedef priority_queue<ll, vll, greater<ll> > r_pqll;
typedef priority_queue<pii, vpii, greater<pii> > r_pqpii;
typedef priority_queue<pll, vpll, greater<pll> > r_pqpll;
typedef long double ld;
const ll INF = 1e15;
const ld eps = 1e-10;
struct Line {
ll m, b;
ld xLeft;
ll eval(ll x) const {
return m * x + b;
}
};
vector<Line> hull;
stack<vector<Line>> history; // store previous hull states
ld intersectX(const Line &l1, const Line &l2) {
return (ld)(l1.b - l2.b) / (ld)(l2.m - l1.m);
}
void addLine(ll m, ll b) {
Line newL {m, b, 0.0L};
history.push(hull); // save the current hull before modification
if (hull.empty()) {
newL.xLeft = -1e30L;
hull.push_back(newL);
return;
}
while (true) {
Line &l = hull.back();
if (l.m == newL.m) {
if (l.b <= newL.b) return; // keep smaller b for min CHT
else hull.pop_back();
} else {
ld x = intersectX(l, newL);
if (x <= l.xLeft) hull.pop_back();
else break;
}
if (hull.empty()) break;
}
if (hull.empty()) newL.xLeft = -1e30L;
else newL.xLeft = intersectX(hull.back(), newL);
hull.push_back(newL);
}
void undo() {
if (!history.empty()) {
hull = history.top();
history.pop();
}
}
ll query(ll x) {
if (hull.empty()) return INF;
int low = 0, high = hull.size() - 1;
while (low < high) {
int mid = (low + high + 1) / 2;
if (hull[mid].xLeft - eps <= (ld)x) low = mid;
else high = mid - 1;
}
return hull[low].eval(x);
}
vvpll adj;
vll ans;
vpll har;
void dfs(int u, int p = -1, ll d = 0) {
if(u == 0) {
addLine(0, 0);
}
else {
auto [s, t] = har[u];
ans[u] = query(t) + s + t * d;
addLine(-d, ans[u]);
}
for(auto [v, w] : adj[u]) {
if(v == p) continue;
dfs(v, u, d + w);
}
undo();
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int n;
cin>>n;
adj = vvpll(n);
REP(i, n-1) {
int u, v, d;
cin>>u>>v>>d;
u--, v--;
adj[u].pushb(mp(v, d));
adj[v].pushb(mp(u, d));
}
har = vpll(n);
ans = vll(n);
REP(i, 1, n) {
cin>>har[i].fir>>har[i].sec;
}
dfs(0);
REP(i, 1, n) {
cout<<ans[i]<<' ';
}
}
