#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
#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<pll> vpll;
typedef vector<vpll> vvpll;
typedef long double ld;
const ll INF = 1e15;
const ld eps = 1e-12;
struct Line {
ll m, b;
ll eval(ll x) const { return m * x + b; }
};
Line stk[200005];
int stk_max = 0;
inline long double intersect(const Line &l1, const Line &l2) {
return (long double)(l2.b - l1.b) / (long double)(l1.m - l2.m);
}
ll query(ll x) {
int l = 0, r = stk_max - 1;
while (l < r) {
int m = (l + r) >> 1;
if (intersect(stk[m], stk[m + 1]) < x)
l = m + 1;
else
r = m;
}
return stk[l].eval(x);
}
int remove_pos(const Line &l) {
if (stk_max < 2 ||
intersect(l, stk[stk_max - 1]) >=
intersect(stk[stk_max - 1], stk[stk_max - 2]))
return stk_max;
int lpos = 1, rpos = stk_max - 1;
while (lpos < rpos) {
int m = (lpos + rpos) >> 1;
if (intersect(l, stk[m]) <
intersect(stk[m], stk[m - 1]))
rpos = m;
else
lpos = m + 1;
}
return lpos;
}
vvpll adj;
vll ans;
vpll har;
void dfs(int u, int p = -1, ll d = 0) {
int prev_max = stk_max;
Line prev_line;
if (u == 0) {
stk[stk_max++] = {0, 0};
} else {
auto [s, t] = har[u];
ans[u] = query(t) + s + t * d;
Line nl = {-d, ans[u]};
int pos = remove_pos(nl);
prev_line = stk[pos];
stk_max = pos;
stk[stk_max++] = nl;
}
for (auto [v, w] : adj[u]) {
if (v == p) continue;
dfs(v, u, d + w);
}
stk_max = prev_max;
if (u != 0) stk[remove_pos({-d, ans[u]})] = prev_line;
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
int n;
cin >> n;
adj.assign(n, {});
REP(i, n - 1) {
int u, v, w;
cin >> u >> v >> w;
u--, v--;
adj[u].pushb(mp(v, w));
adj[v].pushb(mp(u, w));
}
har.assign(n, {});
ans.assign(n, 0);
REP(i, 1, n) cin >> har[i].fir >> har[i].sec;
dfs(0);
REP(i, 1, n) cout << ans[i] << ' ';
cout << '\n';
}
