#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define v vector
#define lp(i, s, e) for (int i = s; i < e; ++i)
struct Line {
ll m, b;
ll f(ll x) { return m * x + b; }
};
struct CHT {
v<Line> dq;
struct History {
int idx, sz;
Line old;
v<Line> removed;
bool changed;
bool replaced;
};
bool bad(Line l1, Line l2, Line l3) {
__int128 left = (__int128)(l3.b - l1.b) * (__int128)(l1.m - l2.m);
__int128 right = (__int128)(l2.b - l1.b) * (__int128)(l1.m - l3.m);
return left <= right;
}
History insert(Line add) {
History h;
h.idx = 0;
h.sz = dq.size();
h.old = {0, 0};
h.removed.clear();
h.changed = false;
h.replaced = false;
if (!dq.empty() && dq.back().m == add.m) {
if (dq.back().b <= add.b)
return h;
h.old = dq.back();
dq.pop_back();
h.removed.push_back(h.old);
h.changed = true;
h.replaced = true;
}
while (dq.size() >= 2 && bad(dq[dq.size() - 2], dq[dq.size() - 1], add)) {
h.removed.push_back(dq.back());
dq.pop_back();
h.changed = true;
}
dq.push_back(add);
h.changed = true;
return h;
}
void rollback(History h) {
if (!h.changed)
return;
dq.pop_back();
for (int i = h.removed.size() - 1; i >= 0; --i)
dq.push_back(h.removed[i]);
}
ll query(ll x) {
if (dq.empty())
return 0;
int l = 0, r = dq.size() - 1;
while (l < r) {
int mid = (l + r) / 2;
if (dq[mid].f(x) >= dq[mid + 1].f(x))
l = mid + 1;
else
r = mid;
}
return dq[l].f(x);
}
};
v<ll> dp, dpt;
ll n;
#define pll pair<ll, ll>
v<pll> kn;
v<v<pll>> g;
void dfs(int node, int par, CHT &cht) {
auto h = cht.insert({-dpt[node], dp[node]});
for (auto [it, c] : g[node]) {
if (it == par)
continue;
dpt[it] = dpt[node] + c;
dp[it] = kn[it].first + kn[it].second * dpt[it] + cht.query(kn[it].second);
dfs(it, node, cht);
}
cht.rollback(h);
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n;
g.resize(n);
dp.resize(n);
kn.resize(n);
dpt.resize(n);
lp(i, 1, n) {
int a, b;
ll w;
cin >> a >> b >> w;
a--;
b--;
g[a].push_back({b, w});
g[b].push_back({a, w});
}
lp(i, 1, n) { cin >> kn[i].first >> kn[i].second; }
CHT cht;
dpt[0] = 0;
dp[0] = 0;
dfs(0, -1, cht);
lp(i, 1, n) { cout << dp[i] << " "; }
}
