#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; }
long double inter(Line other) { return (long double)(other.b - b) / (m - other.m); }
};
struct CHT {
v<Line> dq;
struct History {
int idx, sz;
Line old;
};
History insert(Line add) {
int l = 1, r = dq.size() - 1;
int pos = dq.size();
while (l <= r) {
int mid = l + (r - l) / 2;
if (dq[mid - 1].inter(dq[mid]) >= dq[mid - 1].inter(add)) {
pos = mid;
r = mid - 1;
} else {
l = mid + 1;
}
}
History h = {pos, (int)dq.size(), {0, 0}};
if (pos < dq.size())
h.old = dq[pos];
if (pos < dq.size())
dq[pos] = add;
else
dq.push_back(add);
dq.resize(pos + 1);
return h;
}
void rollback(History h) {
dq.resize(h.sz);
if (h.idx < h.sz)
dq[h.idx] = h.old;
}
ll query(ll x) {
if (dq.empty())
return 0;
int l = 0, r = dq.size() - 2;
int idx = dq.size() - 1;
while (l <= r) {
int mid = l + (r - l) / 2;
if (dq[mid].inter(dq[mid + 1]) >= x) {
idx = mid;
r = mid - 1;
} else {
l = mid + 1;
}
}
return dq[idx].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] << " "; }
}
