#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using line = pair<ll, ll>;
#define m first
#define b second
template <class a, class b> ostream& operator<<(ostream &l, const pair<a, b> &r) {
l << "(" << r.first << ", " << r.second << ")";
return l;
}
template <class t, unsigned long int s> ostream& operator<<(ostream &l, const array<t, s> &r) {
l << "[";
for (int i = 0; i + 1 < s; i++) l << r[i] << ", ";
if (s > 0) l << r[s - 1];
l << "]";
return l;
}
template <class t> ostream& operator<<(ostream &l, const vector<t> &r) {
l << "{";
for (int i = 0; i + 1 < r.size(); i++) l << r[i] << ", ";
if (!r.empty()) l << r.back();
l << "}";
return l;
}
ll fdiv(ll a, ll b) {
return a / b - ((a ^ b) < 0 && (a % b));
}
ll inter(const line &l, const line &r) {
return fdiv(l.b - r.b, r.m - l.m);
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n;
cin >> n;
vector<vector<pair<int, int>>> adj(n);
for (int i = 1; i < n; i++) {
int a, b, c;
cin >> a >> b >> c;
a--, b--;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
vector<int> s(n), t(n);
for (int i = 1; i < n; i++) {
cin >> s[i] >> t[i];
}
vector<ll> dp(n);
vector<line> dq(n);
dq[0] = {0, 0};
int size = 1;
auto qry = [&](ll x) -> ll {
int l = 0, r = size - 1;
while (l < r) {
int mi = (l + r) / 2;
if (inter(dq[mi], dq[mi + 1]) >= x) {
r = mi;
} else {
l = mi + 1;
}
}
return dq[l].m * x + dq[l].b;
};
auto ins = [&](const line &x) -> int {
// first spot where inter(x, dq[i + 1]) <= inter(dq[i], dq[i + 1])
int l = 0, r = size - 1;
while (l < r) {
int mi = (l + r) / 2;
if (inter(x, dq[mi + 1]) <= inter(dq[mi], dq[mi + 1])) {
r = mi;
} else {
l = mi + 1;
}
}
return l;
};
// dp[i] = s[i] + min_p(dp[p] + t[i] * (d[i] - d[p]))
// = s[i] + min_p(dp[p] - t[i] * d[p]) + t[i] * d[i]
// t[i] arbitrary -> queries arbitrary
// d[p] increases -> slope decreases
// negate both m and b -> flip across y axis -> query for min becomes max, lines inserted in increasing slope
auto dfs = [&](int v, int p, ll d, auto &&self) -> void {
int cp, sz;
line x;
if (p != -1) {
dp[v] = -qry(t[v]) + s[v] + d * t[v];
// where the line would go
x = {d, -dp[v]};
cp = ins(x) + 1;
swap(dq[cp], x);
sz = size + 1;
size = cp;
}
for (pair<int, int> &i : adj[v]) {
if (i.first != p) {
self(i.first, v, d + i.second, self);
}
}
if (p != -1) {
size = sz;
swap(dq[cp], x);
}
};
dfs(0, -1, 0, dfs);
for (int i = 1; i < n - 1; i++) {
cout << dp[i] << " ";
}
cout << dp[n - 1] << '\n';
}
