#include <bits/stdc++.h>
#define all(x) begin(x), end(x)
using namespace std;
using ll = long long;
const char nl = '\n', sp = ' ';
const int N = 1e5 + 9;
struct Line {
ll m, c;
ll eval(ll x) {
return m * x + c;
}
};
struct LiChaoNode {
Line line;
int l, r;
LiChaoNode() {
line = Line({0, numeric_limits<long long>::max() / 2});
l = 0, r = 0;
}
LiChaoNode(Line line) : line(line), l(0), r(0) {
}
} t[15 * N]; // change if needed?
int T;
int upd(int pre, Line nw, int l, int r) {
int m = (l + r) / 2;
int id = ++T;
t[id].line = t[pre].line;
bool lef = nw.eval(l) < t[id].line.eval(l);
bool mid = nw.eval(m) < t[id].line.eval(m);
if (mid) swap(t[id].line, nw);
if (l == r) return id;
if (lef != mid) {
if (!t[pre].l) t[id].l = ++T, t[T] = LiChaoNode(nw);
else t[id].l = upd(t[pre].l, nw, l, m);
t[id].r = t[pre].r;
} else {
if (!t[pre].r) t[id].r = ++T, t[T] = LiChaoNode(nw);
else t[id].r = upd(t[pre].r, nw, m + 1, r);
t[id].l = t[pre].l;
}
return id;
}
ll Query(int cur, int x, int l, int r) {
ll val = t[cur].line.eval(x);
int m = (l + r) / 2;
if (l < r) {
if (x <= m && t[cur].l) val = min(val, Query(t[cur].l, x, l, m));
if (x > m && t[cur].r) val = min(val, Query(t[cur].r, x, m + 1, r));
}
return val;
}
struct PersistentLiChaoTree {
int L, R;
vector<int> roots;
PersistentLiChaoTree() {
roots = {1};
T = 1;
L = -1e9;
R = 1e9;
}
PersistentLiChaoTree(int L, int R) : L(L), R(R) {
T = 1;
roots.push_back(1);
}
int add_line(int i, Line line) {
int root = upd(roots[i], line, L, R);
roots.push_back(root);
return root;
}
ll query(int i, int x) {
return Query(roots[i], x, L, R);
}
};
const int inf = 1e15;
void solve() {
int n;
cin >> n;
vector<vector<pair<int, int> > > g(n);
for (int i = 0; i < n - 1; i++) {
int u, v, w;
cin >> u >> v >> w;
--u, --v;
g[u].emplace_back(v, w);
g[v].emplace_back(u, w);
}
vector<pair<int, int> > a(n);
for (int i = 1; i < n; i++) {
cin >> a[i].first >> a[i].second;
}
PersistentLiChaoTree lc(0, 1e9 + 1);
vector<int> ans(n);
vector<int> versions(n);
lc.add_line(0, {0, 0});
versions[0] = 1;
vector<int> cost(n);
int cnt = 1;
auto dfs = [&](auto &&dfs, int u, int p, int d) -> void {
auto &[s, v] = a[u];
if (u != 0) {
cost[u] = lc.query(versions[p], v) + s + v * d;
lc.add_line(versions[p], {-d, cost[u]});
versions[u] = ++cnt;
}
for (auto &[v, w]: g[u]) {
if (v == p) continue;
dfs(dfs, v, u, d + w);
}
};
dfs(dfs, 0, -1, 0);
for (int i = 1; i < n; i++) {
cout << cost[i] << sp;
}
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
#ifdef LOCAL
freopen("../in.txt", "r", stdin);
freopen("../out.txt", "w", stdout);
#endif
int t = 1;
// cin >> t;
while (t--) {
solve();
}
}
