#include <unordered_map>
#include <iostream>
#include <vector>
using namespace std;
#define ll long long
#define li pair <int, int>
#define fi first
#define se second
#define lxl pair <line*, line>
const int N = 1e5 + 10;
const ll INF = 9e18;
const int INT = 2e9;
int n, x, y, mxv;
int a[N], v[N], w;
vector <li> g[N];
struct line {
ll y;
int x;
line () {
x = -INT;
y = INF;
}
line (int X, ll Y) {
x = X;
y = Y;
}
int slope() {return x;}
ll get(int z) {
if (x == -INF) return INF;
return 1ll * x * z + y;
}
};
struct lichao {
struct node {
node *l, *r;
line f;
node () {
l = r = nullptr;
f = line();
}
};
vector <int> sz;
vector <lxl> his;
node *root;
lichao() {
sz.clear();
his.clear();
root = new node();
}
void update(int l, int r, line f, node *cur) {
int m = (l + r) >> 1;
if (cur->f.get(m) > f.get(m)) {
his.push_back(lxl(&cur->f, cur->f));
swap(cur->f, f);
}
if (l == r) return;
if (f.slope() > cur->f.slope()) {
if (cur->l == nullptr) cur->l = new node();
update(l, m, f, cur->l);
}
if (f.slope() < cur->f.slope()) {
if (cur->r == nullptr) cur->r = new node();
update(m + 1, r, f, cur->r);
}
}
void call_update(int l, int r, line f) {
sz.push_back(his.size());
update(l, r, f, root);
}
ll get(int l, int r, int u, node *cur) {
if (cur == nullptr) return INF;
int m = (l + r) >> 1;
ll VAL = cur->f.get(u);
if (l == r) return VAL;
if (u <= m) return min(VAL, get(l, m, u, cur->l));
return min(VAL, get(m + 1, r, u, cur->r));
}
lxl cur;
void roll() {
while (his.size() > sz.back()) {
cur = his.back();
*cur.fi = cur.se;
his.pop_back();
}
sz.pop_back();
}
} CHT;
ll dp[N];
void DFS(int s = 1, int p = -1, int h = 0) {
CHT.call_update(1, mxv, line(-h, dp[s]));
for (li z: g[s]) {
if (z.se == p) continue;
dp[z.se] = a[z.se] + v[z.se] * 1ll * (h + z.fi) + CHT.get(1, mxv, v[z.se], CHT.root);
DFS(z.se, s, h + z.fi);
}
CHT.roll();
}
int main() {
cin.tie(0); cout.tie(0);
ios_base::sync_with_stdio(false);
cin >> n;
for (int i = 1; i < n; ++i) {
cin >> x >> y >> w;
g[x].push_back(li(w, y));
g[y].push_back(li(w, x));
}
for (int i = 2; i <= n; ++i) {
cin >> a[i] >> v[i];
mxv = max(mxv, v[i]);
}
DFS();
for (int i = 2; i <= n; ++i) {
cout << dp[i] << " ";
}
return 0;
}
