#include <unordered_map>
#include <iostream>
#include <vector>
using namespace std;
#define ll long long
#define li pair <ll, int>
#define fi first
#define se second
#define lxl pair <line*, line>
const int N = 1e5 + 10;
const ll INF = 9e18;
int n, x, y, mxv;
int a[N], v[N], w;
vector <li> g[N];
struct line {
ll x, y;
line () {
x = -INF;
y = INF;
}
line (ll X, ll Y) {
x = X;
y = Y;
}
ll slope() {return x;}
ll get(ll z) {
if (x == -INF) return INF;
return x * z + y;
}
};
struct lichao {
vector <int> sz;
vector <lxl> his;
unordered_map < int, line > mp;
lichao() {
sz.clear();
his.clear();
mp.clear();
}
void update(int l, int r, line f) {
int m = (l + r) >> 1;
if (mp[m].get(m) > f.get(m)) {
his.push_back(lxl(&mp[m], mp[m]));
swap(mp[m], f);
}
if (l == r) return;
if (f.slope() > mp[m].slope()) update(l, m, f);
if (f.slope() < mp[m].slope()) update(m + 1, r, f);
}
void call_update(int l, int r, line f) {
sz.push_back(his.size());
update(l, r, f);
}
ll get(int l, int r, int u) {
int m = (l + r) >> 1;
ll cur = mp[m].get(u);
if (l == r) return cur;
if (u <= m) return min(cur, get(l, m, u));
return min(cur, get(m + 1, r, u));
}
void roll() {
while (his.size() > sz.back()) {
lxl 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, ll 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] * (h + z.fi) + CHT.get(1, mxv, v[z.se]);
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;
}
