#include <unordered_map>
#include <iostream>
#include <vector>
using namespace std;
#define ll long long
#define ld long double
#define li pair <ll, int>
#define ii pair <int, int>
#define lxl pair <ii, line>
#define fi first
#define se second
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;
}
int slope() {return x;}
ll get(ll z) {
if (x == -INF) return INF;
return x * z + y;
}
};
ld intersect(line x, line y) {
return 1.0l * (x.y - y.y) / (1.0l * (y.x - x.x));
}
struct CHT {
vector <lxl> his;
vector <line> lines;
int sz;
CHT () {
sz = 0;
his.clear();
lines.resize(N);
}
void update(line f) {
int l = 1, r = sz - 1, need = sz;
while (l <= r) {
int m = (l + r) >> 1;
if (intersect(f, lines[m - 1]) <= intersect(lines[m - 1], lines[m])) {
need = m;
r = m - 1;
} else {
l = m + 1;
}
}
his.push_back(lxl(ii(sz, need), lines[need]));
sz = need + 1;
lines[need] = f;
}
ll get(int val) {
int l = 0, r = sz - 1;
while (l < r) {
int m = (l + r) >> 1;
if (lines[m].get(val) >= lines[m + 1].get(val)) l = m + 1;
else r = m;
}
return lines[l].get(val);
}
lxl cur;
void roll() {
cur = his.back(); his.pop_back();
sz = cur.fi.fi;
lines[cur.fi.se] = cur.se;
}
} cht;
ll dp[N];
void DFS(int s = 1, int p = -1, ll h = 0) {
if (s != 1) dp[s] = a[s] + v[s] * h + cht.get(v[s]);
cht.update(line(-h, dp[s]));
for (li z: g[s]) {
if (z.se == p) continue;
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;
}
