#include <bits/stdc++.h>
using namespace std;
#define Aboeldahab ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define ll long long
// #define int long long
#define ld long double
#define all(x) x.begin(),x.end()
#define mem(x, y) memset(x,y,sizeof x)
#define endl '\n'
const int dx8[8] = {0, 0, 1, -1, 1, -1, -1, 1};
const int dy8[8] = {1, -1, 0, 0, 1, -1, 1, -1};
const int dx[4] = {0, 0, 1, -1};
const int dy[4] = {1, -1, 0, 0};
char direction[4] = {'r', 'l', 'd', 'u'};
void READFILE() {
#ifndef ONLINE_JUDGE
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
freopen("errors.txt", "w", stderr);
#endif
}
const int inf = 1e9 + 5, N = 1e5 + 5, M = 5e3 + 1, MAX_X = 2001, LG = 15, mod =
1e9 + 7, p1 = 31, p2 = 37, SQ = 470;
const ll LLinf = 8e18;
struct PT {
ll x, y;
PT(ll x = 0, ll y = 0): x(x), y(y) {
}
friend ll dot(PT &a, PT &b) {
return 1ll * a.x * b.x + 1ll * a.y * b.y;
}
friend int orientation(PT &a, PT &b, PT &c) {
ll s = 1ll * (b.x - a.x) * (c.y - a.y) - 1ll * (b.y - a.y) * (c.x - a.x);
return (s > 0) - (s < 0);
}
};
struct PersistentCHT {
//minimizes dot product
const static int N = 1e6 + 6;
const static int lg = 22;
ll p[N][lg], sz;
PT pnt[N];
int insert(PT a, int rt) {
for (int u, v, i = lg - 1; i >= 0; i--)
if ((u = p[rt][i]) && (v = p[u][0]) && orientation(pnt[v], pnt[u], a) <= 0)
rt = u;
if (p[rt][0] && orientation(pnt[p[rt][0]], pnt[rt], a) <= 0) rt = p[rt][0];
pnt[++sz] = a;
p[sz][0] = rt;
for (int i = 1; i < lg; i++) p[sz][i] = p[p[sz][i - 1]][i - 1];
return sz;
}
ll query(PT a, int rt) {
for (int u, v, i = lg - 1; i >= 0; i--)
if ((u = p[rt][i]) && (v = p[u][0]) && dot(a, pnt[v]) > dot(a, pnt[u]))
rt = u;
if (p[rt][0] && dot(a, pnt[p[rt][0]]) > dot(a, pnt[rt])) rt = p[rt][0];
return rt ? dot(a, pnt[rt]) : -1e18;
}
} cht;
vector<pair<int, ll> > adj[N], Harbingers(N);
ll dist[N], root[N], dp[N];
void dfs(int node, int p = 0) {
if (node) {
dp[node] = Harbingers[node].first + Harbingers[node].second * dist[node];
dp[node] += cht.query(PT(Harbingers[node].second, 1), root[p]);
}
root[node] = cht.insert(PT(-dist[node], dp[node]), root[p]);
for (auto [v,w]: adj[node]) {
if (v == p) continue;
dist[v] = dist[node] + w;
dfs(v, node);
}
}
void solve() {
int n;
cin >> n;
for (int i = 1; i < n; i++) {
int u, v, d;
cin >> u >> v >> d;
u--, v--;
adj[u].push_back({v, d});
adj[v].push_back({u, d});
}
for (int i = 1; i < n; ++i) {
int s, v;
cin >> s >> v;
Harbingers[i] = {s, v};
}
dfs(0);
for (int i = 1; i < n; ++i) cout << dp[i] << " ";
}
signed main() {
//READFILE();
Aboeldahab
int tc = 1;
// cin >> tc;
while (tc--) {
solve();
}
return 0;
}
