#include<iostream>
#include<cstdio>
#include<string>
#include<vector>
#include<cstring>
#include<algorithm>
#include<set>
#include<map>
#include<complex>
#include<cassert>
#include<stack>
using namespace std;
typedef long long ll;
typedef complex<double> pt;
typedef pair<ll, ll> pii;
#define x() real()
#define y() imag()
#define smx(a, b) a = max(a, b)
#define smn(a, b) a = min(a, b)
#define in(mp, v) (mp.find(v) != mp.end())
const int MAXN = 100005;
const int MOD = 1000000007;
class cht {
private:
vector<long long> m, b;
int sz = 0;
bool test(int i, int j, ll mk, ll bk) {
return (b[j]-b[i])*(mk-m[i]) > (bk-b[i])*(m[j]-m[i]);
}
long long eval(int i, long long x) {
return m[i]*x+b[i];
}
public:
pair<int, pii> insert(long long mv, long long bv) {
int rem = 0;
while (sz >= 2 && !test(sz-2, sz-1, mv, bv)) {
sz--;
rem++;
}
if (rem == 0) {
m.push_back(mv);
b.push_back(bv);
sz++;
return {0, {8888, -1}};
}
pii old = {m[sz], b[sz]};
m[sz] = mv; b[sz] = bv;
sz++;
return {rem, old};
}
long long query(long long x) {
int l = 0, r = sz-2;
while (l <= r) {
int mid = (l+r)/2;
if (eval(mid, x) > eval(mid+1, x)) {
l = mid+1;
} else {
r = mid-1;
}
}
return eval(l, x);
}
void rest(int cnt, ll mv, ll bv) {
if (cnt == 0) {
sz--;
return;
}
m[sz-1] = mv; b[sz-1] = bv;
sz += cnt-1;
}
void popLast() {
m.pop_back();
b.pop_back();
sz--;
}
};
int n;
vector<pair<int, ll>> adj[MAXN];
ll si[MAXN], vi[MAXN];
cht ch;
ll ans[MAXN];
void dfs(int x, int p, ll d) {
if (x != 1) ans[x] = ch.query(vi[x])+d*vi[x]+si[x];
auto rem = ch.insert(-d, ans[x]);
for (auto pv : adj[x]) {
if (pv.first != p) {
dfs(pv.first, x, d+pv.second);
}
}
ch.rest(rem.first, rem.second.first, rem.second.second);
}
int main() {
ios_base::sync_with_stdio(0); cin.tie(0);
cin >> n;
for (int i = 0; i < n-1; i++) {
int u, v; ll d; cin >> u >> v >> d;
adj[u].push_back({v, d});
adj[v].push_back({u, d});
}
for (int i = 2; i <= n; i++) {
cin >> si[i] >> vi[i];
}
dfs(1, 1, 0);
for (int i = 2; i <= n; i++) {
cout << ans[i];
if (i < n) cout << " ";
}
cout << endl;
return 0;
}
