//Huyduocdithitp
#include <bits/stdc++.h>
#define int long long
typedef long long ll;
#define endl '\n'
#define yes cout<<"YES"<<endl;
#define no cout<<"NO"<<endl;
#define fi first
#define se second
#define pii pair<ll, ll>
#define inf 1e18
#define faster ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define MP make_pair
#define TASK "ghuy4g"
#define start if(fopen(TASK".inp","r")){freopen(TASK".inp","r",stdin);freopen(TASK".out","w",stdout);}
#define LOG 19
#define N 100005
using namespace std;
struct Line {
ll a, b;
};
struct Node {
pii cu;
ll pos, sz;
};
vector<Node> undo;
ll n, d[N], F[N];
vector<pii> adj[N];
ll S[N], V[N], sz = 0;
Line A[200005];
ll ptr = 0;
bool bad(Line l1, Line l2, Line l3) {
return double(l3.b - l1.b) / (l1.a - l3.a) < double(l2.b - l1.b) / (l1.a - l2.a);
}
void add(ll u, ll v) {
Line xet = {u, v};
ll l = 1, r = sz - 1, ans = sz;
while (l <= r) {
ll mid = (l + r) / 2;
if (bad(A[mid - 1], A[mid], xet)) {
ans = mid;
r = mid - 1;
}
else {
l = mid + 1;
}
}
undo.push_back({{A[ans].a, A[ans].b}, ans, sz});
A[ans] = xet;
sz = ans + 1;
}
void Undo() {
sz = undo.back().sz; A[undo.back().pos] = {undo.back().cu.fi, undo.back().cu.se};
undo.pop_back();
}
ll cal(Line U, ll x) {
return U.a * x + U.b;
}
ll qr(ll x) {
if (sz == 0) return 0;
ll ans = cal(A[0], x);
/*for (int i = 1; i < sz; i ++) {
ans = min(ans, cal(A[i], x));
}
return ans;*/
ll l = 1, r = sz - 1;
while (l <= r) {
ll mid = (l + r) / 2;
if (cal(A[mid], x) < cal(A[mid - 1], x)) {
ans = min(ans, cal(A[mid], x));
l = mid + 1;
}
else {
r = mid - 1;
}
}
return ans;
}
void dfs(ll u, ll parent) {
if (u == 1) {
add(0, 0);
}
else {
F[u] = qr(V[u]) + S[u] + V[u] * d[u];
add(-d[u], F[u]);
}
for (auto v : adj[u]) {
if (v.fi == parent) continue;
d[v.fi] = d[u] + v.se;
dfs(v.fi, u);
}
if (u != 1) {
Undo();
}
}
signed main(void) {
faster;
cin >> n;
for (int i = 1; i <= n - 1; i ++) {
ll u, v, w;
cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
for (int i = 2; i <= n; i ++) {
cin >> S[i] >> V[i];
}
dfs(1, 1);
for (int i = 2; i <= n; i ++) {
cout << F[i] << " ";
}
return 0;
}
