#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using T = tuple<ll, ll, ll>;
#define int long long
#define Base 41
#define sz(a) (int)a.size()
#define FOR(i, a, b) for ( int i = a ; i <= b ; i++ )
#define FORD(i, a, b) for (int i = b; i >= a; i --)
#define REP(i, n) for (int i = 0; i < n; ++i)
#define REPD(i, n) for (int i = n - 1; i >= 0; --i)
#define all(x) x.begin() , x.end()
#define pii pair<int , int>
#define fi first
#define se second
#define Lg(x) 31 - __builtin_clz(x)
#define MASK(i) (1LL << (i))
#define BIT(x, i) (((x) >> (i)) & 1)
constexpr ll LINF = (1ll << 60);
constexpr int INF = (1ll << 30);
constexpr int MAX = 2e5 + 5;
constexpr int Mod = 1e9 + 7;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
void setupIO(){
#define name "Whisper"
//Phu Trong from Nguyen Tat Thanh High School for gifted student
srand(time(NULL));
cin.tie(nullptr)->sync_with_stdio(false); cout.tie(nullptr);
// freopen(name".inp", "r", stdin);
// freopen(name".out", "w", stdout);
cout << fixed << setprecision(10);
}
template <class X, class Y>
bool minimize(X &x, const Y &y){
X eps = 1e-9;
if (x > y + eps) {x = y; return 1;}
return 0;
}
template <class X, class Y>
bool maximize(X &x, const Y &y){
X eps = 1e-9;
if (x + eps < y) {x = y; return 1;}
return 0;
}
vector<int> comp;
struct Line{
int a, b;
Line(): a(0), b(LINF){}
Line(int _a, int _b):a(_a), b(_b){}
int f(int x){
return a * comp[x] + b;
}
} f[4 * MAX];
stack<vector<pair<Line, int>>> st;
int numNode;
vector<pii> adj[MAX];
void addLine(int id, int l, int r, Line line, vector<pair<Line, int>> &state){
if (l == r){
if (line.f(l) < f[id].f(l)){
state.push_back({f[id], id});
f[id] = line;
}
return;
}
int mid = (l + r) >> 1;
if (line.a > f[id].a){
state.push_back({f[id], id});
swap(line, f[id]);
}
if (line.f(mid) < f[id].f(mid)){
state.push_back({f[id], id});
swap(f[id], line);
addLine(id << 1, l, mid, line, state);
} else {
addLine(id << 1 | 1, mid + 1, r, line, state);
}
}
int query(int id, int l, int r, int x){
int ans = f[id].f(x);
if (l == r) return ans;
int mid = (l + r) >> 1;
if (x <= mid) return min(ans, query(id << 1, l, mid, x));
return min(ans, query(id << 1 | 1, mid + 1, r, x));
}
void addLine(int a, int b, vector<pair<Line, int>> &state){
addLine(1, 0, numNode - 1, Line(a, b), state);
}
int query(int x){
return query(1, 0, numNode - 1, x);
}
int dp[MAX], dis[MAX];
void rollback(){
if (st.empty()) return;
vector<pair<Line, int>> state = st.top();
st.pop();
reverse(all(state));
for (auto&[line, id] : state){
f[id] = line;
}
}
#define Find(x) lower_bound(all(comp), x) - comp.begin()
int s[MAX], v[MAX];
void dfs(int u, int p){
if (u != 1)
dp[u] = query(Find(-v[u])) + v[u] * dis[u] + s[u];
vector<pair<Line, int>> state;
addLine(dis[u], dp[u], state);
st.push(state);
for (auto&[v, w] : adj[u]) if(v ^ p){
dis[v] = dis[u] + w;
dfs(v, u);
}
rollback();
}
void Whisper(){
cin >> numNode;
for (int i = 1; i < numNode; ++i){
int u, v, w; cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
comp.push_back(0);
for (int i = 2; i <= numNode; ++i){
cin >> s[i] >> v[i];
comp.push_back(-v[i]);
}
sort(all(comp));
dfs(1, 0);
for (int i = 2; i <= numNode; ++i) cout << dp[i] << " ";
}
signed main(){
setupIO();
int Test = 1;
// cin >> Test;
for ( int i = 1 ; i <= Test ; i++ ){
Whisper();
if (i < Test) cout << '\n';
}
}
