///***LTT***///
/// ->NHAT QUOC GIA<- ///
#include<bits/stdc++.h>
//#pragma GCC optimize ("O3")
//#pragma GCC optimize ("unroll-loops")
//#pragma GCC target("popcnt")
#define int long long
#define endl "\n"
#define F first
#define S second
#define pb push_back
using namespace std;
//vector <int> lg2;
//void LOG_ARR(int n){
// lg2.resize(n + 3);
// for (int i = 1;i <= n;++i){
// lg2[i] = __lg(i);
// }
//}
const long long oo = 1e9+7;
const int N = 2 * 1e5 + 10;
int n;
typedef long long ll;
vector <pair <int, long long>> adj[N];
long long dp[N];
long long h[N];
long long s[N], v[N];
namespace sub1{
int parent[N];
void dfs(int u, int p){
if (u - 1){
int tmp = parent[u];
dp[u] = 1ll * h[u] * v[u] + s[u];
while (tmp - 1){
dp[u] = min(dp[u], dp[tmp] + s[u] + v[u] * (h[u] - h[tmp]));
tmp = parent[tmp];
}
}
for (int i = 0;i < adj[u].size();++i){
int v = adj[u][i].F;
int w = adj[u][i].S;
if (v == p) continue;
parent[v] = u;
h[v] = h[u] + w;
dfs(v, u);
}
}
void solve(){
dfs(1, 0);
for (int i = 2;i <= n;++i){
cout << dp[i] <<" ";
}
return;
}
};
bool dsub2(){
for (int i = 1;i <= n;++i){
if (adj[i].size() > 2) return false;
}
return true;
}
namespace sub2{
struct Line{
mutable long long k, m, p;
bool operator<(const Line& o) const {return k > o.k;}
bool operator<(long long x) const {return p < x;}
};
struct CHT : multiset <Line, less<>>{
/// double : INF = 1/.0 div(a,b) = a/b;
static const long long inf = LLONG_MAX;
long long div(long long a, long long b){
return a/b;
}
long long bad(iterator x,iterator y){
if (y == end()) return x->p = inf, 0;
if (x->k == y->k) x->p = x->m < y->m ? inf : - inf;
else x->p = div(y->m - x->m, x->k - y->k);
return x->p >= y-> p;
}
void add(long long k, long long m){
auto z = insert({k, m, 0}), y = z++, x = y;
while(bad(y,z)) z = erase(z);
if (x != begin() and bad(--x,y)) bad(x, y = erase(y));
while ( (y = x) != begin() and (--x)->p >= y->p ){
bad(x, erase(y));
}
}
long long query(long long x){
assert(!empty());
Line l = *lower_bound(x);
return l.k * x + l.m;
}
};
CHT a[2];
void dfs(int u, int p, int id, bool qr){
dp[u] = 1ll * h[u] * v[u] + s[u];
if (qr)
dp[u] = min(dp[u], a[id].query(v[u]) + s[u] + v[u] * h[u]);
a[id].add(-h[u], dp[u]);
for (int i = 0;i < adj[u].size();++i){
int v = adj[u][i].F;
int w = adj[u][i].S;
if (v == p) continue;
h[v] = h[u] + w;
dfs(v, u, id,1);
}
}
void solve(){
for (int i = 0;i < adj[1].size();++i){
int v = adj[1][i].F;
int w = adj[1][i].S;
h[v] = w;
dfs(v, 1, i, 0);
}
for (int i = 2;i <= n;++i){
cout << dp[i] <<" ";
}
}
};
void solve(){
cin >> n;
for (int i = 1;i < n;++i){
int u, v, d;
cin >> u >> v >> d;
adj[u].pb({v, d});
adj[v].pb({u, d});
}
for (int i = 2;i <= n;++i){
cin >> s[i] >> v[i];
}
if (n <= 5000){
sub1::solve();
return;
}
if (dsub2()){
sub2::solve();
return;
}
return;
}
signed main(){
ios_base::sync_with_stdio(NULL);
cin.tie(NULL);
cout.tie(NULL);
if (fopen("harb.inp", "r")){
freopen("harb.inp", "r", stdin);
freopen("harb.out", "w", stdout);
}
// int t;
// cin >> t;
// while(t--){
solve();
// }
return 0;
}
//////
