///*** Sown_Vipro ***///
/// ->NHI QUOC GIA<- ///
#include<bits/stdc++.h>
using namespace std;
//#pragma GCC optimize ("O3")
//#pragma GCC optimize ("unroll-loops")
//#pragma GCC target("popcnt")
#define F first
#define S second
#define pb push_back
#define pi pair<int, int>
#define pii pair<int, pair<int, int> >
#define FOR(i, a, b) for(int i = a; i <= b; ++i)
#define REP(i, a, b) for(int i = a; i >= b; --i)
#define all(s) s.begin(), s.end()
#define szz(s) int(s.size())
#define ll long long
//#define int long long
const string NAME = "harb";
const int N = 1e5 + 5, MAX = 1e6, oo = 1e9 + 5, MOD = 1e9 + 7;
void maxi(int &x, int y){ if(x < y) x = y; }
void mini(long long &x, long long y){ if(x > y) x = y; };
void add(int &x, int y){ x += y; x += MOD * (x < 0); x -= MOD * (x >= MOD); };
int n;
pi s[N];
vector<pi> e[N];
namespace sub1{
int TIME;
int in[N], out[N], t[N], p[N], d[N];
long long dp[N];
void pre(int u){
in[u] = ++TIME;
for(pi edge : e[u]){
int v = edge.F, w = edge.S;
if(v != p[u]){
p[v] = u;
d[v] = d[u] + w;
pre(v);
}
}
}
bool cmp(int u, int v){
return in[u] < in[v];
}
long long f(int u){
int sum = 0, v = p[u];
long long res = 1e18;
while(v){
// cout << v << " " << dp[v] << " " << (d[u] - d[v]) * s[u].S << " " << s[u].F << "\n";
mini(res, dp[v] + 1ll * (d[u] - d[v]) * s[u].S + s[u].F);
v = p[v];
}
return res;
}
void solve(){
pre(1);
FOR(u, 1, n) t[u] = u;
sort(t + 1, t + 1 + n, cmp);
// cout << f(2);
FOR(i, 2, n){
int u = t[i];
dp[u] = f(u);
}
FOR(u, 2, n) cout << dp[u] << " ";
}
}
namespace sub2{
// #define int long long
struct Line {
mutable ll k, m, p;
bool operator<(const Line& o) const { return k < o.k; }
bool operator<(ll x) const { return p < x; }
};
struct LineContainer : multiset<Line, less<>> {
// (for doubles, use inf = 1/.0, div(a,b) = a/b)
static const ll inf = LLONG_MAX;
ll div(ll a, ll b) { // floored division
return a / b - ((a ^ b) < 0 && a % b); }
bool isect(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(ll k, ll m) {
auto z = insert({k, m, 0}), y = z++, x = y;
while (isect(y, z)) z = erase(z);
if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
while ((y = x) != begin() && (--x)->p >= y->p)
isect(x, erase(y));
}
ll query(ll x) {
assert(!empty());
// cout << size() << "\n";
auto l = *lower_bound(x);
return l.k * x + l.m;
}
} hull;
int m, root;
int t[N], ver[N], d[N];
long long dp[N];
void getLine(int u, int p){
t[++m] = u;
ver[u] = m;
root = u;
for(pi edge : e[u]){
int v = edge.F, w = edge.S;
if(v != p){
getLine(v, u);
}
}
}
void caldist(int u, int p){
for(pi edge : e[u]){
int v = edge.F, w = edge.S;
if(v != p){
d[v] = d[u] + w;
caldist(v, u);
}
}
}
void solve(){
getLine(1, 0);
m = d[root] = 0;
getLine(root, 0);
caldist(1, 0);
hull.add(d[1], -dp[1]);
FOR(i, ver[1] + 1, n){
int u = t[i];
dp[u] = 1ll * -hull.query(s[u].S) + 1ll * d[u] * s[u].S + s[u].F;
hull.add(d[u], -dp[u]);
}
hull.clear();
hull.add(d[1], -dp[1]);
REP(i, ver[1] - 1, 1){
int u = t[i];
dp[u] = 1ll * -hull.query(s[u].S) + 1ll * d[u] * s[u].S + s[u].F;
hull.add(d[u], -dp[u]);
}
FOR(u, 2, n) cout << dp[u] << " ";
}
}
void solve(){
cin >> n;
FOR(i, 2, n){
int u, v, w; cin >> u >> v >> w;
e[u].pb({v, w});
e[v].pb({u, w});
}
FOR(u, 2, n) cin >> s[u].F >> s[u].S;
// sub2::solve();
if(n <= 2500){
sub1::solve();
}else{
sub2::solve();
}
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
if(fopen((NAME + ".inp").c_str(), "r")){
freopen((NAME + ".inp").c_str(), "r", stdin);
freopen((NAME + ".out").c_str(), "w", stdout);
}
int t = 1;
// cin >> t;
while(t--){
solve();
}
}
/*
5
1 2 20
2 3 12
2 4 1
4 5 3
26 9
1 10
500 2
2 30
*/
