#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef double dou;
#define pii pair<int, int>
#define fi first
#define se second
#define pb push_back
#define ALL(v) v.begin(), v.end()
#define BITJ(x, j) (((x)>>(j))&1)
#define MASK(x) (1LL << (x))
template<typename T> bool maximize(T& x, const T& y) {
if (x < y) {x = y; return 1;}
return 0;
}
template<typename T> bool minimize(T& x, const T& y) {
if (x > y) {x = y; return 1;}
return 0;
}
const int maxn = 1e5+5;
struct Line{
ll m, b;
Line(ll _m = 0, ll _b = 0) {
m = _m;
b = _b;
}
ll cal(ll x) {
return m*x+b;
}
}; ///<
ll divi(ll x, ll y) {
return x/y+(x%y && (x^y)<0);
}
dou inter(Line a, Line b) {
return ((dou)(b.b-a.b))/((dou)(a.m-b.m));
}
//ll inter(Line a, Line b) {
// return divi(b.b-a.b, a.m-b.m);
//}
struct change{
int pos, sz;
Line a;
change(int _pos, int _sz, Line _a) {
pos = _pos;
sz = _sz;
a = _a;
}
};
struct CHT{
int sz;
vector<Line> hull;
vector<change> stk;
CHT() {
sz = 0;
hull.assign(maxn, Line());
}
bool check(int pos, Line a) {
// assert(pos >= 0);
return inter(hull[pos-1], a) <= inter(hull[pos-1], hull[pos]);
}
void insline(Line a) {
//binsearch
int k = sz;
if (sz > 1) {
for (int j = sz/2+1; j; j >>= 1) {
while (k-j > 0 && check(k-j, a)) k -= j;
}
}
//ins + stk
// assert(k > -1);
stk.pb(change(k, sz, hull[k]));
hull[k] = a;
sz = k+1;
}
void remline() {
change e = stk.back();
stk.pop_back();
sz = e.sz;
hull[e.pos] = e.a;
}
ll query(ll x) {
int k = 0;
for (int j = sz>>1; j; j >>= 1) {
while (k+j < sz && x > inter(hull[k+j-1], hull[k+j])) k += j;
}
// assert(k < sz);
// if (k > 0) cout << "query " << x << ' ' << k << ' ' << inter(hull[k-1], hull[k]) << "\n";
return hull[k].cal(x);
}
void check() {
for (int i = 0; i < sz; i++) {
cout << hull[i].m << ' ' << hull[i].b << "\n";
}
}
};
int n;
vector<pii> adj[maxn];
int a[maxn], b[maxn];
CHT cht;
ll dis[maxn], dp[maxn];
void dfs(int u, int p) {
// cout << u << "\n";
// cht.check();
if (u != 1) {
dp[u] = a[u]+b[u]*dis[u];
if (cht.sz > 0) minimize(dp[u], a[u]+b[u]*dis[u]+cht.query(b[u]));
cht.insline(Line(-dis[u], dp[u]));
}
for (int i = 0; i < (int)adj[u].size(); i++) {
int v = adj[u][i].fi, w = adj[u][i].se;
if (v == p) continue;
dis[v] = dis[u]+w;
dfs(v, u);
}
if (u > 1) cht.remline();
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
// #define name "task"
// if (fopen(name".inp", "r")) {
// freopen(name".inp", "r", stdin);
// freopen(name".out", "w", stdout);
// }
cin >> n;
for (int i = 1; i < n; i++) {
int u, v, w;
cin >> u >> v >> w;
adj[u].pb({v, w});
adj[v].pb({u, w});
}
for (int i = 2; i <= n; i++) {
cin >> a[i] >> b[i];
}
dis[1] = dp[1] = 0;
dfs(1, -1);
for (int i = 2; i <= n; i++) {
cout << dp[i] << ' ';
}
}
