#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll INFLL = LLONG_MAX;
struct Line { ll m, b; // y = m*x + b
};
struct Change { int idx; Line prev; };
struct LiChao {
int n;
vector<ll> xs;
vector<Line> seg;
vector<Change> changes;
LiChao(const vector<ll>& _xs) {
xs = _xs;
n = xs.size();
seg.assign(4*n, {0, (ll)9e18});
}
inline ll eval(const Line &ln, ll x) {
return ln.m * x + ln.b;
}
void add_line(Line ln, int id=1, int l=0, int r=-1) {
if (r==-1) r = n-1;
int m = (l+r)>>1;
ll xl = xs[l], xm = xs[m], xr = xs[r];
Line cur = seg[id];
// record change
changes.push_back({id, cur});
// at mid, which line is better?
if (eval(ln, xm) < eval(cur, xm)) swap(ln, seg[id]);
// now seg[id] is better at xm
if (l==r) return;
if (eval(ln, xl) < eval(seg[id], xl)) {
// new line better on left
add_line(ln, id<<1, l, m);
} else if (eval(ln, xr) < eval(seg[id], xr)) {
// new line better on right
add_line(ln, id<<1|1, m+1, r);
}
}
ll query(ll xq, int id=1, int l=0, int r=-1) {
if (r==-1) r = n-1;
int m = (l+r)>>1;
ll res = eval(seg[id], xq);
if (l==r) return res;
if (xq <= xs[m]) return min(res, query(xq, id<<1, l, m));
else return min(res, query(xq, id<<1|1, m+1, r));
}
int snapshot() { return changes.size(); }
void rollback(int snap) {
while ((int)changes.size() > snap) {
auto ch = changes.back(); changes.pop_back();
seg[ch.idx] = ch.prev;
}
}
};
const int MN = 100000 + 5;
int n;
vector<pair<int,ll>> adj[MN];
ll s[MN], v[MN];
ll dp[MN], distd[MN];
vector<ll> allX;
void dfs(int u, int p, LiChao &cht) {
int snap = cht.snapshot();
// add line for u
cht.add_line({-distd[u], dp[u]});
for (auto &ed : adj[u]) {
int w = ed.first;
ll c = ed.second;
if (w == p) continue;
distd[w] = distd[u] + c;
// query cht at x = v[w]
ll best = cht.query(v[w]);
dp[w] = best + v[w] * distd[w] + s[w];
dfs(w, u, cht);
}
cht.rollback(snap);
}
int main(){
ios::sync_with_stdio(false);
cin.tie(NULL);
cin >> n;
for (int i = 1; i < n; i++) {
int u, w; ll c;
cin >> u >> w >> c;
adj[u].push_back({w, c});
adj[w].push_back({u, c});
}
for (int i = 2; i <= n; i++) {
cin >> s[i] >> v[i];
allX.push_back(v[i]);
}
// include root's v if needed
allX.push_back(0);
sort(allX.begin(), allX.end());
allX.erase(unique(allX.begin(), allX.end()), allX.end());
LiChao cht(allX);
// initialize root dp and dist
dp[1] = 0;
distd[1] = 0;
// add base line y = 0*x + 0
cht.add_line({0, 0});
dfs(1, 0, cht);
for (int i = 2; i <= n; i++) cout << dp[i] << " ";
cout << '\n';
return 0;
}
