#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using vll = vector <ll>;
using ii = pair <ll, ll>;
const ll MAXN = 1E5+16, INF = ll(1E18)+16;
vector <pair <int, int> > adj[MAXN];
ll dp[MAXN];
int dis[MAXN];
int sleep[MAXN], slow[MAXN];
const ii maxf = {0, INF};
struct LiChao{
int ind=0, L, R;
vector<int> left, right;
vector<ii> line;
LiChao(int L, int R): L(L), R(R), left(MAXN,-1), right(MAXN,-1), line(MAXN,maxf){}
ll eval(ii a, ll x) {return a.first*x+a.second;}
void update(ii ln, vector <vector <pair <int, ii> > > &ups){
int u=0, l=L, r=R, mid;
while(true){
mid=(l+r)>>1;
if(eval(line[u],mid) > eval(ln,mid)) {
swap(line[u],ln);
ups.back().push_back({u, ln});
}
if(ln==maxf || l==r) return;
if(eval(line[u],l) < eval(ln,l)) l = mid+1, u=(right[u] == -1 ? right[u] = ++ind : right[u]);
else r=mid, u=(left[u] == -1 ? left[u] = ++ind : left[u]);
}
}
ll query(int x){
ll ans=INF;
int u=0, l=L, r=R, mid;
while(true){
mid=(l+r)>>1;
ans=min(ans,eval(line[u],x));
if(l==r) return ans;
if(x>mid && right[u]!=-1) l=mid+1, u=right[u];
else if(x<=mid && left[u]!=-1) r=mid, u=left[u];
else return ans;
}
}
} st(0, 1E9);
vector <vector <pair <int, ii> > > ups;
void rollback () {
auto th = ups.back(); ups.pop_back();
for (auto [stPtr, lastFun] : th) {
st.line[stPtr] = lastFun;
}
}
void dfs (ll u, ll par) {
dp[u] = ll(sleep[u])+ll(slow[u])*dis[u];
dp[u] = min(dp[u], st.query(slow[u]) +ll(sleep[u])+ll(slow[u])*dis[u]);
ups.push_back({});
st.update({-dis[u], dp[u]}, ups);
for (auto [v, w] : adj[u]) {
if (v == par) continue;
dis[v] = dis[u]+w;
dfs(v, u);
}
rollback();
}
int main () {
cin.tie(nullptr) -> sync_with_stdio(false);
ll n;
cin >> n;
for (ll i = 1; i < n; i++) {
ll u, v, w;
cin >> u >> v >> w;
u--; v--;
adj[u].push_back({ v, w });
adj[v].push_back({ u, w });
}
for (ll i = 1; i < n; i++) cin >> sleep[i] >> slow[i];
dis[0] = 0;
dp[0] = 0;
dfs(0, 0);
for (ll i = 1; i < n; i++) cout << dp[i] << ' ';
cout << '\n';
return 0;
}
