#include <bits/stdc++.h>
using namespace std;
#define F first
#define S second
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
const int N = 2e5 + 10;
int n;
int s[N], req[N], d[N];
ll dp[N];
vector<pii> g[N];
vector<pll> hull, del[N];
inline bool cmp(pll x, pll y){
if ((x.F / x.S) != (y.F / y.S))
return (x.F / x.S) > (y.F / y.S);
x.F %= x.S;
y.F %= y.S;
return (x.F * y.S) > (y.F * x.S);
}
inline bool useful(pll &x, pll &y, pll &z){
return cmp({x.S - y.S, y.F - x.F}, {y.S - z.S, z.F - y.F});
}
inline void insert(int v, pll L){
while (hull.size() > 1 and !useful(hull[hull.size() - 2], hull.back(), L)){
del[v].push_back(hull.back());
hull.pop_back();
}
hull.push_back(L);
}
inline ll f(pll &L, int &x){
return L.F * x + L.S;
}
ll ans, ans1, ans2;
int lo, hi, mid;
inline ll query(int x){
ans = f(hull[0], x);
lo = 0, hi = hull.size();
while (hi - lo > 1){
mid = (lo + hi) / 2;
ans1 = f(hull[mid - 1], x);
ans2 = f(hull[mid], x);
if (ans1 < ans2){
ans = ans1;
hi = mid;
}
else{
ans = ans2;
lo = mid;
}
}
return ans;
}
void dfs(int v, int p = -1){
for (auto &[w, u] : g[v]){
if (u == p) continue;
d[u] = d[v] + w;
dp[u] = query(-s[u]) + 1ll * s[u] * d[u] + req[u];
insert(u, {d[u], dp[u]});
dfs(u, v);
}
hull.pop_back();
while (del[v].size())
hull.push_back(del[v].back()), del[v].pop_back();
del[v].resize(0);
}
int main(){
cin >> n;
for (int i = 0; i < n - 1; i ++){
int u, v, w;
cin >> u >> v >> w;
g[u].push_back({w, v});
g[v].push_back({w, u});
}
for (int i = 2; i <= n; i ++)
cin >> req[i] >> s[i];
insert(1, {0, 0});
dfs(1);
for (int i = 2; i <= n; i ++)
cout << dp[i] << " ";
cout << endl;
}
