#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define ii pair<int, int>
#define f first
#define s second
#define pb push_back
#define mp make_pair
#define all(x) x.begin(), x.end()
#define F0R(i, n) for (int i = 0; i < n; i++)
#define FOR(i, a, b) for (int i = a; i < b; i++)
#define inf 1000000010
#define maxn 100000
int n;
vector<ii> adj[maxn];
ll dp[maxn];
ll d[maxn];
ii A[maxn];
void dfsd(int u, int p, ll di = 0) {
d[u] = di;
for (auto v : adj[u]) {
if (v.f != p) dfsd(v.f, u, di+v.s);
}
}
struct Func {
ll m, b;
long double intersectX(Func other) {
return (long double)(other.b-b)/(m-other.m);
}
ll eval(ll x) {
return m*x+b;
}
};
Func dq[100001];
int dqSz = 0;
vector<int> nums;
auto cmp = [](int idx, int x) {
return dq[idx].intersectX(dq[idx+1]) < x;
};
void dfs(int u, int p) {
if (u == 0) {
dp[u] = 0;
} else {
int idx = *lower_bound(nums.begin(), nums.begin() + dqSz-1, A[u].s, cmp);
ll v = dq[idx].eval(A[u].s);
dp[u] = A[u].f + (ll)A[u].s*d[u] + v;
}
int oldSz = dqSz;
Func f = {-d[u], dp[u]};
while (dqSz >= 2 && dq[dqSz-1].intersectX(dq[dqSz-2]) >= dq[dqSz-2].intersectX(f)) {
dqSz--;
}
Func backup = dq[dqSz];
dq[dqSz++] = f;
for (auto v : adj[u]) {
if (v.f != p) dfs(v.f, u);
}
dq[dqSz-1] = backup;
dqSz = oldSz;
}
int main() {
cin.tie(0)->sync_with_stdio(0);
cin >> n;
F0R(i, n-1) {
int u, v, d; cin >> u >> v >> d; --u; --v;
adj[u].pb(mp(v, d));
adj[v].pb(mp(u, d));
}
F0R(i, n-1) {
int a, b; cin >> a >> b;
A[i+1] = mp(a, b);
}
dfsd(0, 0);
nums = vector<int>(n);
for (int i = 0; i < n; i++) nums[i] = i;
dfs(0, 0);
FOR(i, 1, n) {
cout << dp[i] << " \n"[i == n-1];
}
return 0;
}
