#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ll long long
#define FOR(i, l, r) for (int i = (l); i <= (r); i++)
#define FOD(i, r, l) for (int i = (r); i >= (l); i--)
#define fi first
#define se second
#define pii pair<int, int>
const ll INF = (ll)1e18;
const int MAXN = 100000 + 1;
int n, s[MAXN], p[MAXN], d[MAXN];
vector<pii> adj[MAXN];
int f[MAXN];
vector<int> A, B, xoaA[MAXN], xoaB[MAXN];
bool bad(int l1, int l2, int l3) {
int lhs = (int)(B[l3] - B[l1]) * (A[l1] - A[l2]);
int rhs = (int)(B[l2] - B[l1]) * (A[l1] - A[l3]);
return lhs < rhs;
}
void add(int a, int b, int u) {
A.push_back(a);
B.push_back(b);
while ((int)A.size() >= 3 && bad(A.size() - 3, A.size() - 2, A.size() - 1)) {
int m = A.size();
xoaA[u].push_back(A[m - 2]);
xoaB[u].push_back(B[m - 2]);
A.erase(A.end() - 2);
B.erase(B.end() - 2);
}
}
void hoi(int u) {
A.pop_back();
B.pop_back();
FOD(i, (int)xoaA[u].size() - 1, 0) {
A.push_back(xoaA[u][i]);
B.push_back(xoaB[u][i]);
}
xoaA[u].clear();
xoaB[u].clear();
}
int queryCHT(int x) {
int sz = A.size();
if (sz == 0) return 0;
if (sz == 1) return A[0] * x + B[0];
int l = 1, r = sz - 1, id = 1;
int ans = INF;
while (l <= r) {
int mid = (l + r) >> 1;
int y1 = A[mid] * x + B[mid];
int y2 = A[mid - 1] * x + B[mid - 1];
if (y1 < y2) {
id = mid;
ans = min(ans, y1);
l = mid + 1;
} else {
ans = min(ans, y2);
r = mid - 1;
}
}
ans = min(ans, A[id] * x + B[id]);
if (id - 1 >= 0) ans = min(ans, A[id - 1] * x + B[id - 1]);
if (id + 1 < sz) ans = min(ans, A[id + 1] * x + B[id + 1]);
return ans;
}
void dfs2() {
struct Item { int u, par, state; };
vector<Item> st;
st.reserve(n * 2);
d[1] = 0;
st.push_back({1, 0, 0});
while (!st.empty()) {
Item it = st.back();
st.pop_back();
int u = it.u, par = it.par, state = it.state;
if (state == 0) {
if (u != 1) {
int best = queryCHT(p[u]);
f[u] = best + d[u] * p[u] + s[u];
} else {
f[u] = 0;
}
add(-d[u], f[u], u);
st.push_back({u, par, 1});
for (int i = adj[u].size() - 1; i >= 0; i--) {
int v = adj[u][i].fi, c = adj[u][i].se;
if (v == par) continue;
d[v] = d[u] + c;
st.push_back({v, u, 0});
}
} else {
hoi(u);
}
}
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n;
FOR(i, 1, n) {
adj[i].clear();
xoaA[i].clear();
xoaB[i].clear();
}
FOR(i, 1, n - 1) {
int u, v, c;
cin >> u >> v >> c;
adj[u].push_back({v, c});
adj[v].push_back({u, c});
}
FOR(i, 2, n) {
cin >> s[i] >> p[i];
}
A.clear();
B.clear();
dfs2();
FOR(i, 2, n) {
cout << f[i] << ' ';
}
cout << "\n";
return 0;
}
