//
// Created by liasa on 13/12/2025.
//
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define v vector
#define lp(i, s, e) for (int i = s; i < e; ++i)
#define pll pair<ll, ll>
vector<int> values;
const ll inf = 4e18;
v<ll> dp;
int n;
v<pll> kn;
v<v<pll>> g;
v<int> dpt;
ll wh_line(int id, ll x) {
if (id == -1)
return inf;
return dp[id] - 1LL * dpt[id] * x;
}
struct LiChao {
v<int> seg;
struct Hist {
int idx, old_id;
};
stack<Hist> st;
int sz = 1;
LiChao(int n1) {
for (; sz < n1; sz *= 2)
;
seg.resize(2 * sz, -1);
}
void update(int i, int l, int r, int add_id) {
int mid = (l + r) / 2;
ll x_val = values[mid];
int cur_id = seg[i];
if (wh_line(add_id, x_val) < wh_line(cur_id, x_val)) {
st.push({i, cur_id});
seg[i] = add_id;
add_id = cur_id;
}
if (l == r)
return;
ll x_l = values[l], x_r = values[r];
if (wh_line(add_id, x_l) < wh_line(seg[i], x_l)) {
update(i * 2, l, mid, add_id);
} else
update(i * 2 + 1, mid + 1, r, add_id);
}
ll query(int i, int l, int r, ll x) {
ll res = wh_line(seg[i], x);
if (l == r)
return res;
int mid = (l + r) / 2;
ll mid_val = values[mid];
if (x <= mid_val) {
return min(res, query(i * 2, l, mid, x));
} else
return min(res, query(i * 2 + 1, mid + 1, r, x));
}
};
int values_n;
void rollback(LiChao &lc, ll pic) {
while (lc.st.size() > pic) {
auto h = lc.st.top();
lc.seg[h.idx] = h.old_id;
lc.st.pop();
}
}
// dp[v] = st[v] + sp[v]*dpt[v] + min(dp[u] - sp[v]*dpt[u]
void dfs(int node, int par, LiChao &lc) {
ll pic = lc.st.size();
int d = dpt[node];
if (node == 0) {
dp[node] = 0;
} else {
auto [st, sp] = kn[node];
ll qu = lc.query(1, 0, values_n - 1, sp);
ll my_dp = st + 1LL * sp * d + qu;
dp[node] = my_dp;
}
lc.update(1, 0, values_n - 1, node);
for (auto [it, d_add] : g[node]) {
if (it != par) {
dfs(it, node, lc);
}
}
rollback(lc, pic);
}
void dfs1(ll node, ll par, ll dpa) {
// values.push_back(dpa);
dpt[node] = dpa;
for (auto [it, d_add] : g[node]) {
if (it != par)
dfs1(it, node, dpa + d_add);
}
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n;
g.resize(n);
dp.resize(n);
kn.resize(n);
dpt.resize(n, 0);
lp(i, 0, n - 1) {
ll a, b, c;
cin >> a >> b >> c;
a--;
b--;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
dp[0] = 0;
dfs1(0, -1, 0);
lp(i, 1, n) {
ll st, speed;
cin >> st >> speed;
values.push_back(speed);
kn[i] = {st, speed};
}
sort(values.begin(), values.end());
values.erase(unique(values.begin(), values.end()), values.end());
values_n = values.size();
LiChao lc(values_n);
lc.update(1, 0, values_n - 1, 0);
dfs(0, -1, lc);
lp(i, 1, n) { cout << dp[i] << " "; }
return 0;
}
