#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
#define int long long
#define endl "\n"
//-------------------\\
const ll INF = 2e18;
const ll MIN_X = 0, MAX_X = 1e9;
struct Line {
ll m, c;
Line(ll _m = 0, ll _c = INF) : m(_m), c(_c) {}
ll get(ll x) const { return m * x + c; }
};
struct LiChaoTree {
struct Node {
Line line;
int left = -1, right = -1;
};
vector<Node> tree;
LiChaoTree() {
tree.push_back(Node());
}
void add(Line nw, ll l = MIN_X, ll r = MAX_X, int u = 0) {
ll mid = l + (r - l) / 2;
bool lef = nw.get(l) < tree[u].line.get(l);
bool midf = nw.get(mid) < tree[u].line.get(mid);
if (midf) swap(tree[u].line, nw);
if (l == r) return;
if (lef != midf) {
if (tree[u].left == -1) {
tree[u].left = tree.size();
tree.push_back(Node());
}
add(nw, l, mid, tree[u].left);
} else {
if (tree[u].right == -1) {
tree[u].right = tree.size();
tree.push_back(Node());
}
add(nw, mid + 1, r, tree[u].right);
}
}
ll query(ll x, ll l = MIN_X, ll r = MAX_X, int u = 0) const {
if (u == -1) return INF;
ll res = tree[u].line.get(x);
if (l == r) return res;
ll mid = l + (r - l) / 2;
if (x <= mid) return min(res, query(x, l, mid, tree[u].left));
return min(res, query(x, mid + 1, r, tree[u].right));
}
};
struct SegTreeOfLiChao {
int n;
vector<LiChaoTree> st;
SegTreeOfLiChao(int _n) : n(_n) {
st.resize(4 * n + 1);
}
void add_line(int node, int l, int r, int ql, int qr, Line line) {
if (ql > r || qr < l) return; // ??? ??????
if (ql <= l && r <= qr) {
st[node].add(line);
return;
}
int mid = l + (r - l) / 2;
add_line(2 * node, l, mid, ql, qr, line);
add_line(2 * node + 1, mid + 1, r, ql, qr, line);
}
ll query_min(int node, int l, int r, int idx, ll x) {
ll res = st[node].query(x);
if (l == r) return res;
int mid = l + (r - l) / 2;
if (idx <= mid) res = min(res, query_min(2 * node, l, mid, idx, x));
else res = min(res, query_min(2 * node + 1, mid + 1, r, idx, x));
return res;
}
void add(int ql, int qr, Line line) {
add_line(1, 1, n, ql, qr, line);
}
ll get_min(int idx, ll x) {
return query_min(1, 1, n, idx, x);
}
};
void solve() {
int n; cin >> n;
vector<vector<array<int,2>>> adj(n+1);
for (int i = 1;i < n; i++) {
int u,v,d; cin >> u >> v >> d;
adj[u].push_back({v,d});
adj[v].push_back({u,d});
}
int wait[n+1] = {}, speed[n+1] = {};
for (int i = 2; i <= n; i++) cin >> wait[i] >> speed[i];
int timer = 1, in[n + 1], out[n + 1], dist[n + 1] = {};
// [in[u], out[u]]
function<void(int,int)> dfs = [&](int u, int p) {
in[u] = timer++;
for (auto [v,d] : adj[u]) {
if (v == p) continue;
dist[v] = dist[u] + d;
dfs(v, u);
}
out[u] = timer - 1;
}; dfs(1,0);
int ans[n+1] = {};
SegTreeOfLiChao lct(out[1] + 2);
function<void(int,int)> go = [&](int u, int p) {
if (u != 1) ans[u] = lct.get_min(in[u], speed[u]) + dist[u] * speed[u] + wait[u];
lct.add(in[u], out[u], {-dist[u], ans[u]});
for (auto [v,d] : adj[u]) {
if (v == p) continue;
go(v, u);
}
}; go(1,0);
for (int i = 2;i <= n; i++) cout << ans[i] << " ";
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
cout << fixed << setprecision(9);
int t = 1;
// cin >> t;
while (t--) solve();
return 0;
}
