#include <bits/stdc++.h>
#define ll long long
using namespace std;
const int N = (int)1e5 + 1;
const int M = (int)1e9 + 1;
const ll inf = (ll)1e18;
ll dp[N], s[N], vv[N], dep[N];
vector<pair<int, int>> adj[N];
int cnt = 0;
struct LiChaoTree {
struct Line {
ll m, c;
ll y(ll x) { return m * x + c; }
Line() : m(0), c(inf) {}
Line(ll m, ll c) : m(m), c(c) {}
};
struct Node {
Line L;
int u = -1, l = -1, r = -1;
Node() {}
Node(const Node &u) { L = u.L, l = u.l, r = u.r; }
};
vector<Node> node = vector<Node> (4*N);
void insert(Line L, int u, int l, int r) {
int mid = l + (r - l) / 2;
bool c1 = L.y(l) < node[u].L.y(l);
bool c2 = L.y(mid) < node[u].L.y(mid);
if (c2) swap(L, node[u].L);
if (l == r) return;
if (c1 != c2) {
if (node[u].l != -1) node[cnt] = Node(node[node[u].l]);
else node[cnt] = Node();
node[u].l = cnt;
node[node[u].l].u = cnt++;
insert(L, node[u].l, l, mid);
} else {
if (node[u].r != -1) node[cnt] = Node(node[node[u].r]);
else node[cnt] = Node();
node[u].r = cnt;
node[node[u].r].u = cnt++;
insert(L, node[u].r, mid+1, r);
}
}
ll query(int u, int l, int r, ll x) {
if (l == r) return node[u].L.y(x);
int mid = l + (r - l) / 2;
ll ans = node[u].L.y(x);
if (x <= mid && node[u].l != -1) ans = min(ans, query(node[u].l, l, mid, x));
if (x > mid && node[u].r != -1) ans = min(ans, query(node[u].r, mid+1, r, x));
return ans;
}
void insert(ll m, ll c, int u) { insert(Line(m, c), u, 0, M); }
ll query(ll x, int u) { return min(0LL, query(u, 0, M, x)); }
} T;
vector<int> root;
void dfs(int u, int p) {
dp[u] = dep[u] * vv[u] + s[u] + T.query(vv[u], root[p]);
root[u] = cnt, T.node[cnt] = LiChaoTree::Node(T.node[root[p]]);
cnt++;
T.insert(-dep[u], dp[u], root[u]);
for (auto &[w, v] : adj[u]) {
if (v == p) continue;
dep[v] = dep[u] + w;
dfs(v, u);
}
}
int main() {
ios_base::sync_with_stdio(0); cin.tie(0);
int n; cin >> n;
root.resize(n+1);
for (int i = 1; i < n; i++) {
int u, v, w;
cin >> u >> v >> w;
adj[u].emplace_back(w, v), adj[v].emplace_back(w, u);
}
for (int i = 2; i <= n; i++) cin >> s[i] >> vv[i];
root[0] = 0;
dfs(1, 0);
for (int i = 2; i <= n; i++) cout << dp[i] << ' ';
}
