#include <bits/stdc++.h>
#define ll long long
using namespace std;
const int NMAX = 1e5;
const int INFx = 1e9;
const ll INF = 1e18;
int n;
ll dp[NMAX + 1];
ll sp[NMAX + 1];
int st[NMAX + 1], v[NMAX + 1];
vector<pair<int, int>> g[NMAX + 1];
int parent[NMAX + 1];
struct Line {
ll a, b;
Line() : a(0), b(INF) {}
Line(ll a, ll b) : a(a), b(b) {}
ll eval(int x) {
return a * x + b;
}
};
struct Node {
Line line;
int left = -1, right = -1;
};
struct LiChao {
vector<Node> aint;
stack<pair<int, Line>> st;
int create_node() {
aint.push_back(Node());
return aint.size() - 1;
}
LiChao() {
create_node();
}
pair<int, int> add_line(int node, int left, int right, Line new_line) {
if(node == -1) {
node = create_node();
}
int mid = (left + right) / 2;
int cnt = 0;
bool left_sign = new_line.eval(left) < aint[node].line.eval(left);
bool mid_sign = new_line.eval(mid) < aint[node].line.eval(mid);
bool right_sign = new_line.eval(right) < aint[node].line.eval(right);
if(mid_sign) {
cnt++;
st.push({node, aint[node].line});
swap(aint[node].line, new_line);
}
if(left == right) {
return {node, cnt};
}
if(left_sign != mid_sign) {
pair<int, int> left_node = add_line(aint[node].left, left, mid, new_line);
aint[node].left = left_node.first;
cnt += left_node.second;
}
else if(mid_sign != right_sign) {
pair<int, int> right_node = add_line(aint[node].right, mid + 1, right, new_line);
aint[node].right = right_node.first;
cnt += right_node.second;
}
return {node, cnt};
}
ll query_min(int node, int left, int right, int x) {
if(node == -1) {
return INF;
}
if(left == right) {
return aint[node].line.eval(x);
}
int mid = (left + right) / 2;
if(x <= mid) {
return min(aint[node].line.eval(x), query_min(aint[node].left, left, mid, x));
}
return min(aint[node].line.eval(x), query_min(aint[node].right, mid + 1, right, x));
}
int add_line(Line line) {
return add_line(0, 1, INFx, line).second;
}
ll query_min(int x) {
return query_min(0, 1, INFx, x);
}
void rollback(int k) {
assert(k <= st.size());
while(k--) {
auto [node, line] = st.top();
st.pop();
aint[node].line = line;
}
}
}li_chao;
//ll get_dp(int node) {
// ll mini = INF;
// int dad = parent[node];
// while(dad != 0) {
// mini = min(mini, dp[dad] - sp[dad] * v[node]);
// dad = parent[dad];
// }
// return st[node] + sp[node] * v[node] + mini;
//}
void DFS(int node, int dad = 0) {
parent[node] = dad;
if(node != 1) {
dp[node] = st[node] + sp[node] * v[node] + li_chao.query_min(v[node]);
}
int cnt = li_chao.add_line(Line(-sp[node], dp[node]));
for(auto [next_node, c] : g[node]) {
if(next_node != dad) {
sp[next_node] = sp[node] + c;
DFS(next_node, node);
}
}
// li_chao.rollback(cnt);
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cin >> n;
for(int i = 1; i <= n - 1; i++) {
int a, b, c;
cin >> a >> b >> c;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
for(int i = 2; i <= n; i++) {
cin >> st[i] >> v[i];
}
DFS(1);
for(int i = 2; i <= n; i++) {
cout << dp[i] << ' ';
}
return 0;
}
