#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ar array
int binary_search(function<bool(int)> f, int lb, int rb) {
while(lb < rb) {
int mb = (lb + rb + 1) / 2;
if (f(mb)) lb = mb;
else rb = mb - 1;
}
return lb;
}
const int mxN = 100000;
int n, delay[mxN], speed[mxN];
ll d[mxN], dp[mxN];
vector<pair<int, int>> adj[mxN];
struct Line {
ll m = 0, b = 0;
ll eval(ll x) {return m * x + b;}
};
double isect(Line& a, Line& b) {
return (double)(a.b - b.b) / (b.m - a.m);
}
int sz = 1;
Line q[mxN];
void dfs(int u, int p) {
int ind = binary_search([&](int i) {return speed[u] > isect(q[i], q[i - 1]);} , 0, sz - 1);
dp[u] = d[u] * speed[u] + delay[u] + q[ind].eval(speed[u]);
Line cur = {-d[u], dp[u]};
int l = 1, r = sz;
while(l < r) {
int mid = (l + r) / 2;
if (isect(cur, q[mid - 1]) < isect(q[mid], q[mid - 1])) r = mid;
else l = mid + 1;
}
ind = l;
swap(cur, q[ind]);
int new_size = ind + 1;
swap(sz, new_size);
for (pair<int, int> v : adj[u]) if (v.first != p) {
d[v.first] = d[u] + v.second;
dfs(v.first, u);
}
swap(cur, q[ind]);
swap(sz, new_size);
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
cin >> n;
for (int i = 1; i < n; ++i) {
int a, b, c; cin >> a >> b >> c, --a, --b;
adj[a].emplace_back(b, c);
adj[b].emplace_back(a, c);
}
for (int i = 1; i < n; ++i) {
cin >> delay[i] >> speed[i];
}
for (pair<int, int> p : adj[0]) {
d[p.first] = p.second;
dfs(p.first, 0);
}
for (int i = 1; i < n; ++i) {
cout << dp[i] << " ";
}
return 0;
}
