#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
#include <utility>
#include <cmath>
#include <ctime>
#include <cassert>
#include <set>
#include <stack>
#include <map>
#include <queue>
#include <random>
#include <chrono>
#include <array>
#include <bitset>
#include <sstream>
#include <unordered_map>
using ll = long long;
#define debug(x) cout << #x << " = " << x << '\n'
#define separator "===============================================\n"
#define all(a) a.begin(), a.end()
#define SZ(a) ((int)(a).size())
using namespace std;
const int mxn = 1e5 + 3;
const ll mod = 1e9 + 7;
const int inf32 = 2e9;
const ll inf64 = 4e18;
struct line {
ll a, b;
ll operator()(ll x) const { return a * x + b; }
};
long double intersect(line l, line r){
return (long double)(l.b - r.b) / (long double)(r.a - l.a);
}
line lines[mxn];
stack<tuple<int, int, line>> history;
int sz = 1; // lines are on [0, sz)
void add(line L){
int pos = sz, l = 1, r = sz - 1;
while(l <= r){
int mid = (l + r) / 2;
if (intersect(L, lines[mid - 1]) >= intersect(L, lines[mid]))
pos = mid, r = mid - 1;
else l = mid + 1;
}
history.emplace(pos, sz, lines[pos]);
sz = pos + 1;
lines[pos] = L;
}
void rollback(){
int pos, old_sz; line l;
tie(pos, old_sz, l) = history.top();
history.pop();
sz = old_sz;
lines[pos] = l;
}
ll query(ll x){
int pos = 0, l = 1, r = sz - 1;
while(l <= r){
int mid = (l + r) / 2;
if (lines[mid - 1](x) >= lines[mid](x))
pos = mid, l = mid + 1;
else r = mid - 1;
}
return lines[pos](x);
}
int n;
ll prep[mxn], speed[mxn], dist[mxn], dp[mxn];
vector<pair<int, int>> g[mxn];
void dfs(int u, int pre, int pre_w){
dist[u] = dist[pre] + pre_w;
dp[u] = query(speed[u]) + prep[u] + speed[u] * dist[u];
add({-dist[u], dp[u]});
for (auto e : g[u]){
int v, w; tie(v, w) = e;
if (v == pre) continue;
dfs(v, u, w);
}
rollback();
}
void solve(){
cin >> n;
for (int i = 1, u, v, w; i <= n - 1; ++i){
cin >> u >> v >> w;
g[u].emplace_back(v, w);
g[v].emplace_back(u, w);
}
for (int i = 2; i <= n; ++i)
cin >> prep[i] >> speed[i];
for (auto e : g[1]){
int u, w; tie(u, w) = e;
dfs(u, 1, w);
}
for (int i = 2; i <= n; ++i)
cout << dp[i] << ' ';
}
int main(){
auto start = chrono::steady_clock::now();
ios_base::sync_with_stdio(false);
cin.tie(NULL);
if (fopen("read.inp", "r")){
freopen("read.inp", "r", stdin);
freopen("write.out", "w", stdout);
}
int t = 1;
// cin >> t;
while(t--) solve();
chrono::duration<double> elapsed {chrono::steady_clock::now() - start};
cerr << "\n>> Runtime: " << elapsed.count() << "s\n";
}
