#include <cstdio>
#include <stack>
#include <cstring>
#include <cassert>
#include <string>
#include <deque>
#include <vector>
#include <map>
#include <queue>
#include <algorithm>
#include <iostream>
#include <utility>
using namespace std;
using ll = long long;
using ld = long double;
#define ShinLena cin.tie(nullptr)->sync_with_stdio(false)
#pragma GCC optimize("O3")
#pragma GCC target("avx2")
#define N 100005
#define ALL(x) x.begin(), x.end()
struct line
{
int m, c;
line(ll m, ll c) : m(m), c(c) {}
line() : m(0), c(0) {}
inline ll operator[](ll x) { return m*x+c; }
inline ll intersect(line &l) { return (ll)(c-l.c)/(l.m-m); }
};
int n, s[N], v[N];
ll rt[N], dp[N];
vector<pair<int, int>> g[N];
line cht[N]; int sz;
inline int add(line k)
{
if (sz > 1 && cht[sz].intersect(k) >= cht[sz].intersect(cht[sz-1])) return sz+1;
int l = 2, r = sz, z = sz+1;
for (; l <= r;)
{
int m = (l+r)/2;
if (cht[m].intersect(cht[m-1]) > cht[m].intersect(k)) z = m, r = m - 1;
else l = m + 1;
}
return z;
}
inline ll qry(ll x)
{
int l = 1, r = sz - 1;
for (;l <= r;)
{
int m = (l+r)/2;
if (cht[m].intersect(cht[m+1]) <= x) l = m + 1;
else r = m - 1;
}
return cht[l][x];
}
void dfs(int u, int p)
{
int at, psz = sz;
if (u != 1) dp[u] = s[u] + 1ll*v[u]*rt[u] - qry(v[u]);
line nw{rt[u], -dp[u]}, overwrote = cht[at = add(nw)];
cht[at] = nw, sz = at;
for (auto [w, v] : g[u]) if (v != p) rt[v] = rt[u] + w, dfs(v, u);
sz = psz; cht[at] = overwrote;
}
int main()
{
ShinLena;
cin >> n;
for (int u, v, w, i = 1; i < n; ++i) cin >> u >> v >> w, g[u].emplace_back(w, v), g[v].emplace_back(w, u);
for (int i = 2; i <= n; ++i) cin >> s[i] >> v[i];
dfs(1, 1);
for (int i = 2; i <= n; ++i) cout << dp[i] << ' ';
return 0;
}
