#include <iostream>
// #include <fstream>
// std::ifstream cin ("pushabox.in");
// std::ofstream cout ("pushabox.out");
// includes
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <string>
#include <vector>
#include <array>
#include <algorithm>
#include <numeric>
#include <iomanip>
#include <unordered_set>
#include <stack>
#include <ext/pb_ds/assoc_container.hpp>
#include <random>
#include <chrono>
#include <bitset>
#include <complex>
// usings
using namespace std;
using namespace __gnu_pbds;
// misc
#define ll long long
#define ld long double
#define pb push_back
#define pq priority_queue
#define ub upper_bound
#define lb lower_bound
template <typename T, typename U>
bool emin(T &a, const U &b) { return b < a ? a = b, true : false; }
template <typename T, typename U>
bool emax(T &a, const U &b) { return b > a ? a = b, true : false; }
typedef uint64_t hash_t;
// vectors
#define vi vector<int>
#define vvi vector<vi>
#define vvvi vector<vvi>
#define vpii vector<pair<int, int>>
#define vvpii vector<vector<pair<int, int>>>
#define vppipi vector<pair<int, pair<int, int>>>
#define vl vector<ll>
#define vvl vector<vl>
#define vvvl vector<vvl>
#define vpll vector<pair<ll, ll>>
#define vvpll vector<vpll>
#define vb vector<bool>
#define vvb vector<vb>
#define vvvb vector<vvb>
#define vs vector<string>
#define sz(x) (int)x.size()
#define rz resize
#define all(x) x.begin(), x.end()
#define vc vector<char>
#define vvc vector<vc>
// pairs
#define pii pair<int, int>
#define pll pair<ll, ll>
#define mp make_pair
#define f first
#define s second
// sets
#define si set<int>
#define sl set<ll>
#define ss set<string>
#define in insert
template <class T>
using iset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
// maps
#define mii map<int, int>
#define mll map<ll, ll>
// loops
#define FR(x, z, y) for (int x = z; x < y; x++)
#define FRE(x, z, y) FR(x, z, y + 1)
#define F(x, y) FR(x, 0, y)
#define FE(x, y) F(x, y + 1)
#define A(x, y) for (auto &x : y)
ld isect(pll a, pll b) { return (ld) (a.s - b.s) / (ld) (b.f - a.f); }
int n;
vl d, dp; vvpll a; vpll b, c;
int sz = 1;
int add(ll k, ll m){
if(sz == 1 || isect(c[sz - 2], c[sz - 1]) <= isect(c[sz - 1], {k, m})) return sz;
int l = 1, r = sz - 1;
while(l < r) {
int m = (l + r) / 2;
if(isect(c[m - 1], c[m]) > isect(c[m], {k, m})) r = m;
else l = m + 1;
}
// return l;
for(int i = l; i <= sz; i++) {
if(isect(c[i - 1], c[i - 2]) >= isect(c[i - 1], {k, m})) {
return i;
}
}
// return 1;
}
ll get(ll x){
int l = 1, r = sz - 1;
while(l < r){
int m = (l + r - 1) / 2;
if(isect(c[m], c[m + 1]) <= x) l = m + 1;
else r = m;
}
return c[l].f * x + c[l].s;
}
void dfs(int x, int p){
int pos, prev = sz; pll past;
if(p != -1) {
dp[x] = b[x].f + b[x].s * d[x] + min(get(b[x].s), 0ll);
pos = add(-d[x], dp[x]);
past = c[pos];
c[pos] = { -d[x], dp[x] };
sz = pos + 1;
}
A(u, a[x]) {
if(u.f == p) continue;
d[u.f] = d[x] + u.s;
dfs(u.f, x);
}
if(p != -1) {
sz = prev;
c[pos] = past;
}
}
int main() {
cin >> n;
a = vvpll(n);
b = c = vpll(n, {(ll) 1e9, (ll) 1e9});
c[0] = {0, 0};
d = dp = vl(n, 0);
F(i, n - 1){
ll x, y, z; cin >> x >> y >> z; x--; y--;
a[x].pb({y, z}); a[y].pb({x, z});
}
F(i, n - 1) cin >> b[i + 1].f >> b[i + 1].s;
dfs(0, -1);
F(i, n - 1) cout << dp[i + 1] << " ";
}
