#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MASK(i) (1ULL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(a, b);}
ll lcm(ll a, ll b){return a / gcd(a, b) * b;}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ull mask){return __builtin_popcountll(mask);}
int ctz(ull mask){return __builtin_ctzll(mask);}
int logOf(ull mask){return 63 - __builtin_clzll(mask);}
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
ll rngesus(ll l, ll r){return l + (ull) rng() % (r - l + 1);}
double rngesus_d(double l, double r){
double wow = (double) ((ull) rng()) / ((ull)(0-1));
return wow * (r - l) + l;
}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
struct Line{
int a;
ll b;
Line(int a = 0, ll b = 0): a(a), b(b){}
};
ll f(Line cur, ll x){
return cur.a * x + cur.b;
}
struct LichaoTree{
int n;
vector<ll> b;
vector<Line> a;
vector<pair<int, Line>> history;
LichaoTree(vector<ll> _b){
b = _b;
n = b.size() - 1;
a.resize(n * 2 + 2, Line(1e9, 1e18));
}
int get_version(){
return history.size();
}
void update(Line x){
update(x, 1, n, 1);
}
void update(Line x, int l, int r, int id){
if (f(a[id], b[l]) <= f(x, b[l]) && f(a[id], b[r]) <= f(x, b[r])) return;
if (f(a[id], b[l]) >= f(x, b[l]) && f(a[id], b[r]) >= f(x, b[r])) {
history.push_back({id, a[id]});
a[id] = x;
return;
}
int mid = (l + r) >> 1;
update(x, l, mid, id + 1);
update(x, mid+1, r, id + (mid - l + 1) * 2);
}
ll get(ll x){
return get(x, 1, n, 1);
}
ll get(ll x, int l, int r, int id){
ll ans = f(a[id], x);
if (l == r) return ans;
int mid = (l + r) >> 1;
if (b[mid] >= x) minimize(ans, get(x, l, mid, id + 1));
else minimize(ans, get(x, mid+1, r, id + (mid - l + 1) * 2));
return ans;
}
void roll_back(int version){
while(get_version() > version){
auto i = history.back(); history.pop_back();
a[i.first] = i.second;
}
}
};
const int N = 1e5 + 69;
int n;
vector<pair<ll, ll>> graph[N];
ll h[N];
ll dp[N];
vector<ll> s, v;
void dfs(int u, int p, LichaoTree &lct){
int cur_version = lct.get_version();
if (u != 1){
dp[u] = s[u] + lct.get(v[u]) + v[u] * h[u];
}
lct.update(Line(-h[u], dp[u]));
for(pair<ll, ll> v: graph[u]) if (v.first != p){
h[v.first] = h[u] + v.second;
dfs(v.first, u, lct);
}
lct.roll_back(cur_version);
}
void solve(){
cin >> n;
for(int i = 1; i < n; ++i){
int u, v, d; cin >> u >> v >> d;
graph[u].push_back({v, d});
graph[v].push_back({u, d});
}
s.resize(n+1); v.resize(n+1);
for(int i = 2; i <= n; ++i) cin >> s[i] >> v[i];
vector<ll> b = v;
b.push_back(-1);
remove_dup(b);
LichaoTree lct(b);
dfs(1, 0, lct);
for(int i = 2; i <= n; ++i) cout << dp[i] << " ";
cout << "\n";
}
int main(void){
ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
clock_t cock = clock();
solve();
cerr << "Time elapsed: " << clock() - cock << "ms!\n";
return 0;
}
