#include <bits/stdc++.h>
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define compact(v) v.erase(unique(all(v)), v.end())
#define dbg(v) "[" #v " = " << (v) << "]"
#define el "\n"
#define int long long
using namespace std;
typedef long long ll;
typedef long double ld;
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
long long randRange(long long l, long long r){ return uniform_int_distribution<long long>(l,r)(rng); }
const int N = 2e5 + 5;
int n;
vector < pair<int, ll> > adj[N];
ll dist[N], v[N], c[N], dp[N];
struct Line {
ll a, b;
Line (ll a = 0, ll b = 0) : a(a), b(b) {}
ll f(ll x) {
return a * x + b;
}
ld intersect(Line Other) {
return 1.0 * (Other.b - b) / (a - Other.a);
}
// decreasing slope
friend bool bad(Line d1, Line d2, Line d3) {
return d1.intersect(d3) <= d1.intersect(d2);
}
};
struct CHT {
vector <Line> hull;
stack < pair< pair<int, int>, Line> > st;
int curSZ;
CHT() {
hull.clear();
curSZ = 0;
}
void init(int n) {
hull.resize(n + 5);
}
ll query(ll x) {
int l = 0;
int r = curSZ - 1;
ll ans = LLONG_MAX;
while(l <= r) {
int mid = (l + r) >> 1;
ll cur = hull[mid].f(x);
ans = min(ans, cur);
if (mid > 0 && hull[mid - 1].f(x) < cur) r = mid - 1;
else if (mid < curSZ - 1 && hull[mid + 1].f(x) < cur) l = mid + 1;
else break;
}
return ans;
}
void add(Line d) {
int l = 1;
int r = curSZ - 1;
int pos = curSZ;
while(l <= r) {
int mid = (l + r) >> 1;
if (bad(hull[mid - 1], hull[mid], d)) {
pos = mid;
r = mid - 1;
}
else {
l = mid + 1;
}
}
st.push({{pos, curSZ}, hull[pos]});
curSZ = pos + 1;
hull[pos] = d;
}
void rollback() {
if (st.empty()) return;
auto v = st.top();
st.pop();
hull[v.first.first] = v.second;
curSZ = v.first.second;
}
};
CHT cht;
void dfs(int i, int par) {
dp[i] = dist[i] * v[i] + c[i];
// cerr << i << el;
ll cur = cht.query(v[i]) + v[i] * dist[i] + c[i];
// cerr << v[i] << " " << dist[i] << " " << c[i] << el;
dp[i] = min(dp[i], cur);
// cout << dp[2] << el;
cht.add(Line(-dist[i], dp[i]));
for(auto [v, w] : adj[i]) {
if (v == par) continue;
dist[v] = dist[i] + w;
dfs(v, i);
}
cht.rollback();
}
void solve() {
cin >> n;
for(int i = 1; i < n; ++i) {
int u, v;
ll w;
cin >> u >> v >> w;
adj[u].eb(v, w);
adj[v].eb(u, w);
}
memset(dp, 0x3f, sizeof(dp));
dp[1] = 0;
for(int i = 2; i <= n; ++i) {
cin >> c[i] >> v[i];
}
cht.init(n);
dfs(1, -1);
for(int i = 2; i <= n; ++i) {
cout << dp[i] << " ";
}
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
#define task "task"
if(fopen(task".inp", "r")) {
freopen(task".inp", "r", stdin);
freopen(task".out", "w", stdout);
}
solve();
return 0;
}
/*
634 100 611 1526 260
*/
