#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template<class T> bool cmin(T &i, T j) { return i > j ? i=j,true:false; }
template<class T> bool cmax(T &i, T j) { return i < j ? i=j,true:false; }
mt19937 mrand(chrono::steady_clock::now().time_since_epoch().count());
uniform_int_distribution<int> ui(0, 1 << 30);
int rng() {
return ui(mrand);
}
const int N = 100100;
vector<pair<int,int>> adj[N];
ll start[N];
ll speed[N];
ll depth[N];
ll dp[N];
int n;
struct line {
ll m,q;
ll eval(ll x) { return m * x + q; }
double intersect(line &l) { return (double)(q - l.q) / (l.m - m); }
};
int sz[N],head[N],par[N];
vector<line> containers[N];
void dfs(int u = 0,int p = -1) {
sz[u] = 1;
par[u] = p;
for (auto &[v,w]: adj[u]) if (v != p) {
depth[v] = depth[u] + w;
dfs(v,u);
sz[u] += sz[v];
}
sort(adj[u].begin(),adj[u].end(),[&](auto &x,auto &y) {
return sz[x.first] > sz[y.first];
});
}
void dfs2(int u = 0,int p = -1,int h = 0) {
bool g = 1;
head[u] = h;
for (auto &[v,w]: adj[u]) if (v != p) {
if (!g) {
dfs2(v,u,h);
g = 0;
} else {
dfs2(v,u,v);
}
}
}
ll eval(vector<line> &dq,ll x) {
if (dq.empty())
return 1LL << 60;
int lo = 0, hi = dq.size();
while(lo < hi) {
int mid = lo + (hi - lo) / 2;
if (mid + 1 == dq.size() || dq[mid].intersect(dq[mid + 1]) >= x) {
hi = mid;
} else {
lo = mid + 1;
}
}
return dq[lo].eval(x);
}
void dfs3(int u = 0,int p = -1) {
if (u > 0) {
int uu = u;
dp[u] = 1LL << 60;
while(uu != -1) {
uu = head[uu];
cmin(dp[u],eval(containers[uu],speed[u]));
uu = par[uu];
}
dp[u] += start[u] + depth[u] * speed[u];
}
line cur{-depth[u],dp[u]};
auto &dq = containers[head[u]];
while(dq.size() >= 2 && cur.intersect(dq[dq.size() - 1]) <= dq[dq.size() - 1].intersect(dq[dq.size() - 2])) {
dq.pop_back();
}
dq.push_back(cur);
reverse(adj[u].begin(),adj[u].end());
for (auto &[v,w]: adj[u]) if (v != p)
dfs3(v,u);
}
void solve() {
cin >> n;
for (int u,v,w,i=1;i<n;i++) {
cin >> u >> v >> w;
--u,--v;
adj[u].emplace_back(v,w);
adj[v].emplace_back(u,w);
}
for (int i = 1; i < n; i++)
cin >> start[i] >> speed[i];
dfs();
dfs2();
dfs3();
for (int i = 1; i < n; i++)
cout << dp[i] << " ";
cout << "\n";
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int testcases = 1;
// cin >> testcases;
for (int i = 1; i <= testcases; i++)
solve();
}
