#include <bits/stdc++.h>
using namespace std;
#define ff first
#define ss second
#define bl ' '
#define endl '\n'
#define all(v) (v).begin(), (v).end()
#define comp(v) (v).erase(unique(all(v)), (v).end())
#define lbd(v,x) lower_bound(all(v), (x))-(v).begin()
#define ubd(v,x) upper_bound(all(v), (x))-(v).begin()
typedef long long ll;
typedef pair<int, int> pi;
typedef pair<pi, int> pii;
typedef pair<int, pi> ipi;
typedef pair<pi, pi> pipi;
typedef pair<ll, ll> pll;
const int MAXN = 100100*1;
const ll MOD = 1e9+7;
const ll INF = 2e9;
vector<pi> adj[MAXN];
int S[MAXN], V[MAXN];
int dst[MAXN]; ll dp[MAXN];
struct Lichao {
struct Line {
int a; ll b;
ll get(ll x) {
return a*x+b;
}
};
struct Node {
int l, r; Line line;
};
vector<Node> tree;
Node base = {0, 0, {0, LLONG_MAX}};
int root[MAXN];
void init() {
root[1] = 1;
tree.push_back(base); tree.push_back({0, 0, {0, 0}});
}
void update(int pv, int node, ll s, ll e, Line line) {
Line low = tree[node].line, high = line;
if(low.get(s) > high.get(s)) swap(low, high);
if(low.get(e) <= high.get(e)) {
tree[node].line = low; return;
}
ll mid = s+e>>1;
if(low.get(mid) >= high.get(mid)) {
tree[node].line = high;
tree[node].l = tree.size();
tree.push_back(tree[tree[pv].l]);
update(tree[pv].l, tree[node].l, s, mid, low);
} else {
tree[node].line = low;
tree[node].r = tree.size();
tree.push_back(tree[tree[pv].r]);
update(tree[pv].r, tree[node].r, mid+1, e, high);
}
}
ll solve(int node, int s, int e, int x) {
if(node == 0) return LLONG_MAX;
int mid=s+e>>1; ll res = tree[node].line.get(x);
if(x <= mid) res = min(res, solve(tree[node].l, s, mid, x));
else res = min(res, solve(tree[node].r, mid+1, e, x));
return res;
}
}lichao;
void dfs(int here, int par) {
for(auto [there,w]:adj[here]) {
if(there==par) continue;
dst[there] = dst[here]+w;
dfs(there, here);
}
}
void solve(int here, int par) {
for(auto [there,w] : adj[here]) {
if(there==par) continue;
dp[there] = S[there]+(ll)V[there]*dst[there] + lichao.solve(lichao.root[here], 0, INF, V[there]);
lichao.root[there] = lichao.tree.size(); lichao.tree.push_back(lichao.tree[lichao.root[here]]);
lichao.update(lichao.root[here], lichao.root[there], 0, INF, {-dst[there], dp[there]});
solve(there, here);
}
}
int main() {
ios_base::sync_with_stdio(0); cin.tie(0);
int n; cin>>n;
for(int i=1; i<n; i++) {
int a, b, c; cin>>a>>b>>c;
adj[a].push_back(pi(b,c));
adj[b].push_back(pi(a,c));
}
for(int i=2; i<=n; i++) cin>>S[i]>>V[i];
dfs(1, 1);
dp[1] = 0; lichao.init();
solve(1, 1);
for(int i=2; i<=n; i++) cout<<dp[i]<<bl;
}
