#include <bits/stdc++.h>
using namespace std;
#define int long long
const int N = 3e5+5;
const int inf = 1e17;
int dp[N],st[N],en[N],dis[N],prep[N],v[N];
vector<pair<int,int> > A[N];
int timer = 1;
// lichao with segment and min
int n;
struct Line{
int a,b;
int operator()(int x) {return a * x + b;};
Line(int x,int y) {
a=x,b=y;
}
};
struct Node{
Line* line;
Node *left, *right;
Node(Line* ln) {
line = ln;
left=right=nullptr;
}
Node() {
line=nullptr;
left=right=nullptr;
}
void upd(Line* nw,int ll,int rr,int l = 1,int r = n) {
if(l > rr || r < ll || l > r)return;
int mid = l + (r-l)/2;
if(l>=ll&&r<=rr){
if(!line) {
line=nw;
return;
}
int ls = (*nw)(l) < (*line)(l);
int ms = (*nw)(mid) < (*line)(mid);
if(ms)swap(line,nw);
if(l==r)return;
if(ms!=ls){
if(!left)left = new Node(nw);
else left->upd(nw,ll,rr,l,mid);
} else {
if(!right)right = new Node(nw);
else right->upd(nw,ll,rr,mid+1,r);
}
} else {
if(!(rr < l || ll > mid)) {
if(!left) left = new Node();
left->upd(nw,ll,rr,l,mid);
}
if(!(rr < mid + 1 || ll > r)){
if(!right)right = new Node();
right->upd(nw,ll,rr,mid+1,r);
}
}
}
int qry(int x,int l = 1,int r = n) {
int res = (line ? (*line)(x) : inf);
if(l==r)return res;
int mid = l + (r-l)/2;
if(x<=mid) {
if(left)return min(res,left->qry(x,l,mid));
} if(right) return min(res,right->qry(x,mid+1,r));
return res;
}
}t;
void dfs2(int i,int par = -1) {
if(par!=-1) {
dp[i] = prep[i] + v[i] * dis[i] + t.qry(v[i]);
t.upd(new Line(-dis[i],dp[i]),st[i],en[i]);
}
for(auto [nxt,w] : A[i])if(nxt!=par)dfs2(nxt,i);
}
void dfs(int u,int par = -1) {
// do parents
st[u]=timer++;
for(auto [nxt,w] : A[u])if(nxt!=par){
dis[nxt] = dis[u] + w;
dfs(nxt,u);
}
en[u]=timer;
}
int32_t main() {
cin.tie(0)->sync_with_stdio(0);
int a,b,w;
cin >> n;
for(int i = 0;i<n-1;i++) {
cin >> a >> b >> w;
A[a].push_back({b,w});
A[b].push_back({a,w});
}
for(int i = 2;i<=n;i++)cin>>prep[i]>>v[i];
t.upd(new Line(0,0),1,n);
// get dis values + do lichao
dfs(1);
dfs2(1);
for(int i = 2;i<=n;i++) cout << dp[i] << " ";
}
