/****ThanhCodeDao*****/
/*******Azazel*******/
#include<bits/stdc++.h>
using namespace std;
#define F first
#define S second
#define pb push_back
#define checkbit(mask,i) ((mask>>i)&1)
#define bit(i) (1<<i)
#define MLog 21
typedef long long ll;
const ll maxN = 1e5+3, modd = 1e9+7;
struct Point{
ll x,y;
};
ll cross(Point p,Point q,Point r){ // vi tri r voi duong pq >0 la ben trai, =0 la thang hang
ll val = (q.x-p.x)*(r.y-q.y) - (q.y-p.y)*(r.x-q.x);
if(val < 0) return -1;
if(val > 0) return 1;
return 0;
}
ll dot(Point vecA,Point vecB){ // tra ve >0 la nhon, <0 la tu, =0 la vuong, 2 vecto phai chung goc
ll val = vecA.x*vecB.x + vecA.y*vecB.y;
if(val < 0) return -1;
if(val > 0) return 1;
return 0;
}
double triarea(Point p,Point q,Point r){ // cross(pq * pr) / 2
double cross = (q.x-p.x)*(r.y-q.y) - (q.y-p.y)*(r.x-q.x);
return fabs(cross)/2.0;
}
int n;
ll S[maxN],V[maxN];
ll d[maxN], dp[maxN];
int parent[maxN];
vector<pair<int,int>> adj[maxN];
void pre_dfs(int u,int par){
parent[u] = par;
for(pair<int,int> pp : adj[u]){
int v = pp.F, w = pp.S;
if(v==par) continue;
d[v] = d[u] + w;
pre_dfs(v,u);
}
}
namespace sub1{
ll cost(int u,int v){
return V[v]*(d[v] - d[u]) + S[v];
}
void dfs(int u,int par){
for(pair<int,int> pp : adj[u]){
int v = pp.F, w = pp.S;
if(v==par) continue;
int vv = v;
while(vv != 0){
dp[v] = min(dp[v],dp[vv] + cost(vv,v));
vv = parent[vv];
}
dfs(v,u);
}
}
void solve(){
dfs(1,0);
for(int i = 2;i<=n;i++) cout << dp[i] << " ";
}
}
namespace sub2{
struct Line{
ll a,b;
} good[maxN],lines[maxN];
double e[maxN];
int k = 0;
double gd(Line l1,Line l2){
assert((l1.a - l2.a)!=0);
return double(l2.b - l1.b) / double(l1.a - l2.a);
}
bool isdelete(Line l1,Line l2,Line l3){
if(l2.a == l3.a) return (l2.b >= l3.b);
if(k==1) return false;
double x1 = gd(l1,l2);
double x2 = gd(l1,l3);
return x2 <= x1;
}
void upl(Line val){
while(k>=1 and isdelete(good[k-1],good[k],val)){
--k;
}
good[++k] = val;
if(k>=2) e[k-1] = gd(good[k-1],good[k]);
e[k] = 1e18;
}
Line getl(ll x){
int best = lower_bound(e+1,e+1+k,x) - e;
return good[best];
}
void dfs(int u,int par){
Line f = getl(V[u]);
dp[u] = V[u] * d[u] + V[u]*f.a + S[u] + f.b;
lines[u].a = -d[u], lines[u].b = dp[u];
upl(lines[u]);
for(pair<int,int> pp : adj[u]){
int v = pp.F;
if(v==par) continue;
dfs(v,u);
}
}
void calc(int s){
k = 0;
lines[0] = {0,0};
upl(lines[0]);
dfs(s,1);
}
void solve(){
for(pair<int,int> pp : adj[1]){
int u = pp.F;
calc(u);
}
for(int i = 2;i<=n;i++) cout << dp[i] << " ";
}
}
void solve() {
cin >> n;
for(int i = 2;i<=n;i++){
int u,v,w;
cin >> u >> v >> w;
adj[u].pb({v,w});
adj[v].pb({u,w});
}
for(int i = 2;i<=n;i++){
cin >> S[i] >> V[i];
dp[i] = 1e18;
}
pre_dfs(1,0);
if(n<=2500){
sub1::solve();
return;
}
sub2::solve();
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0), cout.tie(0);
//freopen("inp.txt","r",stdin);
//freopen("out.txt","w",stdout);
solve();
return 0;
}
