#define here cerr<<"===========================================\n"
#define dbg(x) cerr<<#x<<": "<<x<<endl;
#include <bits/stdc++.h>
#define llinf 100000000000000000LL // 10^17
#define iinf 2000000000 // 2*10^9
#define pb push_back
#define eb emplace_back
#define popb pop_back
#define fi first
#define sc second
#define endl '\n'
#define all(a) a.begin(),a.end()
#define ceri(a,l,r) {cerr<<#a<<": ";for(ll i_ = l;i_<=r;i_++) cerr<<a[i_]<< " ";cerr<<endl;}
#define cer(a) {cerr<<#a<<": ";for(ll x_ : a) cerr<<x_<< " ";cerr<<endl;}
#define si(a) (ll)(a.size())
using namespace std;
using ld = double;
using ll = int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
#define mod 1
ll add(ll x,ll y){
x+=y;
if(x<0){
x%=mod;
x+=mod;
}else{
if(x>=mod) x%=mod;
}
return x;
}
ll mul(ll a,ll b){
a = add(a,0);
b = add(b,0);
ll ans = (a*b)%mod;
if(ans<0) ans+=mod;
return ans;
}
const ll maxn = 100005;
const ll lg = 18;
ll n;
vector<pll> g[maxn];
ll dub[maxn];
pll a[maxn];
long long dp[maxn];
#define pld array<ld,3>
ld f(pld a,pld b) {
return (a[1]-b[1])/(b[0]-a[0]);
}
pld stk[maxn];
ll up[lg][maxn];
ll id[maxn],tsz = 0;
void dfs(ll u,ll p) {
for(pll q : g[u]) {
ll s = q.fi,w = q.sc;
if(s==p) continue;
dub[s] = dub[u] + w;
id[s] = ++tsz;
up[0][tsz] = id[u];
for(ll j = 1;j<lg;j++) up[j][tsz] = up[j-1][up[j-1][tsz]];
ll cur = tsz;
for(ll j = lg-1;j>=0;j--) {
if(a[s].sc<stk[up[j][cur]][2]) cur = up[j][cur];
}
cur = up[0][cur];
dp[s] = (long long)a[s].fi + (long long)a[s].sc*(long long)dub[s] + (long long)stk[cur][0]*(long long)a[s].sc + (long long)stk[cur][1];
stk[tsz] = {-dub[s]*1.0,dp[s]*1.0,1.0*llinf};
cur = tsz;
for(ll j = lg-1;j>=0;j--) {
ld cx = f(stk[up[j][cur]],stk[tsz]);
if(cx<=stk[up[j][cur]][2]) cur = up[j][cur];
}
cur = up[0][cur];
ld cx = f(stk[cur],stk[tsz]);
stk[tsz] = {-dub[s]*1.0,dp[s]*1.0,cx};
up[0][tsz] = cur;
for(ll j = 1;j<lg;j++) up[j][tsz] = up[j-1][up[j-1][tsz]];
dfs(s,u);
}
}
void tc(){
cerr<<fixed<<setprecision(12);
cin >> n;
for(ll i = 1;i<=n-1;i++) {
ll x,y,d; cin >> x >> y >> d;
g[x].pb({y,d});
g[y].pb({x,d});
}
for(ll i = 2;i<=n;i++) cin >> a[i].fi >> a[i].sc;
dp[1] = 0;
id[1] = 0;
stk[0] = {0,0,-llinf};
dfs(1,1);
for(ll i = 2;i<=n;i++) cout<<dp[i]<< " ";
cout<<endl;
}
int main(){
ios_base::sync_with_stdio(false);cerr.tie(0);cout.tie(0);cin.tie(0);
int t; t = 1;
while(t--){
tc();
}
return (0-0);
}
