#include<bits/stdc++.h>
#define fi first
#define se second
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pii;
const ll INF=1e15;
const ll N=1e5+5;
struct line
{
ll a,b;
line() {a=b=0;}
line(ll _a,ll _b)
{
a=_a;
b=_b;
}
ll val(ll x){return a*x+b;}
};
double inter(line a,line b)
{
return (1.0*(b.b-a.b))/(1.0*(a.a-b.a));
}
ll n,cn;
line lines[N];
vector<pair<pii,line>> liem;
vector<pii> graph[N];
ll h[N],s[N],v[N];
ll dp[N];
void addline(line f)
{
ll l=1,r=cn-1,temp=cn;
while(l<=r)
{
ll mid=(l+r)>>1;
if(inter(lines[mid],lines[mid-1])>=inter(lines[mid],f))
{
temp=mid;
r=mid-1;
}
else l=mid+1;
}
liem.push_back({{temp,cn},lines[temp]});
cn=temp+1;
lines[temp]=f;
}
void rollback()
{
lines[liem.back().fi.fi]=liem.back().se;
cn=liem.back().fi.se;
liem.pop_back();
}
ll get(ll x)
{
ll l=1,r=cn-1,temp=0;
while(l<=r)
{
ll mid=(l+r)>>1;
if(inter(lines[mid],lines[mid-1])<x)
{
temp=mid;
l=mid+1;
}
else r=mid-1;
}
return lines[temp].val(x);
}
void dfs_init(ll u,ll p)
{
for(ll i=0;i<(ll)graph[u].size();i++)
{
ll v=graph[u][i].fi,w=graph[u][i].se;
if(v==p) continue;
h[v]=h[u]+w;
dfs_init(v,u);
}
}
void dfs(ll u,ll p)
{
//cout << u << ' ' << p << ' ' << cn << ":" << endl;
//for(ll i=1;i<=cn;i++) cout << lines[i].a << ' ' << lines[i].b << endl;
//cout << "===" << endl;
if(u!=1) dp[u]=get(v[u])+1ll*h[u]*v[u]+s[u];
addline(line(-h[u],dp[u]));
for(ll i=0;i<(ll)graph[u].size();i++)
{
ll v=graph[u][i].fi;
if(v==p) continue;
dfs(v,u);
}
rollback();
}
void solve()
{
cin >> n;
for(ll i=1;i<n;i++)
{
ll u,v,w;
cin >> u >> v >> w;
graph[u].push_back({v,w});
graph[v].push_back({u,w});
}
for(ll i=2;i<=n;i++) cin >> s[i] >> v[i];
dfs_init(1,1);
dfs(1,1);
for(ll i=2;i<=n;i++) cout << dp[i] << ' ';
cout << endl;
}
int main()
{
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
if(fopen("lftroq.inp","r"))
{
freopen("lftroq.inp","r",stdin);
freopen("lftroq.out","w",stdout);
}
solve();
return 0;
}
