#include <bits/stdc++.h>
using namespace std;
mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
#define N 100010
#define K 102
#define MV 1000000010
#define INFLL 1000000000000000010
#define pb push_back
#define ppb pop_back
#define pf push_front
#define ppf pop_front
typedef long long ll;
typedef pair<ll,ll> pll;
typedef vector< ll > vl;
typedef vector< pll > vll;
struct Node
{
ll a;
ll b;
ll u;
ll getval(ll x)
{
return a*x+b;
}
};
struct Line
{
vector<Node>nodes;
ll lef=-1;
ll rig=-1;
};
stack<ll>pilha;
vector<Line>lines;
Line lx;
vector<pll>grafo[N];
ll dp[N];
ll d[N];
ll s[N];
ll c[N];
bool active[N];
ll createl()
{
lines.pb(lx);
lines.back().nodes.pb({0,0,1});
return lines.size()-1;
}
void update(ll i,ll l,ll r,Node cur)
{
ll mid=((l+r)>>1LL);
ll lef=lines[i].lef;
ll rig=lines[i].rig;
while(!active[lines[i].nodes.back().u])
{
lines[i].nodes.ppb();
}
ll pos=lines[i].nodes.size()-1;
if(l==r-1)
{
if(cur.getval(l)<lines[i].nodes[pos].getval(l))
{
lines[i].nodes.pb(cur);
}
return;
}
Node auxc=cur;
Node auxl=lines[i].nodes[pos];
bool swi=false;
if(auxc.a>auxl.a)
swap(auxc,auxl),swi=true;
if(auxc.getval(mid)<auxl.getval(mid))
{
lines[i].nodes.pb(auxc);
cur=auxl;
if(lef==-1)
lef=createl();
update(lef,l,mid,cur);
}else
{
lines[i].nodes.pb(auxl);
cur=auxc;
if(rig==-1)
rig=createl();
update(rig,mid,r,cur);
}
lines[i].lef=lef;
lines[i].rig=rig;
return;
}
ll query(ll i,ll l,ll r,ll x)
{
if(i==-1)
return INFLL;
while(!active[lines[i].nodes.back().u])
{
lines[i].nodes.ppb();
}
ll pos=lines[i].nodes.size()-1;
if(l==r-1)
return lines[i].nodes[pos].getval(x);
ll mid=((l+r)>>1LL);
ll lef=lines[i].lef;
ll rig=lines[i].rig;
if(x<mid)
return min(lines[i].nodes[pos].getval(x),query(lef,l,mid,x));
return min(lines[i].nodes[pos].getval(x),query(rig,mid,r,x));
}
void DFS(ll u,ll p)
{
active[u]=true;
if(u==p)
{
createl();
}
dp[u]=d[u]*s[u]+c[u]+query(0,0,MV,s[u]);
Node cur={-d[u],dp[u],u};
update(0,0,MV,cur);
for(auto [v,w] : grafo[u])
{
if(v==p)
continue;
d[v]=d[u]+w;
DFS(v,u);
}
active[u]=false;
return;
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
ll n,u,v,w;
cin >> n;
for(ll i=2;i<=n;i++)
{
cin >> u >> v >> w;
grafo[u].pb({v,w});
grafo[v].pb({u,w});
}
for(ll i=2;i<=n;i++)
{
cin >> c[i] >> s[i];
}
DFS(1,1);
for(ll i=2;i<=n;i++)
{
cout << dp[i] << ((i==n) ? '\n' : ' ');
}
return 0;
}
