#include <bits/stdc++.h>
using namespace std;
#define all(v) v.begin(),v.end()
#define pb push_back
#define ll long long
#define ld long double
#define fi first
#define se second
#define mk make_pair
typedef pair<int,int> pii;
const int maxn = 1e5 + 10;
ll s[maxn],v[maxn];
vector<pii> adj[maxn];
int i,n,t;
struct Line
{
ll a,b;
Line():a(0),b(LLONG_MAX){}
Line(ll _a,ll _b):a(_a),b(_b){}
ll cal(ll x)const
{
return x * a + b;
}
};
struct LC:deque<Line>
{
stack<pair<int,Line>> mem;
stack<int> st;
inline ld xcut(const Line& a,const Line& b)
{
return (ld)(b.b - a.b) / abs(a.a-b.a);
}
inline bool check( const Line &a,const Line &b,const Line &c)
{
return xcut(a,b) <xcut(b,c);
}
LC()
{
push(Line(0,0));
make_checkpoint();
}
inline void rollback()
{
pair<int,Line> tmp = mem.top();
mem.pop();
if(tmp.fi==0)pop_back();
if(tmp.fi==1)push_back(tmp.se);
}
void make_checkpoint()
{
st.push(mem.size());
}
void erase_checkpoint()
{
st.pop();
while(mem.size() > st.top())rollback();
}
void push(Line a)
{
while(size()>1 && !check(end()[-2],end()[-1],a))
{
mem.push(mk(1,back()));
pop_back();
}
mem.push(mk(0,a));
push_back(a);
}
ll get(ll x)
{
int l = 0,r = size()-1;
while(l<r)
{
int mid = (l + r)/2;
if(xcut(at(mid),at(mid+1)) > x) r = mid;
else l = mid + 1;
}
return at(l).cal(x);
}
}CHT;
ll dp[maxn];
void dfs(int i,int pa,ll d)
{
if(pa)
{
dp[i] = s[i] + d * v[i] + CHT.get(v[i]);
CHT.push(Line(-d,dp[i] ));
}
CHT.make_checkpoint();
for(pii k : adj[i])
{
if(k.fi == pa)continue;
dfs(k.fi,i,d + k.se);
}
CHT.erase_checkpoint();
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(0);
if(fopen("harbingers.in","r"))
{
freopen("harbingers.in","r",stdin);
freopen("harbingers.out","w",stdout);
}
cin>>n;
for(i = 1;i<n;i++)
{
int u,v,w;
cin>>u>>v>>w;
adj[u].pb(mk(v,w));
adj[v].pb(mk(u,w));
}
for(i = 2;i<=n;i++)
{
cin>>s[i]>>v[i];
}
dfs(1,0,0);
for(i =2;i<=n;i++)cout<<dp[i]<<' ';
return 0;
}
