#include <bits/stdc++.h>
using namespace std;
#define se second
#define fi first
#define ll long long
#define all(a) a.begin(),a.end()
#define eb push_back
#define ld long double
typedef pair<int,int> pii;
int i,n,t,u,v,w;
const int maxn = 1e5 + 10;
vector<pii> adj[maxn];
ll d[maxn],a[maxn],b[maxn],dp[maxn];
struct line
{
ll a,b;
line():a(0),b(0){};
line(ll A,ll B):a(A),b(B){};
ll cal(const ll &x){return a * x + b;}
friend ld xcut(const line &a,const line &b){return (ld)(b.b - a.b) / (a.a - b.a);}
friend bool check(const line &a,const line &b,const line &c){return xcut(a,b)<xcut(b,c);}
};
struct cht
{
line hull[maxn * 2];
struct mem
{
int pos,S;
line value;
};
stack<mem>st;
int sz = 0;
void push(const line & a)
{
int l = 1,r = sz,mid;
while(l < r)
{
mid = (l + r)/2;
if(!check(hull[mid-1],hull[mid],a))
{
r = mid;
}
else l = mid + 1;
}
l = r;
st.push({l,sz,hull[l]});
hull[l] = a;
sz = l + 1;
}
void fix()
{
if(st.empty())return;
mem tmp = st.top();
st.pop();
hull[tmp.pos] = tmp.value;
sz = tmp.S;
}
ll cal(const ll &x)
{
int l = 0,r = sz-1,mid;
while(l<r)
{
mid = (l + r)/2;
if(xcut(hull[mid],hull[mid+1]) < x)l = mid+1;
else r = mid;
}
return hull[l].cal(x);
}
}lc;
void dfs(int i,int p)
{
// if(i == 6 || i == 8)
// {
// for(int k = 0;k<lc.sz;k++)cout<<lc.hull[k].a<<' '<<lc.hull[k].b<<'\n';
// cout<<d[i]<<'\n';
// }
if(i > 1)
{
dp[i] = a[i] * d[i] + b[i];
if(p != 1)
{
dp[i] = min(dp[i],lc.cal(a[i]) + a[i] * d[i] + b[i]);
}
lc.push(line(-d[i],dp[i]));
}
for(pii k : adj[i])
{
if(k.fi == p)continue;
d[k.fi] = d[i] + k.se;
dfs(k.fi,i);
}
if(i > 1)lc.fix();
}
// dp[j] - d[j] * a[i] + a[i] * d[i] b[i]
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(0);
cin>>n;
for(i = 1;i<n;i++)
{
cin>>u>>v>>w;
adj[u].eb({v,w});
adj[v].eb({u,w});
}
for(i = 2;i<=n;i++)cin>> b[i]>>a[i];
dfs(1,0);
for(i = 2;i<=n;i++)cout<<dp[i]<<' ';
return 0;
}
