#include <bits/stdc++.h>
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
#define all(x) begin(x),end(x)
template<class T>
using iset=tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
void solve(){
int n;
cin>>n;
vector<vector<array<long long,2>>> g(n);
for(int i=1;i<n;i++){
int x,y,z;
cin>>x>>y>>z;
x--;
y--;
g[x].push_back({y,z});
g[y].push_back({x,z});
}
vector<array<long long,2>> a(n);
for(int i=1;i<n;i++){
cin>>a[i][0]>>a[i][1];
}
vector<long long> sol(n);
vector<int> father(n);
vector<long long> depth(n);
auto dfs=[&](auto&&dfs,int x)->void
{
sol[x]=depth[x]*a[x][1]+a[x][0];
{
int y=father[x];
while(y!=0){
sol[x]=min(sol[x], (depth[x]-depth[y])*a[x][1] + a[x][0] + sol[y] );
y=father[y];
}
}
for(auto[y,z]:g[x]){
if(y==father[x])continue;
depth[y]=depth[x]+z;
father[y]=x;
dfs(dfs,y);
}
};
for(auto[x,y]:g[0]){
father[x]=0;
depth[x]=y;
dfs(dfs,x);
}
for(int i=1;i<n;i++){
cout<<sol[i]<<" \n"[i==n-1];
}
}
int main(){
ios::sync_with_stdio(false);
cin.tie(NULL);
int numberOfTests=1;
//cin>>numberOfTests;
while(numberOfTests--){
solve();
}
}
