#include <iostream>
#include <vector>
using namespace std;
#define int long long
const int N = 1<<17, inf = 1e9;
vector<pair<int, int>> nei[N];
int Par[N][20], c[N], m[N], cst[N], dp[N], pre[N], sp[N], start[N];
int intersection(int i, int j){
int k = (c[i] - c[j]) / (m[j] - m[i]);
if ((c[i] - c[j]) % (m[j] - m[i]) != 0 and c[i] - c[j] > 0)
k++;
return k;
}
void dfs(int u, int pr, int id){
dp[u] = cst[u] + pre[u] * sp[u];
if (id > 0){
int k = id;
for (int i=17;i>=0;i--){
if (Par[k][i] == 0 or start[Par[k][i]] <= sp[u])
continue;
k = Par[k][i];
}
if (start[k] > sp[u])
k = Par[k][0];
dp[u] = min(dp[u], dp[k] + cst[u] + (pre[u] - pre[k]) * sp[u]);
// cout<<u<<" "<<k<<endl;
}
m[u] = inf - pre[u];
c[u] = dp[u];
// for (int i=17;i>=0;i--){
// if (Par[id][i] != 0 and intersection(u, Par[id][i]) <= start[Par[id][i]])
// id = Par[Par[id][i]][0];
// }
while (id != 0 and intersection(u, id) <= start[id])
id = Par[id][0];
if (id)
start[u] = intersection(u, id);
Par[u][0] = id;
for (int i=0;i<17;i++)
Par[u][i+1] = Par[Par[u][i]][i];
for (auto [i, w] : nei[u]){
if (i == pr)
continue;
pre[i] = pre[u] + w;
dfs(i, u, u);
}
}
signed main(){
int n;
cin>>n;
for (int i=1;i<n;i++){
int a, b, c;
cin>>a>>b>>c;
nei[a].push_back({b, c});
nei[b].push_back({a, c});
}
for (int i=2;i<=n;i++)
cin>>cst[i]>>sp[i];
dfs(1, 1, 0);
for (int i=2;i<=n;i++)
cout<<dp[i]<<' ';
cout<<'\n';
// cout<<Par[4][0]<<endl;
}
