#include <bits/stdc++.h>
using namespace std;
const int N=1e5+5;
#define fi first
#define se second
struct Line{
long long m,b;
};
struct SAVE{
int x;
int y;
Line z;
};
int n;
vector <pair <int,int>> s[N];
vector <SAVE> Save;
int a[N], b[N];
int d[N];
long long dp[N];
int Size = 0;
Line line[N];
bool bad(Line l1, Line l2, Line l3){
return ((1ll * (l1.b - l2.b) * (l3.m - l1.m)) > (1ll * (l1.b - l3.b) * (l2.m - l1.m)));
}
long long calc(int x, int id){
return 1ll * line[id].m * x + line[id].b;
}
void add_Line(long long m, long long b){
int l = 1, r = Size;
int id = Size + 1;
Line newLine = {m, b};
// while(l <= r){
// int mid = (l + r)/2;
// if (bad(line[mid - 1], line[mid], newLine)){
// id = mid;
// r = mid - 1;
// }
// else l = mid + 1;
// }
for (int i = Size; i >= 2; i--){
if (bad(line[i - 1], line[i], newLine)){
id = i;
}
else break;
}
Save.push_back({id, Size, line[id]});
Size = id;
line[id] = newLine;
}
long long Query(int x){
int l = 1, r = Size;
long long ans = 1e18;
while (l <= r){
int mid = (l + r)/2;
long long u = calc(x, mid);
long long v = calc(x, mid + 1);
if (u >= v) l = mid + 1;
else r = mid - 1;
ans = min({ans, u, v});
}
return ans;
}
void undo(){
int id = Save.back().x;
int re_size = Save.back().y;
Line old_line = Save.back().z;
line[id] = old_line;
Size = re_size;
Save.pop_back();
}
void dfs(int i, int pre){
if (i != pre){
dp[i] = a[i] + 1ll * d[i] * b[i] + Query(b[i]);
}
add_Line( -d[i], dp[i]);
for (auto x: s[i]){
if (x.fi == pre)
continue;
d[x.fi] = d[i] + x.se;
dfs(x.fi, i);
}
undo();
}
void solve()
{
cin >> n;
for (int i = 1; i < n; i++){
int u,v,w;
cin >> u >> v >> w;
s[u].push_back({v,w});
s[v].push_back({u,w});
}
for (int i = 2; i <= n; i++){
cin >> a[i] >> b[i];
}
dfs(1, 1);
for (int i = 2; i <= n; i++){
cout << dp[i] << " ";
}
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);cout.tie(NULL);
solve();
return 0;
}
