///*** Sown_Vipro ***///
/// ->TUYEN QUOC GIA<- ///
#pragma GCC optimize ("O3")
#pragma GCC optimize ("unroll-loops")
#pragma GCC target("popcnt")
#include<bits/stdc++.h>
using namespace std;
#define F first
#define S second
#define pb push_back
#define pi pair<int, int>
#define pii pair<int, pair<int, int> >
#define all(a) a.begin(), a.end()
#define inp(name) if(fopen(name, "r")) freopen(name, "r", stdin);
#define out(name) if(fopen(name, "w")) freopen(name, "w", stdout);
const int N = 1e5 + 5, MAX = 1e9 + 5, MOD = 1e9 + 7;
int n, k;
int a[N], b[N], d[N];
long long dp[N];
double pt[N];
struct line{
long long a, b;
} l[N], s[N];
vector<pi> e[N];
double dis(line A, line B){
return (-1.0 * (A.b - B.b) / (A.a - B.a));
}
int check(line A, int m){
double x1 = dis(A, s[m - 1]);
double x2 = dis(s[m], s[m - 1]);
return x1 < x2;
}
int pos(line ln){
int l = 2, r = k;
while(l <= r){
int mid = (l + r) / 2;
if(check(ln, mid)){
r = mid - 1;
}else l = mid + 1;
}
return r + 1;
}
void dfs(int u, int p){
if(u == 1){
for(auto [v, w] : e[u]){
if(v == p) continue;
d[v] = d[u] + w;
dfs(v, u);
}
return;
}
int id = lower_bound(pt + 1 , pt + 1 + k, b[u]) - pt;
dp[u] = 1ll * d[u] * b[u] - (s[id].a * b[u] + s[id].b) + a[u];
l[u] = {d[u], -dp[u]};
int old_k = k, old_pos = k = pos(l[u]);
line old_line = s[old_pos];
double old_pt1 = pt[old_pos - 1], old_pt2 = pt[old_pos];
// cout << u << " " << o
s[old_pos] = l[u];
pt[old_pos - 1] = dis(s[old_pos - 1], s[old_pos]);
pt[old_pos] = 1.0e18;
for(auto [v, w] : e[u]){
if(v == p) continue;
d[v] = d[u] + w;
dfs(v, u);
}
k = old_k;
s[old_pos] = old_line;
pt[old_pos - 1] = old_pt1;
pt[old_pos] = old_pt2;
}
void solve(){
cin >> n;
for(int i = 2; i <= n; ++i){
int u, v, w; cin >> u >> v >> w;
e[u].pb({v, w});
e[v].pb({u, w});
}
for(int u = 2; u <= n; ++u){
cin >> a[u] >> b[u];
}
s[++k] = {0, 0};
pt[k] = 1.01e18;
dfs(1, 0);
for(int u = 2; u <= n; ++u){
cout << dp[u] << " ";
}
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
inp("in.txt");
// out("out.txt");
solve();
}
