#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ii pair<int, int>
#define fi first
#define se second
const int N = 1e5 + 5,
INF = 1e18;
int n, S[N], V[N], dep[N], dp[N];
vector<ii> ad[N];
void cal_depth(int u, int p){
for(auto [v, w] : ad[u]) if(v != p){
dep[v] = dep[u] + w;
cal_depth(v, u);
}
}
bool ok = false;
struct Line{
int a, b; // y = a*x + b;
Line(){}
Line(int a, int b): a(a), b(b) {}
double x(Line rhs){ return 1.0*(b - rhs.b)/(rhs.a - a); }
int valy(int x){ return a * x + b; }
friend ostream& operator << (ostream& os, Line &rhs){
return os << "(" << rhs.a << ", " << rhs.b << ")";
}
};
struct CHT{
Line convex[N];
pair<Line*, Line> rl[N];
pair<int*, int> rp[N];
int bot = 1, top = 0, it = 0;
int add(Line line){
rp[it] = {&top, top};
int l = bot, r = top, k = top + 1;
while(l <= r){
int mid = l + r >> 1;
if(convex[mid - 1].x(convex[mid]) > convex[mid - 1].x(line)) r = (k = mid) - 1;
else l = mid + 1;
}
top = k;
rl[it] = {convex + top, convex[top]};
convex[top] = line;
it++;
return it - 1;
}
void rollback(int t){
for(; it > t;){
--it;
*rl[it].first = rl[it].second;
*rp[it].first = rp[it].second;
}
}
int query(int x){
int l = bot, r = top, res = convex[l].valy(x);
while(l <= r){
int mid = l + r >> 1;
int y1 = convex[mid].valy(x),
y2 = convex[mid + 1].valy(x);
if(y1 > y2) l = mid + 1;
else r = mid - 1;
res = min({res, y1, y2});
}
return res;
}
} cht;
void dfs(int u, int p){
int it = cht.add(Line(-dep[u], dp[u]));
for(auto [v, w] : ad[u]) if(v != p){
dp[v] = cht.query(V[v]) + dep[v] * V[v] + S[v];
dfs(v, u);
}
cht.rollback(it);
}
int32_t main(){
cin.tie(0)->sync_with_stdio(0);
cin >> n;
for(int i = 2; i <= n; i++){
int u, v, w; cin >> u >> v >> w;
ad[u].push_back({v, w});
ad[v].push_back({u, w});
}
for(int i = 2; i <= n; i++) cin >> S[i] >> V[i];
cal_depth(1, -1);
dfs(1, -1);
for(int i = 2; i <= n; i++) cout << dp[i] << " ";
return 0;
}
