/*
www.youtube.com/YugiHackerChannel
oj.vnoi.info/user/YugiHackerKhongCopCode
*/
#include<bits/stdc++.h>
#define el cout<<"\n"
#define f0(i,n) for(int i=0;i<n;++i)
#define f1(i,n) for(int i=1;i<=n;++i)
#define maxn 100005
#define pii pair<int,int>
#define fi first
#define se second
using namespace std;
int n, S[maxn], V[maxn];
vector <pii> adj[maxn];
long long dp[maxn], depth[maxn];
struct Line {
long long a, b;
long long cal(long long x) const{return a*x + b;}
};
int top;
Line lines[maxn];
struct save{int pos, cur_top; Line L;};
vector<save> roll_backs;
bool check(Line &A, Line &B, Line &C) {
return (double) (A.b - B.b) * (C.a - B.a) >= (double) (C.b - B.b) * (A.a - B.a); /// convex find min
}
void add(Line L) {
int l = 0, r = top;
while (r - l > 1)
{
int m = (l + r) / 2;
if (check(lines[m-1], lines[m], L)) r = m;
else l = m;
}
roll_backs.push_back(save{r, top, lines[r]});
top = r + 1;
lines[r] = L;
}
long long query(long long x) {
int l = 0, r = top - 1;
while (r - l > 2)
{
int m1 = (l + r) / 2;
int m2 = m1 + 1;
if (lines[m1].cal(x) >= lines[m2].cal(x))
l = m1;
else r = m2;
}
long long ans = 1e18;
for (int i=l; i<=r; i++) ans = min(ans, lines[i].cal(x));
return ans;
}
void roll_back() {
auto Save = roll_backs.back();
int pos = Save.pos;
top = Save.cur_top;
lines[pos] = Save.L;
roll_backs.pop_back();
}
/// dp[v] = (depth[v] - depth[u]) * V[v] + dp[u] + S[v]
/// dp[v] = -depth[u] * V[v] + dp[u] + S[v] + depth[v] * V[v];
void dfs(int u, int p=-1){
if (u > 1) dp[u] = query(V[u]) + S[u] + depth[u] * V[u];
add(Line({-depth[u], dp[u]}));
for (auto [v, w] : adj[u]) {
if (v == p) continue;
depth[v] = depth[u] + w;
dfs(v, u);
}
roll_back();
}
main()
{
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
cin >> n;
f1 (i, n-1)
{
int u, v, w;
cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
f1 (i, n-1) cin >> S[i+1] >> V[i+1];
dfs(1);
f1 (i, n-1) cout << dp[i+1] << ' ';
}
