#include<bits/stdc++.h>
#define MASK(i) (1 << (i))
#define pub push_back
#define all(v) v.begin(), v.end()
#define compact(v) v.erase(unique(all(v)), end(v))
#define pii pair<int,int>
#define fi first
#define se second
#define endl "\n"
#define sz(v) (int)(v).size()
#define dbg(x) "[" #x " = " << (x) << "]"
using namespace std;
template<class T> bool minimize(T& a, T b){if(a > b) return a = b, true;return false;}
template<class T> bool maximize(T& a, T b){if(a < b) return a = b, true;return false;}
typedef long long ll;
typedef long double ld;
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
ll rand(ll l, ll r){return uniform_int_distribution<ll>(l, r)(rng);}
const int N = 2e5 + 15;
const ll INF = 1e18;
int n;
vector<pii> g[N];
int wait[N], speed[N];
struct line{
ll slope, c;
line() {}
line(ll slope, ll c) : slope(slope), c(c) {}
ll f(ll x) {return slope*x + c;}
};
struct CHT{
int top = 0;
vector<line> lines;
stack<pair<pii, line>> st;
void luvna(int n){
lines.resize(n + 15, line(0,INF));
}
bool dump(line d1, line d2, line d3){
return 1.0l*(d1.c - d2.c) / (d2.slope - d1.slope) <= 1.0l*(d2.c - d3.c) / (d3.slope - d2.slope);
}
ll query(ll x){
int l = 0, r = top - 1;
while(l < r){
int mid = (l+r) >> 1;
if(lines[mid].f(x) >= lines[mid+1].f(x)) l = mid+1;
else r = mid;
}
return lines[l].f(x);
}
void add(line d){
int l = 1, r = top - 1, pos = top;
while(l <= r){
int mid = (l+r) >> 1;
if(dump(d, lines[mid], lines[mid-1])){
pos = mid;
r = mid-1;
}
else l = mid+1;
}
top = pos + 1;
st.push({pii(pos,top), lines[pos]});
lines[pos] = d;
}
void rollback(){
int pos = st.top().fi.fi;
top = st.top().fi.se;
line d = st.top().se;
lines[pos] = d;
st.pop();
}
};
int h[N];
ll dp[N];
CHT solver;
void dfs(int u, int p){
//cout << solver.top << endl;
if(u > 1) dp[u] = 1LL*speed[u]*h[u] + wait[u] + solver.query(speed[u]);
solver.add(line(-h[u], dp[u]));
for(auto [v, w] : g[u]) if(v != p){
h[v] = h[u] + w;
dfs(v,u);
}
solver.rollback();
}
void solve(){
cin >> n;
for(int i = 1; i < n; i++){
int u, v, w; cin >> u >> v >> w;
g[u].push_back({v,w});
g[v].push_back({u,w});
}
for(int i = 2; i <= n; i++) cin >> wait[i] >> speed[i];
solver.luvna(n);
dfs(1,-1);
for(int i = 2; i <= n; i++) cout << dp[i] << " ";
}
signed main(){
ios_base::sync_with_stdio(NULL);
cin.tie(0); cout.tie(0);
#define task "task"
if(fopen(task".INP", "r")){
freopen(task".INP", "r", stdin);
freopen(task".OUT", "w", stdout);
}
int t; t = 1; //cin >> t;
while(t--) solve();
}
