#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pii pair<int,int>
#define pll pair<ll,ll>
#define vi vector<int>
#define pb push_back
#define all(a) a.begin(),a.end()
ll isect(pll a, pll b){
return (a.second - b.second)/(b.first - a.first);
}
const int mxn = 1e5+1;
vector<pii> g[mxn];
ll vel[mxn],cost[mxn],dp[mxn];
pll vec[mxn+5];
int cur = 1;
ll get(ll x){
int l = 0, r = cur-1;
while(l < r){
int mid = (l+r)>>1;
if(isect(vec[mid],vec[mid+1]) < x) l = mid+1;
else r = mid;
}
return vec[l].first * x + vec[l].second;
}
ll lower(pll Line){
if(cur < 2 || isect(Line,vec[cur-1]) >= isect(vec[cur-2],vec[cur-1]))
return cur;
int l = 1, r = cur-1;
while(l < r){
int mid = (l+r)>>1;
if(isect(Line,vec[mid]) < isect(vec[mid],vec[mid-1])) r = mid;
else l = mid+1;
}
return l;
}
void dfs(int u, int p, ll dep){
dp[u] = get(vel[u]) + dep*vel[u] + cost[u];
pll Line = {-dep,dp[u]};
int prev_cur = cur;
int prev_pos = cur = lower(Line);
pll prev_line = vec[prev_pos];
vec[cur++] = Line;
for(auto [v,c] : g[u]) if(v!=p)
dfs(v,u,dep+c);
cur = prev_cur;
vec[prev_pos] = prev_line;
}
void solve(){
int n; cin >> n;
for(int i = 1; i < n; i++){
int u,v,c; cin >> u >> v >> c;
g[u].pb({v,c}); g[v].push_back({u,c});
}
for(int i = 2; i <= n; i++)
cin >> cost[i] >> vel[i];
vec[0] = {0,0};
for(auto [v,c] : g[1])
dfs(v,1,c);
for(int i = 2; i <= n; i++)
cout << dp[i] << ' ';
}
signed main(){
cin.tie(0)->sync_with_stdio(0);
int t = 1;
// cin >> t;
while(t--){solve();}
}
