#include <bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2")
//#define int long long
#define pii pair<int,int>
#define vi vector<int>
#define ff first
#define ss second
#define sp << " " <<
#define all(x) x.begin(),x.end()
#define big(x) ((int)(x.size()))
using namespace std;
const int MOD = 1e9+7, LIM = 1e9, inf = 2e9,MAXN = 1e6+1;
const int N = 1e5+1;
int s[N],v[N],d[N];
long long dp[N];
vector<pii> edges[N];
#define Line pair<int,long long>
long long eval(const Line& l,int x) {
return 1LL*l.ff*x+l.ss;
}
Line lines[4*N+1];
stack<pair<int,Line>> upds;
int ids = 0;
vi vals;
int idx(int x) {
return upper_bound(all(vals),x)-vals.begin();
}
void update(int node, int l,int r,Line& line) {
if (line.ff == inf && line.ss == inf) return;
int m = (l+r) >> 1;
bool good = eval(lines[node],(vals[l-1])) > eval(line,vals[l-1]);
bool goodmid = eval(lines[node],(vals[m-1])) > eval(line,vals[m-1]);
if (goodmid) {
upds.push({node,lines[node]});
swap(lines[node],line);
}
if (l == r) return;
if (goodmid != good) update(2*node,l,m,line);
else update(2*node+1,m+1,r,line);
};
long long query(int node,int l,int r,const int x) {
if (l == r) return eval(lines[node],(vals[x-1]));
int m = (l+r) >> 1;
if (x <= m) return min(eval(lines[node],(vals[x-1])),query(2*node,l,m,x));
return min( eval(lines[node],(vals[x-1])),query(2*node+1,m+1,r,x));
}
void rollback(int k) {
while (k--) {
lines[upds.top().ff] = upds.top().ss;
upds.pop();
}
}
int n;
void dfs(int node,int p,int der = 0) {
d[node] = der;
if (node > 1) dp[node] = 1LL*s[node]+1LL*v[node]*d[node]+query(1,1,n,idx(v[node]));
else dp[node] = 0;
int crea = upds.size();
Line toadd = {-d[node],dp[node]};
update(1,1,n,toadd);
int crea2 = upds.size();
for (auto it : edges[node]) {
if (it.ff == p) continue;
dfs(it.ff,node,der+it.ss);
}
rollback(crea2-crea);
}
void solve() {
cin >> n;
for (int i = 1;i<=4*n;i++) lines[i] = {inf,inf};
for (int i=1;i<n;i++) {
int a,b,c;
cin >> a >> b >> c;
edges[a].push_back({b,c});
edges[b].push_back({a,c});
}
for (int i=2;i<=n;i++) cin >> s[i] >> v[i];
for (int i=2;i<=n;i++) vals.push_back(v[i]);
sort(all(vals));
vals.erase(unique(all(vals)),vals.end());
int nn = n;
n = vals.size();
dfs(1,1);
for (int i=2;i<=nn;i++) cout << dp[i] << ' ';
cout << '\n';
}
signed main() {
ios_base::sync_with_stdio(0); cin.tie(0);
#ifdef Dodi
freopen("in.txt", "r", stdin);
freopen("out.txt", "w", stdout);
#endif
int t = 1;
//cin >> t;
while (t --> 0) solve();
}
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