#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define pii pair<int,int>
#define pll pair<ll,ll>
#define f first
#define s second
#define chmin(a, b) a = min(a,b)
#define chmax(a, b) a = max(a,b)
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define F0R(i, a) for (int i = 0; i < (a); i++)
#define all(x) x.begin(),x.end()
#define vec vector
const int MAX_N = 100000, l2d = 18;
pii lift[MAX_N+1][l2d];
vec<pii> adj[MAX_N];
ll spd[MAX_N], start[MAX_N];
int par[MAX_N];
ll dist[MAX_N], ans[MAX_N];
double isect(pll a, pll b) {return (double)(a.s-b.s)/(b.f-a.f);}
int main() {
ios::sync_with_stdio(false); cin.tie(0);
int n; cin >> n;
for (int i=0;i<n-1;i++) {
int u, v, d; cin >> u >> v >> d;
adj[--u].pb({--v,d});
adj[v].pb({u,d});
}
for (int i=1;i<n;i++) {cin >> start[i] >> spd[i];}
spd[0] = start[0] = 0;
stack<int> todo, go_back;
vector<pll> hull;
todo.push(0);
dist[0] = ans[0] = 0;
auto qry = [&](int l, int r) {
int i = __builtin_clzll(1)-__builtin_clzll(r-l+1);
return min(lift[r][i],lift[l+(1<<i)-1][i]);
};
while (todo.size()) {
int cur = todo.top(); todo.pop();
ans[cur] = 0;
if (hull.size()) {
int lo = 0, hi = hull.size()-1, mid = (lo+hi)/2, res = 0;
while (lo <= hi) {
auto[x,y] = qry(mid,hull.size()-1);
double pt = (x==-1 ? -1 : isect(hull[x],hull[-y]));
if (pt<=spd[cur]) {res = mid; lo = mid+1;}
else {hi = mid-1;}
mid = (lo+hi)/2;
}
ans[cur] = hull[res].f*spd[cur]+hull[res].s + dist[cur]*spd[cur]+start[cur];
}
hull.pb({-dist[cur],ans[cur]});
int sz = hull.size();
if (sz>1) {
int lo = 1, hi = hull.size()-2, mid = (lo+hi)/2, res = hull.size()-1;
while (lo <= hi) {
// min from [mid,end]
auto[x,y] = qry(mid,sz-2);
if (isect(hull[x],hull.back())<=isect(hull[x],hull[-y])) {
res = mid; hi = mid-1;
} else {lo = mid+1;}
mid = (lo+hi)/2;
}
lift[sz-1][0] = {res-1,-(sz-1)};
} else {
lift[sz-1][0] = {-1,-(sz-1)};
}
for (int i=1;i<l2d;i++) {
lift[sz-1][i] = (sz>=(1<<i) ? min(lift[sz-1][i-1],lift[sz-1-(1<<(i-1))][i-1]) : make_pair(-1,-(sz-1)));
}
int last = -1;
for (auto[x,d] : adj[cur]) {
if (x!=par[cur]) {
par[x] = cur; dist[x] = dist[cur]+d;
todo.push(x);
if (last==-1) {last = x;}
}
}
if (last!=-1) {go_back.push(last);}
//cout << cur << ' ' << last << '\n';
if (adj[cur].size()==1 && cur!=0) {hull.pop_back();}
while (go_back.size() && go_back.top()==cur) {
cur = par[cur]; go_back.pop();
hull.pop_back();
}
}
for (int i=1;i<n;i++) {cout << ans[i] << ' ';}
/*
minimize: dp[j]+(dist[i]-dist[j])spd[i]+start[i]
-dist[j]spd[i]+dp[j] + dist[i]spd[i]+start[i]
*/
}
