#include <bits/stdc++.h>
using namespace std;
#define ll long long
mt19937 rng(time(0));
const ll nx=1e5+5, inf=1e18;
ll n, h[nx], u, v, w, dp[nx], s[nx], vl[nx];
vector<pair<ll, ll>> d[nx];
ll divfloor(ll a, ll b)
{
if ((a%b)==0||((a^b)>=0)) return a/b;
return a/b-1;
}
ll isect(ll m1, ll c1, ll m2, ll c2)
{
return divfloor(c2-c1, m1-m2);
}
struct treap
{
struct node
{
ll m, c, p, key, sz, mx;
node *l, *r;
node(ll m, ll c, ll p): l(0), r(0), m(m), c(c), p(p), sz(1), mx(p), key(rng()){}
};
typedef node* pnode;
pnode rt, hd[nx], tmp;
int size(pnode x)
{
return x?x->sz:0;
}
ll getmax(pnode x)
{
return x?x->mx:-inf;
}
void update(pnode x)
{
if (x) x->sz=1+size(x->l)+size(x->r), x->mx=max(x->mx, getmax(x->r));
}
pnode getleft(pnode x)
{
if (x->l) return getleft(x->l);
return x;
}
void merge(pnode l, pnode r, pnode &k)
{
if (!l) return k=r, void();
if (!r) return k=l, void();
if (l->key>=r->key) merge(l->r, r, l->r), k=l;
else merge(l, r->l, r->l), k=r;
update(k);
}
void splithidden(pnode &l, pnode &r, pnode k, ll m, ll c)
{
if (!k) return l=r=0, void();
if (isect(m, c, k->m, k->c)>=k->p) splithidden(k->r, r, k->r, m, c), l=k;
else splithidden(l, k->l, k->l, m, c), r=k;
update(l); update(r);
}
void split(pnode &l, pnode &r, pnode k, int key)
{
if (!k) return l=r=0, void();
if (1+size(k->l)<=key) split(k->r, r, k->r, key-(1+size(k->l))), l=k;
else split(l, k->l, k->l, key), r=k;
update(l); update(r);
}
ll query(pnode k, ll x)
{
if (x>(k->p)) return query(k->r, x);
if ((k->l)&&x<=(k->l->mx)) return query(k->l, x);
return k->m*x+k->c;
}
} t;
void dfs(int u, int p)
{
if (u!=1) dp[u]=t.query(t.rt, -vl[u])+h[u]*vl[u]+s[u];
t.splithidden(t.hd[u], t.rt, t.rt, h[u], dp[u]);
if (u==1) t.merge(new treap::node(h[u], dp[u], inf), t.rt, t.rt);
else t.merge(new treap::node(h[u], dp[u], isect(h[u], dp[u], t.getleft(t.rt)->m, t.getleft(t.rt)->c)), t.rt, t.rt);
for (auto [v, w]:d[u]) if (v!=p) h[v]=h[u]+w, dfs(v, u);
t.split(t.tmp, t.rt, t.rt, 1);
t.merge(t.hd[u], t.rt, t.rt);
}
int main()
{
cin.tie(NULL)->sync_with_stdio(false);
cin>>n;
for (int i=1; i<n; i++) cin>>u>>v>>w, d[u].push_back({v, w}), d[v].push_back({u, w});
for (int i=2; i<=n; i++) cin>>s[i]>>vl[i];
dfs(1, 1);
for (int i=2; i<=n; i++) cout<<dp[i]<<' ';
}
