#include <bits/stdc++.h>
#define fi(i, a, b) for( int i = a; i <= b; i++ )
#define fid(i, a, b) for( int i = a; i >= b; i-- )
#define getbit(x, i) ((x>>i)&1)
#define ll long long
#define pb push_back
#define pii pair<int,int>
#define pli pair<ll,int>
#define pll pair<ll,ll>
#define st first
#define nd second
#define mp make_pair
#define HTManh ""
#define maxn 100009
#define endl '\n'
using namespace std;
int n;
vector<pii> a[100009];
ll v[100009], s[100009];
struct cht
{
vector<pll> line;
vector<long double> diem;
stack<pair<pll, long double>> s;
long double f(pll dt1, pll dt2)
{
return (double)(dt2.nd - dt1.nd)/(dt1.st - dt2.st);
}
void add(pll x)
{
while(line.size() >= 2)
{
pll dtg = line[(int)line.size()-2];
if (f(dtg, x) < f(line.back(), x)) break;
s.push({line.back(), diem.back()});
diem.pop_back();
line.pop_back();
}
if (line.empty())
{
diem.pb(-1e18);
line.pb(x);
}
else
{
diem.pb(f(line.back(), x));
line.pb(x);
}
s.push({{0, 0}, -1e18-1});
}
ll get(ll x)
{
if (diem.empty()) return 0;
int vt = lower_bound(diem.begin(), diem.end(), x) - diem.begin();
return line[vt-1].st*x+line[vt-1].nd;
}
void rollback(int t)
{
while (s.size() > t)
{
pll dg = s.top().st;
long double pt = s.top().nd;
s.pop();
if (pt == -1e18-1)
{
diem.pop_back();
line.pop_back();
}
else
{
diem.pb(pt);
line.pb(dg);
}
}
}
} mmb;
ll dp[100009];
void dfs(int u, int pre = 0, ll dis = 0)
{
dp[u] = mmb.get(v[u]) + dis*v[u] + s[u];
//cout << u << " " << dp[u] << endl;
int tg = mmb.s.size();
mmb.add({-dis, dp[u]});
for(pii tg: a[u])
{
int v = tg.st, kc = tg.nd;
if (v == pre) continue;
dfs(v,u,dis+kc);
}
mmb.rollback(tg);
}
mt19937_64 rng(time(0));
ll rnd(ll d, ll c)
{
return uniform_int_distribution<ll>(d, c)(rng);
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(NULL); cout.tie(NULL);
if (fopen(HTManh".inp", "r"))
{
freopen(HTManh".inp", "r", stdin);
freopen(HTManh".out", "w", stdout);
}
cin >> n;
fi(i,1,n-1)
{
int x,y,z;
cin >> x >> y >> z;
a[x].pb({y,z});
a[y].pb({x,z});
}
fi(i,2,n) cin >> s[i] >> v[i];
dfs(1);
fi(i,2,n) cout << dp[i] << " ";
cout << endl;
// n = 100000;
// cout << n << endl;
// fi(i,2,n)
// {
// cout << i-1 << " " << i << ' ' << rnd(9e3,1e4) << endl;
// }
// fi(i,2,n)
// {
// cout << rnd(9e8,1e9) << " " << rnd(9e8,1e9) << endl;
// }
}
