#include <bits/stdc++.h>
using namespace std;
int n, v[100100], q[100100], l[100100];
vector<pair<int, int>> a[100100];
long long f[100100];
int bs(int v, int hullSize)
{
int low = 2, high = hullSize, res = 1;
while (low <= high)
{
int mid = (low + high) / 2, j = q[mid], k = q[mid - 1];
if (f[j] - f[k] < 1LL * (l[j] - l[k]) * v)
{
res = j;
low = mid + 1;
}
else high = mid - 1;
}
return res;
}
int bss(long long F, int L, int hullSize)
{
int low = 2, high = hullSize, res = hullSize + 1;
while (low <= high)
{
int mid = (low + high) / 2, j = q[mid], k = q[mid - 1];
if (1. * (F - f[j]) / (L - l[j]) <= 1. * (f[j] - f[k]) / (l[j] - l[k]))
{
res = mid;
high = mid - 1;
}
else low = mid + 1;
}
return res;
}
void visit(int x, int par, int curHullSize)
{
int id, save, newHullSize = curHullSize;
if (par)
{
id = bs(v[x], curHullSize);
f[x] += f[id] + 1LL * (l[x] - l[id]) * v[x];
newHullSize = id = bss(f[x], l[x], curHullSize);
save = q[id];
q[id] = x;
}
for (auto u : a[x])
if (u.first != par)
{
l[u.first] = l[x] + u.second;
visit(u.first, x, newHullSize);
}
if (par)
q[id] = save;
}
int main()
{
ios::sync_with_stdio(0);
cin.tie(0);
int x, y, z;
cin >> n;
for (int i = 1; i < n; i++)
{
cin >> x >> y >> z;
a[x].push_back({y, z});
a[y].push_back({x, z});
}
for (int i = 2; i <= n; i++)
cin >> f[i] >> v[i];
q[1] = 1;
visit(1, 0, 1);
for (int i = 2; i <= n; i++)
cout << f[i] << " \n"[i == n];
}
