#include <bits/stdc++.h>
using namespace std;
#define int long long
const int N = 3e5 + 5;
struct Line
{
int a, b;
int operator()(int x) { return a * x + b; };
} lines[N];
vector<pair<int, int>> A[N];
int dis[N], prep[N], v[N], dp[N];
int sz = 1;
long double inter(Line x, Line y)
{
return (long double)(x.b - y.b) / (long double)(y.a - x.a);
}
stack<tuple<int, int, Line>> his;
void add(Line nw)
{
int pos = sz, l = 1, r = sz - 1;
while (l <= r)
{
int mid = (l + r) / 2;
if (inter(lines[mid - 1], nw) >= inter(lines[mid], nw))
{
pos = mid;
r = mid - 1;
}
else
l = mid + 1;
}
his.emplace(sz, pos, lines[pos]);
lines[pos] = nw;
sz = pos + 1;
}
int query(int x)
{
int pos = 0, l = 1, r = sz - 1;
while (l <= r)
{
int mid = (l + r) / 2;
if(inter(lines[mid-1],lines[mid]) <= x)
{
pos = mid;
l = mid + 1;
}
else
r = mid - 1;
}
return lines[pos](x);
}
void rollback()
{
auto [a, b, c] = his.top();
his.pop();
lines[b] = c;
sz = a;
}
void dfs(int u, int par = -1)
{
if (par != -1)
{
dp[u] = prep[u] + v[u] * dis[u] + query(v[u]);
add({-dis[u], dp[u]});
}
for (auto [nxt, w] : A[u])
if (nxt != par)
{
dis[nxt] = dis[u] + w;
dfs(nxt, u);
}
if (par != -1)
rollback();
}
int32_t main()
{
// if (fopen("read.inp", "r")){
// freopen("read.inp", "r", stdin);
// freopen("write.out", "w", stdout);
// }
cin.tie(0)->sync_with_stdio(0);
int a, b, w, n;
cin >> n;
for (int i = 0; i < n - 1; i++)
{
cin >> a >> b >> w;
A[a].push_back({b, w});
A[b].push_back({a, w});
}
for (int i = 2; i <= n; i++)
cin >> prep[i] >> v[i];
// get dis values + do lichao
dfs(1);
for (int i = 2; i <= n; i++)
cout << dp[i] << " ";
}
