#include <bits/stdc++.h>
#define int long long
using namespace std;
vector< pair<int,int> > G[100005];
int n;
int dp[100005], D[100005], A[100005], B[100005];
struct Line
{
mutable int k, m, p;
bool operator<(const Line& o) const { return k > o.k; }
bool operator<(int x) const { return p < x; }
};
struct CHT : multiset<Line, less<>>
{
stack< pair< Line, vector<Line> > > S;
pair< Line, vector<Line> > pseudo;
static const int INF = LLONG_MAX;
int div(int a, int b)
{
return (a / b) - ((a ^ b) < 0 && a % b);
}
bool isect(iterator x, iterator y)
{
if (y == end()) return x->p = INF, 0;
if (x->k == y->k) x->p = x->m < y->m ? INF : -INF;
else x->p = div(y->m - x->m, x->k - y->k);
return x->p >= y->p;
}
void add(int k, int m)
{
S.push(pseudo);
auto z = insert({k, m, 0}), y = z++, x = y;
while (isect(y, z))
{
if (z != end()) S.top().second.push_back(*z);
z = erase(z);
}
if (x != begin() && isect(--x, y))
{
isect(x, y = erase(y));
}
else S.top().first = *y;
while ((y = x) != begin() && (--x)->p >= y->p)
{
S.top().second.push_back(*y);
isect(x, erase(y));
}
}
void revert()
{
if (S.top().first.k || S.top().first.m)
{
auto z = insert({S.top().first.k, S.top().first.m, 0}), y = next(z), x = prev(z);
if (y != end() && y->k == z->k && y->m == z->m) y = erase(y);
else x = erase(x);
z = erase(z);
}
for (auto v : S.top().second) add(v.k, v.m);
S.pop();
}
int query(int x)
{
assert(!empty());
auto l = *(lower_bound(x));
return l.k * x + l.m;
}
} cht;
void DFS(int u, int pre)
{
for (pair<int,int> T : G[u])
{
int v = T.first;
int w = T.second;
if (v == pre) continue;
D[v] += D[u] + w;
dp[v] = cht.query(B[v]) + A[v] + B[v] * D[v];
cht.add(-D[v],dp[v]);
DFS(v,u);
}
cht.revert();
}
void xuly()
{
cht.add(0,0);
DFS(1,1);
for (int i = 2; i <= n; ++i) cout << dp[i] << " ";
}
void nhap()
{
cin >> n;
int u, v, x;
for (int i = 1; i < n; ++i)
{
cin >> u >> v >> x;
G[u].push_back({v,x});
G[v].push_back({u,x});
}
for (int i = 2; i <= n; ++i) cin >> A[i] >> B[i];
}
signed main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);cout.tie(0);
freopen("harbingers.in","r",stdin);
freopen("harbingers.out","w",stdout);
nhap();
xuly();
return 0;
}
