#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define FileName "test"
#define ll long long
#define ld long double
#define pb emplace_back
#define fi first
#define se second
using namespace std;
using namespace __gnu_pbds;
typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> ord_set;
typedef pair<int, int> pii;
typedef pair<ll, int> plli;
const int N = int(1e5) + 2;
const int oo = int(1e9) + 7;
const ll Cmax = 1ll * oo * oo;
vector<ll> v;
struct Line
{
ll a, b;
Line(ll a = 0, ll b = Cmax): a(a), b(b) {}
ll GetVal(int x) {return a * v[x - 1] + b;}
};
struct TSegmentMin
{
Line cur;
TSegmentMin* left;
TSegmentMin* right;
TSegmentMin(Line cur = Line(), TSegmentMin* left = NULL, TSegmentMin* right = NULL): cur(cur), left(left), right(right) {}
};
TSegmentMin* f[N];
TSegmentMin* Update(TSegmentMin* p, int l, int r, int x, int y, Line val)
{
if(l > y || r < x || l > r) return p;
int mid = (l + r) >> 1;
TSegmentMin* res = p ? new TSegmentMin(p -> cur, p -> left, p -> right): new TSegmentMin();
if(x <= l && r <= y)
{
ll lval = val.GetVal(l);
ll rval = val.GetVal(r);
ll lcur = res -> cur.GetVal(l);
ll rcur = res -> cur.GetVal(r);
if(lcur >= lval && rcur >= rval)
{
res -> cur = val;
return res;
}
if(lcur <= lval && rcur <= rval)
{
return res;
}
ll mval = val.GetVal(mid);
ll mcur = res -> cur.GetVal(mid);
if(lcur >= lval && mcur >= mval)
{
res -> right = Update(res -> right, mid + 1, r, x, y, res -> cur);
res -> cur = val;
return res;
}
if(lcur <= lval && mcur <= mval)
{
res -> right = Update(res -> right, mid + 1, r, x, y, val);
return res;
}
if(mcur >= mval && rcur >= rval)
{
res -> left = Update(res -> left, l, mid, x, y, res -> cur);
res -> cur = val;
return res;
}
if(mcur <= mval && rcur <= rval)
{
res -> left = Update(res -> left, l, mid, x, y, val);
return res;
}
}
res -> left = Update(res -> left, l, mid, x, y, val);
res -> right = Update(res -> right, mid + 1, r, x, y, val);
return res;
}
ll Query(TSegmentMin* p, int l, int r, int x)
{
if(l > x || r < x || !p) return Cmax;
ll res = p -> cur.GetVal(x);
if(l == r) return res;
res = min(res, Query(p -> left, l, (l + r) >> 1, x));
res = min(res, Query(p -> right, (l + r) >> 1 | 1, r, x));
return res;
}
int n;
ll d[N], g[N], vantoc[N], chuanbi[N];
vector<pii> a[N];
void DFS(int u, int par) {
for(pii p: a[u]) {
if(par == p.fi) continue;
d[p.fi] = d[u] + p.se;
DFS(p.fi, u);
}
}
void GetAns(int u, int par) {
///f[v] = -d[u] * vantoc[v] + f[u] + chuanbi[v] + d[v] * vantoc[v];
if(u != 1) {
vantoc[u] = lower_bound(v.begin(), v.end(), vantoc[u]) - v.begin() + 1;
g[u] = Query(f[u], 1, int(v.size()), vantoc[u]) + d[u] * v[vantoc[u] - 1] + chuanbi[u];
}
for(pii p: a[u]) {
if(par == p.fi) continue;
f[p.fi] = Update(f[u], 1, int(v.size()), 1, int(v.size()), Line(-d[u], g[u]));
GetAns(p.fi, u);
}
}
void Enter() {
cin >> n;
for(int i = 1; i < n; ++i) {
int u, v, l;
cin >> u >> v >> l;
a[u].pb(v, l), a[v].pb(u, l);
}
v.clear();
for(int i = 2; i <= n; ++i) {
cin >> chuanbi[i] >> vantoc[i];
v.pb(vantoc[i]);
}
DFS(1, 1);
sort(v.begin(), v.end());
v.erase(unique(v.begin(), v.end()), v.end());
GetAns(1, 1);
for(int i = 2; i <= n; ++i) cout << g[i] << ' ';
}
void Solve() {
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
if(fopen(FileName".inp", "r")) {
freopen(FileName".inp", "r", stdin);
freopen(FileName".out", "w", stdout);
}
Enter(), Solve();
return 0;
}
