#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> ii;
typedef pair<int, ii> iii;
typedef pair<ii, int> ri3;
#define mp make_pair
#define pb push_back
#define fi first
#define sc second
#define SZ(x) (int)(x).size()
#define ALL(x) begin(x), end(x)
#define REP(i, n) for (int i = 0; i < n; ++i)
#define FOR(i, a, b) for (int i = a; i <= b; ++i)
#define RFOR(i, a, b) for (int i = a; i >= b; --i)
const int MAXN = 1e5+5;
int N;
vector<ii> al[MAXN];
int S[MAXN], V[MAXN];
int p[MAXN];
int d[MAXN];
ll r[MAXN];
struct Line { int m; ll b; };
const Line END = {(int)-2e9, (ll)-3e18};
struct Hull {
Line v[MAXN], h[MAXN];
int vi = 0, hi = 0;
int add(Line l) {
//cout << "ADD " << l.m << " " << l.b << endl;
int idx = hi;
while (vi > 2) {
if (((ll)l.b-v[vi-1].b)*((ll)v[vi-2].m-v[vi-1].m) <= (((ll)v[vi-1].b-v[vi-2].b)*((ll)v[vi-1].m-l.m)))
h[hi++] = v[vi-1], --vi;
else break;
}
h[hi++] = END;
v[vi++] = l;
return idx;
}
ll query(int x) {
//cout << "QUERY " << SZ(v) << ": ";
//for (auto l : v) cout << "(" << l.m << "," << l.b << ") ";
//cout << endl;
int lo = 0, hi = vi-1;
while (lo < hi) {
int mid = (lo+hi)/2;
bool ok = ((ll)x*((ll)v[mid].m-v[mid+1].m) <= (ll)v[mid+1].b-v[mid].b);
if (ok) hi = mid;
else lo = mid+1;
}
return (ll)v[hi].m*x + v[hi].b;
}
void undo(int idx) {
//cout << "UNDO " << endl;
while (hi > idx) {
Line cur = h[hi-1];
if (cur.m == END.m && cur.b == END.b) { --vi; }//cout << "\t\tPOP\n"; }
else { v[vi++] = cur; }//cout << "\t\tPUSH " << cur.o.m << " " << cur.o.b << '\n'; }
--hi;
}
}
} ch;
void dfs(int u) {
r[u] = (ll)S[u] + (ll)V[u]*d[u];
//cout << u << " " << p[u] << endl;
//for (int v = p[u]; v != 0; v = p[v]) r[u] = min(r[u], (ll)S[u] + (ll)V[u]*(d[u]-d[v]) + r[v]);
if (u > 1) r[u] = min(r[u], ch.query(V[u]) + (ll)S[u] + (ll)V[u]*d[u]);
int idx = ch.add({ -d[u], r[u] });
for (auto v : al[u]) if (v.fi != p[u]) {
d[v.fi] = d[u] + v.sc;
p[v.fi] = u;
dfs(v.fi);
}
ch.undo( idx );
}
int main() {
//freopen("in.txt", "r", stdin);
ios::sync_with_stdio(false);
cin.tie(0);
cin >> N;
FOR(i,1,N-1){
int u, v, d; cin >> u >> v >> d;
al[u].emplace_back(v, d);
al[v].emplace_back(u, d);
}
FOR(i,2,N){ cin >> S[i] >> V[i]; }
dfs(1);
FOR(i,2,N) cout << r[i] << (i == N ? '\n' : ' ');
}
