#include <bits/stdc++.h>
using namespace std;
#define el '\n'
#define FNAME "harbingers"
using ll = long long;
const int MAXN = 100000 + 5;
const ll INFLL = (ll)1e16 + 15092007;
struct MinHull {
struct Line {
ll a, b;
Line() : a(0), b(0) {}
Line(ll A, ll B) : a(A), b(B) {}
ll eval(ll x) const { return a * x + b; }
};
struct HistEntry {
bool isPop;
Line ln;
long double bubble;
bool addedBubble;
};
vector<Line> lines;
vector<long double> bubble;
vector<HistEntry> history;
static long double intersect(const Line &L1, const Line &L2) {
return (long double)(L2.b - L1.b) / (long double)(L1.a - L2.a);
}
static bool bad(const Line &A, const Line &B, const Line &C) {
long double x1 = intersect(A, B);
long double x2 = intersect(B, C);
return x2 <= x1;
}
int checkpoint() const { return (int)history.size(); }
void addLine(ll a, ll b) {
Line L(a, b);
while (lines.size() >= 2 && bad(lines[lines.size()-2], lines.back(), L)) {
history.push_back({ true, lines.back(), bubble.back(), false });
lines.pop_back();
bubble.pop_back();
}
bool willPushBubble = !lines.empty();
long double newBubble = 0;
if (willPushBubble) {
newBubble = intersect(lines.back(), L);
bubble.push_back(newBubble);
}
lines.push_back(L);
history.push_back({ false, L, newBubble, willPushBubble });
}
void rollback(int cp) {
while ((int)history.size() > cp) {
HistEntry he = history.back();
history.pop_back();
if (!he.isPop) {
if (he.addedBubble) {
if (!bubble.empty()) bubble.pop_back();
}
if (!lines.empty()) lines.pop_back();
} else {
lines.push_back(he.ln);
bubble.push_back(he.bubble);
}
}
}
ll getVal(long long x) const {
if (lines.empty()) return 0;
int pos = int(lower_bound(bubble.begin(), bubble.end(), (long double)x) - bubble.begin());
return lines[pos].eval(x);
}
};
struct Edge {
int v;
ll w;
Edge() : v(0), w(0) {}
Edge(int V, ll W) : v(V), w(W) {}
};
int n;
vector<Edge> graph[MAXN];
vector<ll> S, Vv;
vector<ll> distancia;
vector<ll> dp;
void setup_io() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
if (fopen(FNAME ".inp", "r")) {
freopen(FNAME ".inp", "r", stdin);
freopen(FNAME ".out", "w", stdout);
}
}
void init() {
cin >> n;
for (int i = 1; i <= n; ++i) graph[i].clear();
for (int i = 1; i < n; ++i) {
int u, v; ll w;
cin >> u >> v >> w;
graph[u].push_back(Edge(v, w));
graph[v].push_back(Edge(u, w));
}
S.assign(n + 1, 0);
Vv.assign(n + 1, 0);
for (int i = 2; i <= n; ++i) cin >> S[i] >> Vv[i];
}
void dfsCalDis(int u = 1, int pre = -1) {
for (auto &e : graph[u]) {
if (e.v == pre) continue;
distancia[e.v] = distancia[u] + e.w;
dfsCalDis(e.v, u);
}
}
void dfsDP(int u, int pre, MinHull &cht) {
dp[u] = cht.getVal(Vv[u]) + distancia[u] * Vv[u] + S[u];
int cp = cht.checkpoint();
cht.addLine(-distancia[u], dp[u]);
for (auto &e : graph[u]) {
if (e.v == pre) continue;
dfsDP(e.v, u, cht);
}
cht.rollback(cp);
}
int main() {
setup_io();
init();
distancia.assign(n + 1, 0);
dfsCalDis();
dp.assign(n + 1, 0);
MinHull cht;
dfsDP(1, -1, cht);
for (int i = 2; i <= n; ++i) {
cout << dp[i] << (i == n ? '\n' : ' ');
}
return 0;
}
