/*-----------------------------
Author : TgX.2
11Ti - K28 - CHV
-----------------------------*/
#include <bits/stdc++.h>
using namespace std;
#ifdef TGX
#include "debug.h"
#else
#define debug(...)
#endif
#define FOR(i, a, b) for (int i = (a), _b = (b); i <= _b; i += 1)
#define FORD(i, a, b) for (int i = (a), _b = (b); i >= _b; i -= 1)
#define fi first
#define se second
#define pb push_back
#define len(x) (int)((x).size())
#define all(x) (x).begin(), (x).end()
#define _ << " " <<
#define __ << "\n"
#define ___ << " "
#define ______________TgX______________ main()
#define int long long
#define intmax 1e9
#define intmin -1e9
#define llongmax 1e18
#define llongmin -1e18
#define memo(a, val) memset((a), (val), sizeof((a)))
struct custom {
static uint64_t splitmix64(uint64_t x) {
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
template<class T1, class T2> using cmap = unordered_map<T1, T2, custom>;
template<typename T1, typename T2>
bool mini(T1 &a, T2 b)
{if (a > b) a = b; else return 0; return 1;}
template<typename T1, typename T2>
bool maxi(T1 &a, T2 b)
{if (a < b) a = b; else return 0; return 1;}
/*-----------------------------*/
class PersistentCHT {
private:
struct Line {
int a, b;
double intersectX(const Line &other) const {
return (other.b - b) * 1.0 / (a - other.a);
}
int eval(const int &x) {
return a * x + b;
}
};
int top = 0, n;
vector<Line> hull;
stack<pair<pair<int, int>, Line>> st;
void build() {
hull.resize(n + 7, {0, 0});
}
bool isRedundant(const Line &pre, const Line &cur, const Line &nex) {
return (cur.intersectX(pre) <= nex.intersectX(cur));
}
void add_line(const int &a, const int &b) {
int l = 1, r = top - 1, ans = top;
Line cur = {a, b};
while(l <= r) {
int mid = (l + r) >> 1;
if (isRedundant(cur, hull[mid], hull[mid - 1])) {
ans = mid;
r = mid - 1;
} else l = mid + 1;
}
st.push({{ans, top}, hull[ans]});
top = ans + 1;
hull[ans] = cur;
}
int get_query(const int &x) {
int l = 0, r = top - 1;
while(l < r) {
int mid = (l + r) >> 1;
if (hull[mid].eval(x) >= hull[mid + 1].eval(x)) l = mid + 1;
else r = mid;
}
return hull[l].eval(x);
}
void rollback() {
assert(!st.empty());
int pos = st.top().fi.fi;
top = st.top().fi.se;
Line cur = st.top().se;
hull[pos] = cur;
st.pop();
}
public:
void build(int _n) {
n = _n;
build();
}
void add(const int &a, const int &b) {
add_line(a, b);
}
int get(const int &x){
return get_query(x);
}
void roll() {
rollback();
}
} pcht;
const int maxn = 1e5 + 7;
int n, w[maxn], s[maxn];
vector<pair<int, int>> g[maxn];
int h[maxn], dp[maxn];
void dfs(int u, int pre) {
// debug(u, pre);
dp[u] = s[u] * h[u] + w[u] + pcht.get(s[u]);
pcht.add(-h[u], dp[u]);
for(const pair<int, int> &val : g[u]) {
int v = val.fi, w = val.se;
if (v == pre) continue;
h[v] = h[u] + w;
dfs(v, u);
}
pcht.roll();
}
void process() {
cin >> n;
FOR(i, 2, n) {
int u, v, w; cin >> u >> v >> w;
g[u].pb({v, w});
g[v].pb({u, w});
}
FOR(i, 2, n) cin >> w[i] >> s[i];
pcht.build(n);
dfs(1, -1);
FOR(i, 2, n) cout << dp[i] ___ ;
// pcht.build(n);
}
/*-----------------------------*/
______________TgX______________ {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
if (fopen("temp.inp", "r")) {
freopen("temp.inp", "r", stdin);
freopen("temp.out", "w", stdout);
}
process();
cerr << "Time: " << 1.0 * clock() / CLOCKS_PER_SEC << " s." __ ;
}
/*==============================+
|INPUT |
--------------------------------|
================================+
|OUTPUT |
--------------------------------|
===============================*/
