#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <algorithm>
#include <vector>
#include <set>
#include <numeric>
#include <random>
#include <map>
#include <unordered_map>
#include <iomanip>
#include <string>
#include <array>
#include <unordered_set>
#include <cmath>
#include <tuple>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <time.h>
#include <stack>
#include <deque>
#pragma GCC optimize("O3")
#pragma GCC optimization("Ofast,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
using namespace std;
typedef long long ll;
struct Line {
ll k, b;
Line(ll k, ll b) :k(k), b(b) {}
inline ll eval(ll x) {
return k * x + b;
}
};
int n;
vector<vector<pair<int, int>>> gr;
vector<ll> dp;
vector<ll> s, vel;
inline double cross(const Line& a, const Line& b) {
return (b.b - a.b) * 1.0 / (a.k - b.k);
}
vector<Line> cht;
vector<double> pts;
void dfs(int v, int it = 0, int d = 0, int p = -1) {
if (p != -1) {
int pos = upper_bound(pts.begin(), pts.begin() + it, vel[v]) - pts.begin() - 1;
dp[v] = s[v] + cht[pos].eval(vel[v]) + vel[v] * d;
}
Line ln(-d, dp[v]);
bool removed = false;
int old_it = it;
Line sv(0, 0);
double sv_pt = 0;
if (cht.empty() || (it == cht.size() && cross(cht.back(), ln) > pts.back())) {
if (cht.empty()) {
pts.push_back(-1e18);
} else {
pts.push_back(cross(cht.back(), ln));
}
cht.push_back(ln);
it++;
} else {
removed = true;
if (cross(cht[it - 1], ln) > pts[it - 1]) {
sv = cht[it];
sv_pt = pts[it];
cht[it] = ln;
pts[it] = cross(cht[it - 1], ln);
it++;
} else {
int l = 0, r = it - 1;
while (r - l > 1) {
int m = (l + r) / 2;
if (cross(ln, cht[m - 1]) <= pts[m]) {
r = m;
} else {
l = m;
}
}
sv = cht[r];
sv_pt = pts[r];
cht[r] = ln;
pts[r] = cross(ln, cht[r - 1]);
it = r + 1;
}
}
for (auto& [u, len] : gr[v]) {
if (u != p) {
dfs(u, it, d + len, v);
}
}
if (removed) {
cht[it - 1] = sv;
pts[it - 1] = sv_pt;
}
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
cin >> n;
gr.resize(n);
for (int i = 0; i < n - 1; ++i) {
int u, v, d;
cin >> u >> v >> d;
u--, v--;
gr[u].push_back({ v, d });
gr[v].push_back({ u, d });
}
s.resize(n);
vel.resize(n);
for (int i = 1; i < n; ++i) {
cin >> s[i] >> vel[i];
}
dp.resize(n);
dfs(0);
for (int i = 1; i < n; ++i) {
cout << dp[i] << ' ';
}
}
