/******************************
* author : @marvinthang *
* date :05 / 12 / 2021 *
******************************/
#include <bits/stdc++.h>
using namespace std;
#define superspeed ios_base::sync_with_stdio(false);\
cin.tie(NULL);\
//cout.tie(NULL);
#define file(name) freopen(name".in", "r", stdin);\
freopen(name".out", "w", stdout);
const double PI = 3.1415926535897932384626433832795; // acos((db)-1); atan(-1.0);
const int dx[] = {-1, 0, 1, 0}, dy[] = {0, 1, 0, -1};
const long long oo = 1e18;
const int MAX = 1e5 + 5;
int numNode;
long long Start[MAX], Speed[MAX], dist[MAX];
vector <pair <int, int>> adj[MAX];
void dfs(int u, int par) {
for (pair <int, int> &x: adj[u]) {
int v = x.second, w = x.first;
if (v == par) continue;
dist[v] = dist[u] + w;
dfs(v, u);
}
}
struct Line {
long long a, b;
Line(long long _a = 0, long long _b = 0):
a(_a), b(_b) {};
} L[MAX];
stack <pair <Line, int>> rb;
int numLine;
bool bad(Line a, Line b, Line c) {
return (long double) (c.b - a.b) / (a.a - c.a) < (long double) (b.b - a.b) / (a.a - b.a);
}
void add(Line a) {
int l = 2, r = numLine, res = numLine + 1;
while (l <= r) {
int mid = l + r >> 1;
if (bad(L[mid - 1], L[mid], a)) {
res = mid;
r = mid - 1;
} else l = mid + 1;
}
rb.push(make_pair(L[res], numLine));
numLine = res;
L[res] = a;
// for (int i = 1; i <= numLine; ++i) cout << "*" << L[i].a << ' ' << L[i].b << '\n';
// cout << "============================\n";
}
void rollback() {
pair <Line, int> x = rb.top(); rb.pop();
L[numLine] = x.first;
numLine = x.second;
// cout << "--rollback--\n";
// for (int i = 1; i <= numLine; ++i) cout << "*" << L[i].a << ' ' << L[i].b << '\n';
// cout << "============================\n";
}
long long eval(Line a, long long x) {
return a.a * x + a.b;
}
long long getMin(long long x) {
int l = 1, r = numLine;
long long res = oo;
while (l <= r) {
if (l == r) {
res = min(res, eval(L[l], x));
break;
}
int mid = l + r >> 1;
long long a = eval(L[mid], x);
long long b = eval(L[mid + 1], x);
res = min({res, a, b});
if (a > b) l = mid + 1; else r = mid - 1;
}
return res;
}
// F[v] = (dist[v] - dist[u]) * Speed[v] + Start[v] + F[u]
// = (dist[v] * Speed[v] + Start[v]) + (-dist[u] * Speed[v] + F[u])
// = const + a * x + b
// -dist[u] <<- // Slope <<-
long long F[MAX];
void dfs2(int u, int par) {
add(Line(-dist[u], F[u]));
for (pair <int, int> &x: adj[u]) {
int v = x.second, w = x.first;
if (v == par) continue;
F[v] = 1LL * dist[v] * Speed[v] + Start[v] + getMin(Speed[v]);
dfs2(v, u);
}
rollback();
}
int main() {
superspeed;
file("harbinge");
cin >> numNode;
for (int i = 1; i < numNode; ++i) {
int u, v, w; cin >> u >> v >> w;
adj[u].push_back(make_pair(w, v));
adj[v].push_back(make_pair(w, u));
}
for (int i = 2; i <= numNode; ++i)
cin >> Start[i] >> Speed[i];
dfs(1, 0);
dfs2(1, 0);
for (int i = 2; i <= numNode; ++i) cout << F[i] << ' ';
return 0;
}
