#include <algorithm>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <vector>
using namespace std;
// BEGIN NO SAD
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define trav(a, x) for(auto& a : x)
#define all(x) x.begin(), x.end()
#define sz(x) (int)(x).size()
typedef vector<int> vi;
// END NO SAD
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<vector<ll>> matrix;
typedef pair<ll, ll> pll;
int n;
vector<pii> edges[100005];
ll ret[100005];
ll dist[100005];
ll gain[100005];
ll timeper[100005];
pll bestlines[100005]; // bestlines.first * x + bestlines.second
int numlines;
ll eval(pll a, ll x) {
return a.first*x + a.second;
}
ll qry(ll x) {
assert(numlines > 0);
int lhs = 0;
int rhs = numlines-1;
while(lhs != rhs) {
int mid = (lhs+rhs)/2;
if(eval(bestlines[mid], x) <= eval(bestlines[mid+1], x)) rhs = mid;
else lhs = mid + 1;
}
ll ret = eval(bestlines[lhs], x);
return ret;
}
bool cross(pll a, pll b, pll c){
return (1.0 * (b.second - a.second) / (a.first - b.first) >= 1.0 * (c.second - b.second) / (b.first - c.first));
}
int ins(pll a) {
if(numlines <= 1) return numlines;
int lhs = 0;
int rhs = numlines-1;
while(lhs != rhs) {
int mid = (lhs+rhs)/2;
if(cross(bestlines[mid], bestlines[mid+1], a)) rhs = mid;
else lhs = mid+1;
}
return lhs+1;
}
void dfs(int curr, int par) {
if(curr > 1) {
ret[curr] = gain[curr] + timeper[curr]*dist[curr] + qry(timeper[curr]);
}
int oldnumlines = numlines;
int idx = ins(pll(-dist[curr], ret[curr]));
pll save = bestlines[idx];
for(pii out: edges[curr]) {
if(out.first == par) continue;
numlines = idx+1;
bestlines[idx] = pll(-dist[curr], ret[curr]);
dist[out.first] = dist[curr] + out.second;
dfs(out.first, curr);
}
bestlines[idx] = save;
numlines = oldnumlines;
}
void solve() {
cin >> n;
for(int i = 1; i < n; i++) {
int a, b, w;
cin >> a >> b >> w;
edges[a].emplace_back(b, w);
edges[b].emplace_back(a, w);
}
for(int i = 2; i <= n; i++) cin >> gain[i] >> timeper[i];
dfs(1, -1);
for(int i = 2; i <= n; i++) cout << ret[i] << " \n"[i == n];
}
// are there edge cases (N=1?)
// are array sizes proper (scaled by proper constant, for example 2* for koosaga tree)
// integer overflow?
// DS reset properly between test cases
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL); cout.tie(NULL);
solve();
}
