#include <bits/stdc++.h>
using namespace std;
using LL = long long;
vector<vector<LL>> cht((LL)1e5, vector<LL>(3));
vector<pair<vector<LL>, LL>> era;
LL top;
inline LL getc(vector<LL> A, vector<LL> B){
return (B[2] - A[2]) / (A[1] - B[1]) + ((B[2] - A[2]) % (A[1] - B[1]) > 0);
}
void push(LL A, LL B){
era.push_back({cht[top], top});
cht[top++] = {-(LL)1e18, A, B};
if(top >= 2){
cht[top - 1][0] = getc(cht[top - 2], cht[top - 1]);
}
if(top >= 3){
int s = 1, e = top - 1, mid;
while(s < e){
mid = (s + e) >> 1;
if(cht[mid][0] >= getc(cht[mid], cht[top - 1])){
e = mid;
}
else{
s = mid + 1;
}
}
era.push_back({cht[s], top});
cht[s] = cht[top - 1], top = s + 1;
if(top >= 2){
cht[top - 1][0] = getc(cht[top - 2], cht[top - 1]);
}
}
else{
era.push_back({cht[top - 1], top});
}
}
LL get(LL x){
vector<LL> vc = {x + 1, -(LL)1e18, -(LL)1e18};
LL pos = lower_bound(cht.begin(), cht.begin() + top, vc) - cht.begin() - 1;
return cht[pos][1] * x + cht[pos][2];
}
void del(){
cht[top - 1] = era.back().first, top = era.back().second;
era.pop_back();
cht[top - 1] = era.back().first, top = era.back().second;
era.pop_back();
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
LL N;
cin >> N;
vector<vector<pair<LL, LL>>> way(N);
for(LL i = 0; i < N - 1; ++i){
LL a, b, c; cin >> a >> b >> c; --a; --b;
way[a].push_back({b, c}), way[b].push_back({a, c});
}
vector<pair<LL, LL>> val(N);
for(LL i = 1; i < N; ++i){
cin >> val[i].first >> val[i].second;
}
vector<LL> sum(N), chk(N), dp(N);
function<void(LL, LL)> dfs = [&](LL x, LL dis){
sum[x] = dis;
chk[x] = 1;
if(x){
dp[x] = get(val[x].second) + val[x].first + val[x].second * sum[x];
}
else dp[x] = 0;
push(-sum[x], dp[x]);
for(auto&nxt:way[x]){
if(!chk[nxt.first]){
dfs(nxt.first, dis + nxt.second);
}
}
del();
};
dfs(0, 0);
for(LL i = 1; i < N; ++i){
cout << dp[i] << ' ';
}
return 0;
}
