#include <bits/stdc++.h>
using namespace std;
const int mxN = 1e5 + 5;
#define int long long
const int inf = 5e18;
int ans[mxN], s[mxN], k[mxN], sz[mxN], head[mxN], sum[mxN], parent[mxN];
vector<pair<int, int>> adj[mxN];
struct Line{
int m, c;
Line(int _m, int _c){
m = _m, c = _c;
}
int get(int x){
return x * m + c;
}
};
struct CHT{
vector<Line> hull;
bool bad(Line p, Line c, Line n){
return (p.c - c.c) * 1.0L * (n.m - p.m) > (p.c - n.c) * 1.0L * (c.m - p.m);
};
void add(Line new_line){
while(hull.size() && hull.back().m == new_line.m && hull.back().c > new_line.c) hull.pop_back();
while(hull.size() >= 2 && bad(hull[hull.size() - 2], hull.back(), new_line)) hull.pop_back();
hull.push_back(new_line);
}
int query(int x){
int st = -1, en = hull.size() - 1;
while((en - st) > 1){
int mid = st + (en - st) / 2;
if(hull[mid].get(x) >= hull[mid + 1].get(x)) st = mid;
else en = mid;
}
if(en < 0 || en >= hull.size()) return inf;
return hull[en].get(x);
}
} cht[mxN];
void dfs(int u = 1, int par = 0){
sz[u] = 1;
parent[u] = par;
for(auto it : adj[u]){
if(it.first ^ par){
sum[it.first] = sum[u] + it.second;
dfs(it.first, u);
sz[u] += sz[it.first];
}
}
}
void hld(int u = 1, int par = 0, int chain = 1){
head[u] = chain;
int v = u;
while(v){
ans[u] = min(ans[u], cht[head[v]].query(k[u]) + s[u] + k[u] * sum[u]);
v = parent[head[v]];
}
if(u > 1) cht[head[u]].add(Line(-sum[u], ans[u]));
int heavy = -1;
for(auto it : adj[u]){
if(it.first ^ par){
if(heavy == -1) heavy = it.first;
else{
if(sz[it.first] > sz[heavy]){
heavy = it.first;
}
}
}
}
if(heavy != -1) hld(heavy, u, chain);
for(auto it : adj[u]){
if(it.first ^ par && heavy ^ it.first){
hld(it.first, u, it.first);
}
}
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(nullptr); cout.tie(nullptr);
int n, u, v, d;
cin >> n;
for(int i = 1; i <= n - 1; ++i){
cin >> u >> v >> d;
adj[u].push_back({v, d});
adj[v].push_back({u, d});
}
for(int i = 2; i <= n; ++i){
cin >> s[i] >> k[i];
}
for(int i = 1; i <= n; ++i) cht[i].add(Line(0, 0)), ans[i] = inf;
dfs();
hld();
for(int i = 2; i <= n; ++i) cout << ans[i] << " ";
return 0;
}
