#include <bits/stdc++.h>
#define el '\n'
#define FNAME "harbingers"
#define allof(x) x.begin(),x.end()
#define allof1(x) x.begin()+1,x.end()
#define mset(x,n) memset(x,(n),sizeof(x))
using namespace std;
const long long MOD = (long long) 1e9 + 7;
template<class X,class Y> bool minimize(X &a,Y b){ if (a>b) {a=b; return true;} return false;}
template<class X,class Y> bool maximize(X &a,Y b){ if (a<b) {a=b; return true;} return false;}
void setup(){
ios_base::sync_with_stdio(0);
cin.tie(0);cout.tie(0);
if (fopen(FNAME".inp","r")){
freopen(FNAME".inp","r",stdin);
freopen(FNAME".out","w",stdout);
}
}
const int MAXN = 1e5 + 5;
struct MinHull{
struct Line{
long long a,b;
Line():a(0),b(0) {}
Line(long long A,long long B):a(A),b(B) {}
friend double getIntersection(const Line &x, const Line &y){
return 1.0 * (y.b - x.b) / (x.a - y.a);
}
friend bool overlap(Line A,Line B,Line C){
return getIntersection(B,C) < getIntersection(A,C);
}
long long evaluate(long long x){
return a * x + b;
}
};
vector<Line> lines;
vector<double> bubble;
void addLine(long long a, long long b){
Line newLine = Line(a,b);
while (lines.size() >= 2 and overlap(lines[lines.size()-2], lines.back(), newLine)){
lines.pop_back();
bubble.pop_back();
}
if (!lines.empty()){
bubble.emplace_back(getIntersection(lines.back() , newLine));
}
lines.emplace_back(newLine);
}
long long getVal(long long x){
if (lines.empty()) return 0;
int pos = lower_bound(allof(bubble),x) - bubble.begin();
return lines[pos].evaluate(x);
}
};
struct Edges{
int v;
long long w;
Edges(int V,long long W):v(V),w(W){}
};
int n;
vector<Edges> graph[MAXN];
vector<long long> S,V;
void init(){
cin>>n;
for (int i=1;i<n;i++){
int u,v;
long long w;
cin>>u>>v>>w;
graph[u].emplace_back(v,w);
graph[v].emplace_back(u,w);
}
S.assign(n+1,0);
V.assign(n+1,0);
for (int i=2;i<=n;i++) cin>>S[i]>>V[i];
}
vector<long long> distancia;
void dfsCalDis(int u=1,int pre=-1){
for (Edges x : graph[u]){
if (x.v == pre) continue;
distancia[x.v] = distancia[u] + x.w;
dfsCalDis(x.v,u);
}
}
vector<long long> dp;
/*
* dp[v] = min_j (dp[u] + (dis[u][v]) * V[v] + S[v])
* dp[v] = min_j (dp[u] + dis[u][v] * V[v]) + S[v]
* dis[u][v] = dis[v] - dis[u]
* dp[v] = min_j (dp[u] + dis[v] * V[v] - dis[u] * V[v]) + S[v]
* dp[v] = min_j (dp[u] - dis[u] * V[v]) + dis[v] * V[v] + S[v]
* dp[v] = min_j (-dis[u] * V[v] + dp[u]) + dis[v] * V[v] + S[v]
* a = -dis[u]; b = dp[u]
*/
void dfs(int u,int pre, MinHull &cht){
MinHull newCHT = cht;
dp[u] = newCHT.getVal(V[u]) + distancia[u] * V[u] + S[u];
newCHT.addLine(-distancia[u] , dp[u]);
for (Edges x : graph[u]){
int v = x.v;
if (v==pre) continue;
dfs(v,u,newCHT);
}
}
void sol(){
distancia.assign(n+1,0);
dfsCalDis();
dp.assign(n+1,0);
MinHull cht;
dfs(1,1,cht);
for (int i=2;i<=n;i++) cout<<dp[i]<<" ";
}
int main(){
setup();
init();
sol();
}
