#include<bits/stdc++.h>
using namespace std;
#define int long long
#define pii pair<int, int>
#define point complex<int>
const int OP_RESIZE = 0;
const int OP_SET = 1;
struct Op{
int op_t;
int a;
point b;
};
const int MAX_SZ = 100001;
struct PStack{
array<point, MAX_SZ> elems;
int sz= 0;
vector<Op> ops;
void resize(int new_sz){
ops.push_back(Op{OP_RESIZE, sz, 0});
sz = new_sz;
}
void set(int pos, point elem){
ops.push_back(Op{OP_SET, pos, elems[pos]});
elems[pos] = elem;
}
void push_back(point p){
resize(sz+1);
set(sz, p);
sz++;
}
void undo(Op op){
if(op.op_t == OP_RESIZE){
sz = op.a;
}
else{
elems[op.a] = op.b;
}
}
void go_back(int target_sz){
while(ops.size()>target_sz){
undo(ops.back());
ops.pop_back();
}
}
};
int cross(point a, point b){
return (a*conj(b)).imag();
}
int dot(point a, point b){
return (a*conj(b)).real();
}
bool ok(point a, point b, point c){
return cross(b-a, c-b)>0;
}
struct Hull{
PStack pts;
void push_back(point e){
if(pts.sz>1){
int cur = 0;
for(int step = (1<<20); step>=1; step/=2){
if(cur+step+1<pts.sz){
if(ok(pts.elems[cur+step], pts.elems[cur+step+1], e)){
cur+=step;
}
}
}
pts.resize(cur+1);
}
pts.push_back(e);
}
int get_min(point normal){
//cout<<"getting at "<<normal.real()<<" "<<normal.imag()<<endl;
/*for(int i = 0; i<pts.sz; i++){
cout<<pts.elems[i].real()<<" "<<pts.elems[i].imag()<<endl;
}*/
//cout<<"done "<<endl;
if(pts.elems.size() == 0){
return 0;
}
int cur = 0;
for(int step = (1<<20); step>=1; step/=2){
if(cur+step<pts.sz){
if(dot(normal, pts.elems[cur+step])<dot(normal, pts.elems[cur+step-1])){
cur+=step;
}
}
}
return dot(pts.elems[cur], normal);
}
};
vector<vector<pii>> ch;
vector<pii> params;
vector<int> dp_res;
vector<vector<pii>> adj;
void dfs(int u,int anc, int depth, Hull& h){
int ops_sz = h.pts.ops.size();
int dp_cur = h.get_min({params[u].first, 1})-params[u].first*(depth) + params[u].second;
//cout<<u<<" "<<dp_cur<<endl;
h.push_back({depth, dp_cur});
dp_res[u] = dp_cur;
for(auto e: adj[u]){
if(e.first!=anc){
dfs(e.first,u, depth-e.second, h);
}
}
h.pts.go_back(ops_sz);
}
signed main(){
int n;
cin>>n;
adj.resize(n);
for(int i = 0; i<n-1; i++){
int u, v, d;
cin>>u>>v>>d;
u--;v--;
adj[u].push_back({v, d});
adj[v].push_back({u, d});
}
params.resize(n);
for(int i = 1; i<n; i++){
cin>>params[i].second>>params[i].first;
}
Hull h;
dp_res.resize(n);
dfs(0, -1, 0, h);
for(int i =1; i<n; i++){
cout<<dp_res[i]<<" ";
}
cout<<endl;
}
