#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using ordered_set = tree<T,null_type,less_equal<T>,rb_tree_tag,
tree_order_statistics_node_update>;
#define ll long long
#define pi pair<int,int>
#define vi vector<int>
#define pb push_back
#define all(a) a.begin(),a.end()
#define rep(i,a,b) for(int i = (a); i <= (b); i++)
typedef complex<ll> point;
const ll inf = 1e18;
ll dot(point a, point b){
return (conj(a)*b).real();
}
ll calc(point a, ll x){
return dot(a,{x,1});
}
struct LiChao{
struct Node{
point f;
Node(ll m, ll c){
f = {m,c};
}
int l = -1, r = -1;
};
vector<Node> st;
ll szl, szr;
int tim = 0;
void update(int i, int wch){
if(st[i].l == -1 && wch==0){
st[i].l = ++tim;
st.pb({0,inf});
}
if(st[i].r == -1 && wch==1){
st[i].r = ++tim;
st.pb({0,inf});
}
}
void init(ll l, ll r){
szl = l, szr = r;
st.pb({0,inf});
}
void add(int i, ll l, ll r, point val){
ll m = (l+r)>>1;
bool lef = calc(val,l) < calc(st[i].f,l);
bool mid = calc(val,m) < calc(st[i].f,m);
if(mid) swap(st[i].f,val);
if(l==r) return;
if(lef != mid){
update(i,0);
add(st[i].l,l,m,val);
}
else{
update(i,1);
add(st[i].r,m+1,r,val);
}
}
void add(point val){
add(0,szl,szr,val);
}
ll get(int i, ll l, ll r, ll x){
ll res = calc(st[i].f,x);
if(l==r) return res;
int m = (l+r)>>1;
if(x <= m){
update(i,0);
return min(res,get(st[i].l,l,m,x));
}
update(i,1);
return min(res,get(st[i].r,m+1,r,x));
}
ll get(ll x){
return get(0,szl,szr,x);
}
void clear(){
st.clear();
}
};
const int mxn = 1e5+10;
vector<pi> g[mxn];
int val[mxn][2];
int par[mxn], head[mxn];
int dep[mxn],heavy[mxn];
LiChao st[mxn];
int dfs(int u, int p, int d){
int sz = 1, mx = 0;
for(auto [v,c] : g[u]) if(v!=p){
par[v] = u; dep[v] = d+c;
int vsz = dfs(v,u,d+c);
sz += vsz;
if(mx < vsz)
mx = vsz, heavy[u] = v;
}
return sz;
}
void dfs2(int u, int h){
head[u] = h;
if(heavy[u]) dfs2(heavy[u],h);
for(auto [v,c] : g[u]) if(v!=par[u] && v!=heavy[u])
dfs2(v,v);
}
ll dp[mxn];
void dfs(int u){
int v = u;
dp[u] = inf;
while(v){
dp[u] = min(dp[u],1ll*dep[u]*val[u][1] + val[u][0] + st[head[v]].get(val[u][1]));
v = par[head[v]];
}
st[head[u]].add({-dep[u],dp[u]});
for(auto [v,c] : g[u]) if(v!=par[u]){
if(v!=heavy[u]) st[v].init(1,1e9);
dfs(v);
}
}
void solve(){
int n; cin >> n;
for(int i = 1; i < n; i++){
int u,v,c; cin >> u >> v >> c;
g[u].pb({v,c}); g[v].pb({u,c});
}
for(int i = 2; i <= n; i++) cin >> val[i][0] >> val[i][1];
st[1].init(1,1e9); st[1].add({0,0});
dfs(1,0,0); dfs2(1,1); dfs(1);
for(int i = 2; i <= n; i++) cout << dp[i] << ' ';
}
signed main(){
// freopen("262144.in","r",stdin);
// freopen("262144.out","w",stdout);
cin.tie(0)->sync_with_stdio(0);
int t = 1;
while(t--) solve();
}
