#include<bits/stdc++.h>
// #include<atcoder/modint>
// #include<atcoder/convolution>
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define F first
#define S second
#define rs resize
#define ft front()
#define bk back()
#define int long long
#define vi vector<int>
#define vvi vector<vector<int>>
#define pii pair<int, int>
#define vpii vector<pair<int, int>>
#define vc vector<char>
#define vb vector<bool>
#define mii map<int,int>
#define f0r(i,n) for(int i=0;i<n;i++)
#define FOR(i,k,n) for(int i=k;i<n;i++)
#define r0f(i,n) for(int i = n-1; i >= 0; i--)
#define R0F(i,k,n) for(int i = n-1; i >= k; i--)
#define all(v) (v).begin(),(v).end()
#define rall(v) (v).rbegin(),(v).rend()
#define SUM(v) (accumulate(all(v), 0LL))
#define in(a) int a; cin>>a
#define in2(a,b) int a,b; cin>>a>>b
#define in3(a,b,c) int a,b,c; cin>>a>>b>>c
#define in4(a,b,c,d) int a,b,c,d; cin>>a>>b>>c>>d
#define vin(v,n); vi v(n); f0r(i,n){cin>>v[i];}
#define out(a) cout<<a<<'\n'
#define out2(a,b) cout<<a<<' '<<b<<'\n'
#define out3(a,b,c) cout<<a<<' '<<b<<' '<<c<<'\n'
#define out4(a,b,c,d) cout<<a<<' '<<b<<' '<<c<<' '<<d<<'\n'
#define pout(a) cout<<a.first<<' '<<a.second<<'\n'
#define vout(v) for(auto u : v){cout<<u<<' ';} cout<<endl
#define dout(a) cout<<a<<' '<<#a<<endl
#define dout2(a,b) cout<<a<<' '<<#a<<' '<<b<<' '<<#b<<endl
#define YN(x); if(x){cout<<"YES"<<'\n';}else{cout<<"NO"<<'\n';}
#define yn(x); if(x){cout<<"Yes"<<'\n';}else{cout<<"No"<<'\n';}
#define p2(x) (1LL << (x))
#define pct(x) (__builtin_popcountll((x)))
#define ist(x,y) (((x) >> (y)) & 1)
template<class T, class U> bool ckmin(T& a, const U& b) { return (T)b < a ? a = (T)b, 1 : 0; }
template<class T, class U> bool ckmax(T& a, const U& b) { return a < (T)b ? a = (T)b, 1 : 0; }
const int leg = 1e9 + 7;
const int mod = 998244353;
using namespace std;
// using namespace atcoder;
// using mint = modint998244353;
// using mint = modint1000000007;
const int mxn = 1e5 + 5;
// mint fact[mxn], inv[mxn];
// mint C(int n, int r){return fact[n] * inv[n-r] * inv[r];}
// mint snb(int n, int r){return C(n + r, n);}
int eval(pii a, int x){
return a.first * x + a.second;
}
long double intersect(pii a, pii b){
return (long double)(b.S-a.S)/(long double)(a.F-b.F);
}
vector<pair<signed,signed>> adj[mxn]; int s[mxn], v[mxn], d[mxn], f[mxn];
// vector<pair<int,int>> dq;
pii dq[mxn]; int tp = 0;
vector<vector<pii>> tmp(mxn);
void solve(int node, int from){
if(node!=0){
int lo = 0, hi = tp-1; while(lo < hi){
int mid = lo + (hi-lo)/2;
if(intersect(dq[mid],dq[mid+1]) >= v[node])hi=mid; else lo=mid+1;
}
f[node]=eval(dq[lo],v[node])+s[node]+d[node]*v[node]; ckmin(f[node], s[node]+v[node]*d[node]);
}
// Line l = ;
// pii l = mp(-d[node],f[node]);
while(tp>=2&&intersect(pii{-d[node],f[node]},dq[tp-2]) < intersect(dq[tp-1],dq[tp-2]))tmp[node].pb(dq[tp-1]),tp--;
dq[tp++] = mp(-d[node],f[node]);
for(auto [u,w] : adj[node])if(u!=from)d[u]=d[node]+w,solve(u,node);
tp--; while(!tmp[node].empty())dq[tp++] = tmp[node].back(),tmp[node].pop_back(); tmp[node].shrink_to_fit();
}
signed main(){
ios::sync_with_stdio(false);
cin.tie(NULL);
//ifstream cin(".in");
//ofstream cout(".out");
// fact[0]=1;FOR(i,1,mxn)fact[i]=fact[i-1]*i;inv[mxn-1]=fact[mxn-1].inv();r0f(i,mxn-1)inv[i]=inv[i+1]*(i+1);
in(n); f0r(i,n-1){in3(a,b,w); a--;b--; adj[a].eb(b,w); adj[b].eb(a,w);} f0r(i,n-1)cin>>s[i+1]>>v[i+1];
solve(0,-1); FOR(i,1,n)cout<<f[i]<<' ';
}
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