#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef unsigned int ui;
typedef pair<ll, ll> Line;
#define ii pair<int,int>
#define vi vector<int>
#define vii vector<ii>
#define vll vector<ll>
#define matrix vector<vi>
#define matrixLL vector<vLL>
#define vs vector<string>
#define vui vector<ui>
#define msi multiset<int>
#define mss multiset<string>
#define si set<int>
#define ss set<string>
#define PB push_back
#define PF push_front
#define PPB pop_back
#define PPF pop_front
#define X first
#define Y second
#define MP make_pair
#define FOR(i, a, b) for (int i = int(a); i < int(b); i++)
#define REP(i, n) FOR(i, 0, n)
#define all(x) (x).begin(), (x).end()
const int dx[] = {-1, 1, 0, 0};
const int dy[] = {0, 0, -1, 1};
const int dxx[] = {-1, 1, 0, 0, 1, 1, -1, -1};
const int dyy[] = {0, 0, -1, 1, -1, 1, -1, 1};
const string abc="abcdefghijklmnopqrstuvwxyz";
const string ABC="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const ld pi = 3.14159265;
const int mod = 1e9 + 7;
const int MOD = 1e9 + 7;
const int MAXN = 1e6 + 7;
const int inf = mod;
const ll INF = 1e18;
const ll zero = ll(0);
const int logo = 20;
const int off = 1 << logo;
const int trsz = off << 1;
const int N = 1e5 + 123;
ll f(Line me, ll x){
return me.X * x + me.Y;
}
int CHT[N], n, sz;
vector< pair<int, ll> > g[N];
ll dp[N], d[N], sp[N], sl[N];
Line cf[N];
ll get(ll x){
int l = 1, r = sz - 1;
while(l <= r){
int m = (l + r) / 2;
if(f(cf[CHT[m]], x) < f(cf[CHT[m + 1]], x)) r = m - 1;
else l = m + 1;
}
return f(cf[CHT[r + 1]], x);
}
bool bad(int x, int y, int z) {
return (cf[x].Y - cf[y].Y) * (ld)(1) / (ld)(cf[y].X - cf[x].X) >= (ld)(cf[x].Y - cf[z].Y) * ld(1) / (ld)(cf[z].X - cf[x].X);
}
void dfs(int v, int pr = -1){
if(pr != -1) dp[v] = get(sp[v]) + sl[v] + sp[v] * d[v];
cf[v] = {-d[v], dp[v]};
int l = 2, r = sz;
while(l <= r){
int m = (l + r) / 2;
if(bad(CHT[m - 1], CHT[m], v)) r = m - 1;
else l = m + 1;
}
int bfr = CHT[r + 1];
int bfr_sz = sz;
sz = r + 1, CHT[r + 1] = v;
for(pair<int, ll> to: g[v]) if(to.X != pr) d[to.X] = d[v] + to.Y, dfs(to.X, v);
sz = bfr_sz, CHT[r + 1] = bfr;
}
void solve(){
cin >> n;
for(int i = 1, x, y, z; i<n; i++) cin >> x >> y >> z, g[x].PB({y, z}), g[y].PB({x, z});
for(int i = 2; i <= n; i++) cin >> sl[i] >> sp[i];
dfs(1);
for(int i = 2; i <= n; i++) cout << dp[i] << " ";
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
int t=1;
//cin >> t;
while(t--)solve();
return 0;
}
