#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define fi first
#define se second
#define TranLeThanhTam "TranLeThanhTam"
#define all(v) v.begin(),v.end()
#define reset(a,i) memset(a,i,sizeof(a))
#define FOR(i,a,b) for (int i = (a), _b = (b); i <= _b; ++i)
#define FORD(i,a,b) for (int i = (a), _b = (b); i >= _b; --i)
#define compact(v) sort(all(v)), v.erase(unique(all(v)), end(v))
#define sz(v) (int) v.size()
#define MASK(i) (1 << (i))
typedef long long ll;
typedef long double lb;
typedef pair<ll,ll> pll;
typedef pair<int,int> pii;
const int Thanh_Tam = 1e5 + 17;
const int inf = 1e9 + 17;
const long long infll = 1e18 + 17;
const int MOD = 1e9 + 7;
const int Log = 18;
const int dx[4] = {-1, 0, 0, 1};
const int dy[4] = {0, -1, 1, 0};
const int max_block_size = 600;
const ll P = 311;
const int maxA = 1e2 + 17;
const int addi = 1e9;
const char dir[4] = {'W', 'S', 'N', 'E'};
const int Mod[3] = {998244353, MOD, 759186269};
ll mul(ll a, ll b, ll mod);
ll binpow(ll a, ll b, ll mod)
{
ll res = 1;
while (b > 0)
{
if (b & 1) res = mul(res,a,mod);
b >>= 1;
a = mul(a,a,mod);
}
return res;
}
ll add(ll a, ll b, ll mod = MOD) { return (a + b) % mod; }
ll sub(ll a, ll b, ll mod = MOD) { return (a - b + mod) % mod; }
ll mul(ll a, ll b, ll mod = MOD) { return ((a % mod) * (b % mod)) % mod; }
ll Div(ll a, ll b, ll mod = MOD) { return mul(a, binpow(b, mod - 2, mod), mod); }
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
ll rand_range(ll l, ll r) { return uniform_int_distribution<ll>(l,r)(rng); }
struct Line
{
int a; ll b;
Line() {}
Line(int a, ll b) : a(a), b(b) {}
ll f(int x) { return 1LL * a * x + b; }
};
struct Convex_Hull
{
int real_size = 0;
vector<Line> lines;
stack<pair<pii, Line>> st;
void init(int n)
{
lines.assign(n + 1, Line(0, 0));
real_size = 1;
return;
}
long double intersect(Line C1, Line C2)
{
return (1.0 * (C2.b - C1.b)) / (1.0 * (C1.a - C2.a));
}
void add(Line l)
{
int tmp = real_size, L = 1, R = real_size - 1;
while (L <= R)
{
int mid = (L + R) >> 1;
if (intersect(l, lines[mid - 2]) > intersect(l, lines[mid - 1]))
{
tmp = mid;
L = mid + 1;
}
else R = mid - 1;
}
st.push({{tmp, real_size}, lines[tmp]});
real_size = tmp + 1;
lines[tmp] = l;
return;
}
ll query(ll x)
{
int pos = 0, L = 1, R = real_size - 1;
while (L <= R)
{
int mid = (L + R) >> 1;
if (lines[mid].f(x) <= lines[mid - 1].f(x))
{
pos = mid;
L = mid + 1;
}
else R = mid - 1;
}
return lines[pos].f(x);
}
void rollback()
{
lines[st.top().fi.fi] = st.top().se;
real_size = st.top().fi.se;
st.pop();
return;
}
void print()
{
for (Line T : lines)
cout << T.a << ' ' << T.b << '\n';
cout << '\n';
return;
}
} CHT;
int n;
vector<pii> adj[Thanh_Tam];
int a[Thanh_Tam], b[Thanh_Tam], dis[Thanh_Tam];
ll ans[Thanh_Tam];
void dfs(int u, int par)
{
ans[u] = 1LL * a[u] * dis[u] + 1LL * b[u] + CHT.query(a[u]);
CHT.add(Line(-1LL * dis[u], ans[u]));
for (pii T : adj[u])
{
int v = T.fi, w = T.se;
if (v == par) continue;
dis[v] = dis[u] + w;
dfs(v, u);
}
CHT.rollback();
return;
}
signed main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
if (fopen(TranLeThanhTam".inp","r"))
{
freopen(TranLeThanhTam".inp","r",stdin);
freopen(TranLeThanhTam".out","w",stdout);
}
cin >> n;
FOR(i,2,n)
{
int u, v, w;
cin >> u >> v >> w;
adj[u].pb({v, w});
adj[v].pb({u, w});
}
FOR(i,2,n) cin >> b[i] >> a[i];
CHT.init(n);
for (pii T : adj[1])
{
int v = T.fi, w = T.se;
dis[v] = dis[1] + w;
dfs(v, 1);
}
FOR(i, 2, n) cout << ans[i] << ' ';
return 0;
}
