/*
ID: awesome35
LANG: C++14
TASK: vans
*/
#define _CRT_SECURE_NO_WARNINGS
#include<bits/stdc++.h>
#include<unordered_set>
#include<unordered_map>
#include<chrono>
using namespace std;
typedef pair<int, int> pii;
typedef long long ll;
typedef pair<ll, ll> pll;
// warning: ld is rougly 2x slower than double. Proof: ld: https://oj.uz/submission/319677 double: https://oj.uz/submission/319678
typedef long double ld;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<pair<int, int>> vpi;
typedef vector<pair<ll, ll>> vpll;
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
#define pb push_back
#define mp make_pair
#define rsz resize
#define sz(x) int(x.size())
#define all(x) x.begin(),x.end()
#define f first
#define s second
//#define endl '\n'
#define test int testc;cin>>testc;while(testc--)
const int dx[4] = { 1,0,-1,0 }, dy[4] = { 0,1,0,-1 }; // for every grid problem!!
const ll linf = 4000000000000000000LL;
const ll inf = 1000000007;//998244353
const ld pi = 3.1415926535;
void pv(vi a) { trav(x, a)cout << x << " "; cout << endl; }void pv(vll a) { trav(x, a)cout << x << " "; cout << endl; }void pv(vector<vi>a) {
F0R(i, sz(a)) { cout << i << endl; pv(a[i]); cout << endl; }
}void pv(vector<vll>a) { F0R(i, sz(a)) { cout << i << endl; pv(a[i]); }cout << endl; }void pv(vector<string>a) { trav(x, a)cout << x << endl; cout << endl; }
void build_primes(vi& primes, int size)
{
vi visited;
visited.rsz(size, 0);
FOR(i, 2, size)
{
if (visited[i] == 0)
{
primes.pb(i);
int a = i;
while (a < size)
{
visited[a] = 1;
a += i;
}
}
}
}
vector<vector<ll>> matrix_mult(vector<vector<ll>>& a, vector<vector<ll>>& b)
{
int n = a.size();
vector<vector<ll>> answer;
answer.resize(n);
for (int i = 0; i < n; i++) answer[i].resize(n, 0);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++) // calculate answer[i][j]
{
for (int k = 0; k < n; k++)
answer[i][j] = (answer[i][j] + a[i][k] * b[k][j]) % inf;
}
}
return answer;
}
int modInverse(int a, int m)
{
int m0 = m;
int y = 0, x = 1;
if (m == 1)
return 0;
while (a > 1)
{
// q is quotient
int q = a / m;
int t = m;
// m is remainder now, process same as
// Euclid's algo
m = a % m, a = t;
t = y;
// Update y and x
y = x - q * y;
x = t;
}
// Make x positive
if (x < 0)
x += m0;
return x;
}
ll power(ll x, ll y)
{
ll k = 1LL << 60;
ll z = 1;
while (k != 0)
{
z *= z;
z %= inf;
if (y >= k)
{
z *= x;
z %= inf;
y -= k;
}
k >>= 1;
}
return z;
}
struct point
{
ld x, y;
bool operator<(const point& rhs)const
{
if (x == rhs.x)return y < rhs.y;
return x < rhs.x;
}
};
struct pt
{
ll x, y;
bool operator<(const pt& rhs)const
{
if (x == rhs.x)return y < rhs.y;
return x < rhs.x;
}
};
// remember that you need to take abs
long double area(point x, point y, point z)
{
return (x.y * y.x + y.y * z.x + z.y * x.x - x.x * y.y - y.x * z.y - z.x * x.y) / 2.0;
}
bool clockwise(point x, point y, point z)
{
return area(x, y, z) > 0;
}
// remember that you need to take abs
long double area(pt x, pt y, pt z)
{
return (x.y * y.x + y.y * z.x + z.y * x.x - x.x * y.y - y.x * z.y - z.x * x.y) / 2.0;
}
bool clockwise(pt x, pt y, pt z)
{
return area(x, y, z) > 0;
}
ll gcd(ll a, ll b)
{
if (a > b)swap(a, b);
if (a == 0)return b;
return gcd(a, b % a);
}
int popcount(ll a)
{
int count = 0;
while (a)
{
count += (a & 1);
a >>= 1;
}
return count;
}
ll choose(ll n, ll r)
{
ll p = 1, k = 1;
if (n - r < r)
r = n - r;
if (r != 0) {
while (r) {
p *= n;
k *= r;
long long m = gcd(p, k);
p /= m;
k /= m;
n--;
r--;
}
}
else
p = 1;
return p;
}
vll prefix_hash(string& a, vll& powers, ll mod)
{
int n = sz(a);
vll prefix(n + 1);
F0R(i, n)prefix[i + 1] = (prefix[i] + powers[i] * (a[i] - '1' + 1)) % mod;
return prefix;
}
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
//the return type was size_t. But isnt that problematic?
uint64_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
struct custom_hash_fast {
//the return type was size_t. But isnt that problematic?
uint64_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
x ^= FIXED_RANDOM;
return x ^ (x >> 16);
}
};
void setIO(string s) {
ios_base::sync_with_stdio(0); cin.tie(0);
if (sz(s))
{
freopen((s + ".in").c_str(), "r", stdin);
if (s != "test3")
freopen((s + ".out").c_str(), "w", stdout);
}
}
const int MAXN = 1e5 + 5;
ll m[MAXN], b[MAXN];
int qt = 0;
inline void al(ll mi, ll bi) {
//while (qt >= 2 && (b[qt - 1] - b[qt - 2]) / (m[qt - 2] - m[qt - 1]) >= (bi - b[qt - 1]) / (m[qt - 1] - mi))
// --qt;
m[qt] = mi, b[qt] = bi;
++qt;
}
inline ll qry(ll xi) {
int lb = 0, rb = qt - 1;
while (lb < rb) {
int mb = (lb + rb) / 2;
if (m[mb] * xi + b[mb] < m[mb + 1] * xi + b[mb + 1])
lb = mb + 1;
else
rb = mb;
}
return m[lb] * xi + b[lb];
}
int n;
vector<vpi>adj;
vi S, V, sizes;
vll dp, dist;
//LineContainer hull;
void dfs(int i, int p)
{
sizes[i] = 1;
if (i)
{
dp[i] = -qry(V[i]) + S[i] + dist[i] * V[i];
}
al(dist[i], -dp[i]);
trav(x, adj[i])
{
if (x.f == p)continue;
dist[x.f] = x.s + dist[i];
dfs(x.f, i);
sizes[i] += sizes[x.f];
}
--qt;
}
int main()
{
setIO("");
cin >> n;
adj.rsz(n);
F0R(i, n - 1)
{
int a, b, c;
cin >> a >> b >> c;
adj[--a].pb({ --b,c });
adj[b].pb({ a,c });
}
S.rsz(n);
V.rsz(n);
FOR(i, 1, n)cin >> S[i] >> V[i];
dp.rsz(n);
dist.rsz(n);
sizes.rsz(n);
qt = 0;
dfs(0, -1);
FOR(i, 1, n)cout << dp[i] << " ";
}
