abc222f wa

// Problem: F - Expensive Expense
// Contest: AtCoder - Exawizards Programming Contest 2021（AtCoder Beginner Contest 222）
// URL: https://atcoder.jp/contests/abc222/tasks/abc222_f
// Memory Limit: 1024 MB
// Time Limit: 4000 ms
//
// Powered by CP Editor (https://cpeditor.org)

#include <assert.h>
#include <bits/stdc++.h>
using namespace std;
#define dbg(...) logger(#__VA_ARGS__, __VA_ARGS__)
template <typename... Args> void logger(string vars, Args &&... values)
{
    cerr << vars << " = ";
    string delim = "";
    (..., (cerr << delim << values, delim = ", "));
    cerr << endl;
}

template <class T> inline auto vv(int m) { return vector<vector<T>>(m, vector<T>(m)); }
template <class T> inline auto vv(int m, int n) { return vector<vector<T>>(m, vector<T>(n)); }
template <class T, T init> inline auto vv(int m) { return vector<vector<T>>(m, vector<T>(m, init)); }
template <class T, T init> inline auto vv(int m, int n) { return vector<vector<T>>(m, vector<T>(n, init)); }

template <class T> using mpq = priority_queue<T, vector<T>, greater<T>>;

using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using p4l = pair<pll, pll>;
using vl = vector<ll>;
using vi = vector<int>;

int n;
map<pll, ll> ew;
vl vw;
vl g[200003];
vl ans;

p4l dfs(ll u, ll fa, pll lbt, pll lbnt)
{
    // dbg(u, fa);
    if (g[u].size() == 1) {
        return {{vw[u], u}, {0, u}};
    }
    for (auto v : g[u]) {
        if (v == fa)
            continue;
        auto [st, snt] = dfs(v, u, lbt, lbnt);
        ll weight = ew[{min(u, v), max(u, v)}];
        ans[lbt.second] = max(ans[lbt.second], snt.first + weight + lbt.first);

        if (weight + st.first > lbt.first) {
            lbt.first = weight + st.first;
            lbt.second = lbt.second;
        }

        ans[st.second] = max(ans[st.second], lbnt.first + weight + st.first);
        if (weight + snt.first > lbnt.first) {
            lbnt.first = weight + snt.first;
            lbnt.second = lbnt.second;
        }
    }
    if (u == 1)
        ans[1] = max(ans[1], lbnt.first + vw[1]);
    return {lbt, lbnt};
}

int main(int argc, char **argv)
{
    cin >> n;
    vw = vl(n + 1);
    ans = vl(n + 1);
    ll a, b, c;
    for (int i = 1; i < n; ++i)
        cin >> a >> b >> c, g[a].push_back(b), g[b].push_back(a), ew[{min(a, b), max(a, b)}] = c;
    for (int i = 1; i <= n; ++i)
        cin >> vw[i];

    dfs(1, -1, {0, 0}, {0, 0});
    for (int i = 1; i <= n; ++i)
        cout << ans[i] << '\n';
    return 0;
};