ABC222F AC

// 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;
vector<pll> top1, top2;

pll dfs(ll u, ll fa)
{
    for (auto v : g[u]) {
        if (v == fa)
            continue;
        auto [weight, end_vid] = dfs(v, u);
        pll key = {min(u, v), max(u, v)};
        auto &a = top1[u], &b = top2[u];

        ll r = max(weight, vw[v]) + ew[key];
        if (r > a.first) {
            b = a;
            a = {r, v};
        } else if (r > b.first) {
            b = {r, v};
        }
        /*
        ll new_weight = ew[key] + weight;
        if (a.first < new_weight) {
            b = a;
            a.first = new_weight;
            a.second = v;
        } else if (b.first < new_weight) {
            b.first = new_weight;
            b.second = v;
        }
        */
    }
    return top1[u];
}

void dfs2(ll u, ll fa, ll lp)
{
    ans[u] = max(lp, top1[u].first);
    for (auto v : g[u]) {
        if (v == fa)
            continue;
        pll key = {min(u, v), max(u, v)};
        ll uv_dist = ew[key];
        // ll this_lp = 0;
        // dbg(u, v, top1[u].first, top2[u].first, top1[u].second, top2[u].second, lp);
        ll this_lp = max(lp, vw[u]) + uv_dist;
        if (top1[u].second == v) {
            this_lp = max(this_lp, top2[u].first + uv_dist);
        } else {
            this_lp = max(this_lp, top1[u].first + uv_dist);
        }
        dfs2(v, u, this_lp);
    }
}

int main(int argc, char **argv)
{
    cin >> n;
    vw = vl(n + 1);
    ans = vl(n + 1);
    top1 = top2 = vector<pll>(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);
    dfs2(1, -1, 0);
    for (int i = 1; i <= n; ++i)
        cout << ans[i] << '\n';
    return 0;
};
A