// May this submission get accepted
#include <bits/stdc++.h>

// エイリアス
using  ll = long signed long;
using ull = long unsigned long;
using  ld = long double;
using namespace std;

// AtCoder/Codeforces 用 デバッグ検知
#ifdef ONLINE_JUDGE
constexpr bool DEBUG_MODE = false;
#else
constexpr bool DEBUG_MODE = true;
#endif

// エイリアス (補完・コンパイルが重くなる)
// #include <boost/multiprecision/cpp_int.hpp>
// using mll = boost::multiprecision::cpp_int;

// 汎用マクロ
#define ALL_OF(x) (x).begin(), (x).end()
#define REP(i,n) for (long long i=0, i##_len=(n); i<i##_len; i++)
#define RANGE(i,is,ie) for (long long i=(is), i##_end=(ie); i<=i##_end; i++)
#define DSRNG(i,is,ie) for (long long i=(is), i##_end=(ie); i>=i##_end; i--)
#define STEP(i, is, ie, step) for (long long i=(is), i##_end=(ie), i##_step = (step); i<=i##_end; i+=i##_step)
#define UNIQUE(v) do { sort((v).begin(), (v).end()); (v).erase(unique((v).begin(), (v).end()), (v).end()); } while (false)
#define FOREACH(i,q) for (auto &i : q)
template<class T> bool chmax(T &a, const T b) { if (a < b) {a = b; return true;} return false; }
template<class T> bool chmin(T &a, const T b) { if (a > b) {a = b; return true;} return false; }
constexpr int INF = numeric_limits<int>::max();
constexpr long long LINF = numeric_limits<long long>::max();
constexpr long double EPS = 1e-10L;
#define Yes(q) ((q) ? "Yes" : "No")
#define YES(q) ((q) ? "YES" : "NO")
#define Possible(q) ((q) ? "Possible" : "Impossible")
#define POSSIBLE(q) ((q) ? "POSSIBLE" : "IMPOSSIBLE")
#define IIF(q,t,f) ((q) ? (t) : (f))
#define DUMP(q) DUMP_FUNC(q, #q, __FILE__, __LINE__)
template <typename T> void DUMP_PROC(T x) { if (is_integral<T>() || is_floating_point<T>()) cerr << "\e[32m" << (x == LINF ? "LINF"s : to_string(x)) << "\e[m"; else cerr << x; }
template<> void DUMP_PROC<char>(char x) { cerr << "\e[36m\'" << x << "\'\e[m"; }
template<> void DUMP_PROC<string>(string x) { cerr << "\e[33m\"" << x << "\"\e[m"; }
template <typename T, typename U> void DUMP_PROC(pair<T, U> x) { cerr << "{"; DUMP_PROC(x.first); cerr << ", "; DUMP_PROC(x.second); cerr << "}"; }
template <typename ...T, typename U, U... Seq> void DUMP_PROC(tuple<T...> &x, integer_sequence<U, Seq...>) { (void)(int[]){(cerr << ((const char*[]){"", ", "})[!!Seq] << (DUMP_PROC(get<Seq>(x)), ""), 0)...}; }
template <typename ...T> void DUMP_PROC(tuple<T...> x) {cerr << "{"; DUMP_PROC(x, index_sequence_for<T...>()); cerr << "}";}
template <typename T> void DUMP_PROC(vector<T> x) { cerr << "["; for (auto &xi : x) { DUMP_PROC(xi); cerr << (&xi != &*x.rbegin()?", ":""); } cerr << "]"; }
template <typename T> void DUMP_FUNC(T x, const char* name, const char* fn, int ln) { cerr << "\e[32m[DEBUG]\e[m " << name << ": "; DUMP_PROC(x); cerr << " @ " << fn << "(" << ln << ")" << endl; }

// gcc拡張マクロ
#define popcount __builtin_popcount
#define popcountll __builtin_popcountll

// 標準入出力
struct qin { // query input
    size_t sz;
    qin(size_t _sz = 1) : sz(_sz) {}
    template <typename T> operator T () const { T a; cin >> a; return a; }
    template <typename T> operator vector<T> () const { vector<T> a(sz); for (size_t i = 0; i < sz; i++) cin >> a[i]; return a; }
    template <typename T, typename U> operator pair<T, U> () const { T f; U s; cin >> f >> s; return pair<T, U>(f, s); }
};
qin in1; // input one
template <typename T> void say(const T x, const char* end = "\n") { cout << x << end; }
void say(const ld x, const char* end = "\n") { cout << setprecision(30) << x << end; }
template <typename T> void say(const vector<T> x, const char* sep = " ", const char* end = "\n") { REP(i, x.size()) { cout << x[i] << (i+1 == i_len ? end : sep); } }
template <typename T> void say(const vector<vector<T>> x, const char* sep = " ", const char* end = "\n") { REP(i, x.size()) { say(x[i], sep, end); } }

// モジュール
// [[LIBRARY]]

// 辺ベースのオイラーツアー、ds[i]が頂点iに下る辺、us[i]が頂点iから上る辺に対応、根にも仮の辺がある
struct euler_tour {

    ll idx, n, root;
    vector<vector<ll>> g;
    vector<ll> dep, ds, us;

    // _gは無向木の隣接リスト、_rootは根とする辺
    // 構築にO(N)かかる
    euler_tour(const vector<vector<ll>> &_g, ll _root = 0) :
        idx(0), n(_g.size()), root(_root), g(_g),
        dep(n), ds(n), us(n)
    {
        dfs(root, -1, 0);
        assert(idx == n*2); // gが木ならば、gの任意の頂点に下る/から上る回数はちょうど1回ずつのはず
    }

    void dfs(ll u, ll p, ll d) {
        dep[u] = d;
        ds[u] = idx++;
        for (ll v : g[u]) {
            if (v != p) {
                dfs(v, u, d+1);
            }
        }
        us[u] = idx++;
    }
    
};

// 処理内容
int main() {
    
    ios::sync_with_stdio(false); // stdioを使うときはコメントアウトすること
    cin.tie(nullptr);            // インタラクティブ問題ではコメントアウトすること
    
    ll n = in1;
    vector<ll> a = qin(n);
    vector<vector<ll>> g(n);
    REP(i, n-1) {
        ll u, v; cin >> u >> v;
        u--; v--;
        g[u].push_back(v);
        g[v].push_back(u);
    }

    constexpr ll root = 0;
    euler_tour et(g, root);
    vector el(n*2, make_pair(0LL, 'X'));
    REP(u, n) {
        el[et.ds[u]] = make_pair(u, 'D');
        el[et.us[u]] = make_pair(u, 'U');
    }

    vector op(n, make_pair(-1LL, -1LL));
    vector dp(n, LINF);
    vector dq(n, LINF);
    REP(i, n*2) {
        ll u; char dir; tie(u, dir) = el[i];
        // DUMP(u);
        // DUMP(dir);
        if (dir == 'D') {
            dq[u] = lower_bound(ALL_OF(dp), a[u]) - dp.begin();
            op[u] = make_pair(dq[u], dp[dq[u]]);
            dp[dq[u]] = a[u];
        } else {
            dp[op[u].first] = op[u].second;
        }
        // DUMP(dp);
    }
    
    vector r(n, 0LL);
    iota(ALL_OF(r), 0LL);
    sort(ALL_OF(r), [&](ll i, ll j) {
        return et.dep[i] < et.dep[j];
    });
    REP(i, n) {
        ll u = r[i];
        for (ll v : g[u]) {
            if (et.dep[u] < et.dep[v]) {
                chmax(dq[v], dq[u]);
            }
        }
    }

    REP(k, n) {
        say(dq[k]+1);
    }
    
}

Measured memory_bytes: 56776