// #pragma GCC target ("avx")
// #pragma GCC optimize("Ofast")
// #pragma GCC optimize("unroll-loops")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
using namespace std;
// #define int long long
// #define endl '\n'

#pragma region TEMPLATE

/* TYPE */
typedef long long ll;       typedef long double ld;
typedef pair<int, int> pii; typedef pair<ll, ll> pll;
typedef vector<pii> vpii;   typedef vector<pll> vpll;
typedef vector<int> vi;     typedef vector<ll> vl;
typedef vector<string> vst; typedef vector<bool> vb;
typedef vector<ld> vld;     typedef vector<vector<int>> vvi;
template<typename T, typename Cmp = less<>> using prique = priority_queue<T, vector<T>, Cmp>;
template<typename T> using prique_r = prique<T, greater<>>;
/* CONSTANT */
#define ln '\n'
const int INF = 1 << 30;    const ll INFF = 1LL << 60;  const string ALPHABET = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const int MOD = 1e9 + 7;    const int MODD = 998244353; const string alphabet = "abcdefghijklmnopqrstuvwxyz";
const double EPS = 1e-9;    const ld PI = 3.14159265358979323846264338327950288;
const int dx[] = { 1, 0, -1,  0,  1, -1, -1, 1, 0 };
const int dy[] = { 0, 1,  0, -1, -1, -1,  1, 1, 0 };
/* CONTAINER */
#define PB              emplace_back
#define ALL(v)          (v).begin(), (v).end()
#define RALL(v)         (v).rbegin(), (v).rend()
#define SORT(v)         sort(ALL(v))
#define RSORT(v)        sort(RALL(v))
#define LESS(x, val)    (lower_bound(x.begin(), x.end(), val) - x.begin())
#define LEQ(x, val)     (upper_bound(x.begin(), x.end(), val) - x.begin())
#define GREATER(x, val) (int)(x).size() - LEQ((x), (val))
#define GEQ(x, val)     (int)(x).size() - LESS((x), (val))
#define UNIQUE(v)       sort(ALL(v)); (v).erase(unique(ALL(v)), (v).end())
template<typename T> vector<T> make_v(size_t a) { return vector<T>(a); }
template<typename T, typename... Ts> auto make_v(size_t a, Ts... ts) { return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...)); }
template<typename T, typename U, typename... V> enable_if_t<is_same<T, U>::value != 0> fill_v(U &u, const V... v) { u = U(v...); }
template<typename T, typename U, typename... V> enable_if_t<is_same<T, U>::value == 0> fill_v(U &u, const V... v) { for (auto &e : u) fill_v<T>(e, v...); }
/* LOOP */
#define _overload3(_1, _2, _3, name, ...) name
#define _REP(i, n)      REPI(i, 0, n)
#define REPI(i, a, b)   for (ll i = (ll)a; i < (ll)b; ++i)
#define REP(...)        _overload3(__VA_ARGS__, REPI, _REP,)(__VA_ARGS__)
#define _RREP(i, n)     RREPI(i, n, 0)
#define RREPI(i, a, b)  for (ll i = (ll)a; i >= (ll)b; --i)
#define RREP(...)       _overload3(__VA_ARGS__, RREPI, _RREP,)(__VA_ARGS__)
#define EACH(e, v)      for (auto& e : v)
#define PERM(v)         sort(ALL(v)); for (bool c##p = true; c##p; c##p = next_permutation(ALL(v)))
/* INPUT */
template<typename T> void SSS(T& t) { cin >> t; }
template<typename Head, typename... Tail> void SSS(Head&& head, Tail&&... tail) { cin >> head; SSS(tail...); }
#define SS(T, ...)      T __VA_ARGS__; SSS(__VA_ARGS__);
#define SV(T, v, n)     vector<T> v(n); for (auto& i : v) cin >> i;
#define SVV(T, v, n, m) vector<vector<T>> v(n, vector<T>(m)); for (auto& r : v) for (auto& i : r) cin >> i;
/* OUTPUT */
// PROTOTYPE DECLARATION
template<typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &j);
template<typename... T> ostream &operator<<(ostream &os, const tuple<T...> &t);
template<class C, enable_if_t<!is_same<C, string>::value, decltype(declval<const C &>().begin(), nullptr)> = nullptr> ostream& operator<<(ostream &os, const C &c);
template<typename T> ostream &operator<<(ostream &os, const stack<T> &j);
template<typename T> ostream &operator<<(ostream &os, const queue<T> &j);
template<typename T, typename C, typename Cmp> ostream &operator<<(ostream &os, const priority_queue<T, C, Cmp> &j);
// IMPLEMENTATION
template<typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &j) { return os << '{' << j.first << ", " << j.second << '}'; }
template<size_t num = 0, typename... T> enable_if_t<num == sizeof...(T)> PRINT_TUPLE(ostream &os, const tuple<T...> &t) {}
template<size_t num = 0, typename... T> enable_if_t<num <  sizeof...(T)> PRINT_TUPLE(ostream &os, const tuple<T...> &t) { os << get<num>(t); if (num + 1 < sizeof...(T)) os << ", "; PRINT_TUPLE<num + 1>(os, t); }
template<typename... T> ostream &operator<<(ostream &os, const tuple<T...> &t) { PRINT_TUPLE(os << '{', t); return os << '}'; }
template<class C, enable_if_t<!is_same<C, string>::value, decltype(declval<const C &>().begin(), nullptr)>> ostream& operator<<(ostream &os, const C &c) { os << '{'; for (auto it = begin(c); it != end(c); it++) { if (begin(c) != it) os << ", "; os << *it; } return os << '}'; }
template<typename T> ostream &operator<<(ostream &os, const stack<T> &j) { deque<T> d; for (auto c = j; !c.empty(); c.pop()) d.push_front(c.top());  return os << d; }
template<typename T> ostream &operator<<(ostream &os, const queue<T> &j) { deque<T> d; for (auto c = j; !c.empty(); c.pop()) d.push_back(c.front()); return os << d; }
template<typename T, typename C, typename Cmp> ostream &operator<<(ostream &os, const priority_queue<T, C, Cmp> &j) { deque<T> d; for (auto c = j; !c.empty(); c.pop()) d.push_front(c.top());  return os << d; }
// OUTPUT FUNCTION
template<typename T> int PV(T &v) { int sz = v.size(); for (int i = 0; i < sz; ++i) cout << v[i] << " \n"[i == sz - 1]; return 0; }
inline int print() { cout << endl; return 0; }
template<typename Head> int print(Head&& head){ cout << head; return print(); }
template<typename Head, typename... Tail> int print(Head&& head, Tail&&... tail) { cout << head << " "; return print(forward<Tail>(tail)...); }
#ifdef LOCAL
inline void dump() { cerr << endl; }
template<typename Head> void dump(Head&& head) { cerr << head; dump(); }
template<typename Head, typename... Tail> void dump(Head&& head, Tail&&... tail) { cerr << head << ", "; dump(forward<Tail>(tail)...); }
#define debug(...) do {cerr << __LINE__ << ":\t" << #__VA_ARGS__ << " = "; dump(__VA_ARGS__); } while (false)
#else
#define dump(...)
#define debug(...)
#endif
/* OTHER */
#define fi              first
#define se              second
#define MP              make_pair
#define MT              make_tuple
#define tmax(x, y, z)   max((x), max((y), (z)))
#define tmin(x, y, z)   min((x), min((y), (z)))
template<typename T, typename A, typename B> inline bool between(T x, A a, B b) { return ((a <= x) && (x < b)); }
template<typename A, typename B> inline bool chmax(A &a, const B &b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A &a, const B &b) { if (a > b) { a = b; return true; } return false; }
inline ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
inline ll POW(ll a, ll b)                    { ll r = 1; do { if (b & 1)  r *= a;        a *= a; }       while (b >>= 1); return r; }
inline ll MOP(ll a, ll b, const ll &m = MOD) { ll r = 1; do { if (b & 1) (r *= a) %= m; (a *= a) %= m; } while (b >>= 1); return r; }
struct abracadabra {
	abracadabra() {
		cin.tie(nullptr); ios::sync_with_stdio(false);
		cout << fixed << setprecision(20);
		cerr << fixed << setprecision(5);
	};
} ABRACADABRA;

#pragma endregion
#pragma region compression
// template<typename T> vector<T> compress(vector<T> ord, map<T, int> &rev) {
template<typename T> vector<T> compress(vector<T> ord) { map<T, int> rev;
	vector< T > com = ord;
	sort(com.begin(), com.end());
	com.erase(unique(com.begin(), com.end()), com.end());
	for (int i = 0; i < com.size(); ++i) rev[com[i]] = i;
	vector< T > ret; for (auto& e : ord) ret.emplace_back(rev[e]);
	return ret;
}

/*
・座標圧縮
	> O(NlogN)
[備考] 各数字の対応関係が欲しいときは, 引数にmapを入れてコメントアウトを外す.
[使用例]
1. 引数にmapを入れない場合
vector<long long> com = compress(v);
2. 引数にmapを入れる場合
map<long long, int> rev;
vector<long long> com = compress(v, rev);
*/
#pragma endregion
#pragma region datastructure segment tree
template<typename T> struct SegmentTree {
	using F = function< T(T, T) >;
	vector< T > seg;
	int size;       // データの数以上の最小の2冪, 最下段のデータの個数
	F func;
	T M1 = 0;
	SegmentTree() {}
	SegmentTree(int n, F f) : func(f) {
		size = 1; while (size < n) size <<= 1;
		seg.resize(2 * size - 1, M1);
	}
	void set(int k, T x) {
		seg[k + size - 1] = x;
	}
	void build() {
		for (int i = size - 2; i >= 0; --i) {
			// iの子は, (2 * i + 1, 2 * i + 2)
			seg[i] = func(seg[2 * i + 1], seg[2 * i + 2]);
		}
	}
	void update(int k, T x) {
		// kをseg内の添字に対応させる <- (size - 1)を足す
		k += size - 1;
		seg[k] = x;
		while (k > 0) {
			k = (k - 1) / 2;
			seg[k] = func(seg[2 * k + 1], seg[2 * k + 2]);
		}
	}
	void add(int k, T x) {
		// kをseg内の添字に対応させる <- (size - 1)を足す
		k += size - 1;
		seg[k] += x;
		while (k > 0) {
			k = (k - 1) / 2;
			seg[k] = func(seg[2 * k + 1], seg[2 * k + 2]);
		}
	}
	T query(int a, int b, int k = 0, int l = 0, int r = -1) {
		if (r < 0) r = size;
		if (r <= a || l >= b) return M1;
		if (l >= a && r <= b) return seg[k];
		T f_l = query(a, b, 2 * k + 1, l, (l + r) / 2);
		T f_r = query(a, b, 2 * k + 2, (l + r) / 2, r);
		return func(f_l, f_r);
	}
	void print() {
		for (int i = 0; i < 2 * size - 1; ++i) {
			cerr << seg[i] << " ";
			if (!((i + 2) & (i + 1))) cerr << endl;
		}
	}
};

/*
・セグメント木
	>         build O(N)
	> query, update O(logN)
[備考] 結合律, 単位元を持つ二項演算を, 任意の区間に関してlogNで行うデータ構造
[使用例]
SegmentTree<int> seg(N, [](int a, int b){ return a + b; }, 0 );     // 区間和
SegmentTree<int> seg(N, [](int a, int b){ return min(a,b); }, INF); // 区間min
seg.set(k, x);      // 要素kに値xを設定
seg.build();        // 上のセグメントに値を設定
seg.update(k, x);   // 要素kを値xに変更
seg.add(k, x);      // 要素kに値xを加算
seg.query(l, r);    // 半開区間[l, r)に対する二項演算の結果を返す
*/
#pragma endregion

const int MX = 200200;
int N;
vector<int> A;
vector<int> graph[MX];
SegmentTree<int> seg;
int res[MX];

void euler_tour(int cur, int prv = -1) {
	int num = A[cur];
	res[cur] = seg.query(0, num) + 1;
	int pr = seg.query(num, num + 1);
	seg.update(num, res[cur]);
    res[cur] = seg.query(0, MX);
    for (auto& nxt: graph[cur]) {
        if (prv == nxt) continue;
        euler_tour(nxt, cur);
    }
	seg.update(num, pr);
}

signed main() {

	cin >> N;
	SV(int, B, N);
	A = compress(B);

	REP(i, N - 1) {
		SS(int, U, V);
		--U, --V;
		graph[U].emplace_back(V);
		graph[V].emplace_back(U);
	}

	seg = SegmentTree<int>(MX, [](int a, int b){ return max(a,b); });
	euler_tour(0);
	REP(i, N) print(res[i]);

}


Measured memory_bytes: 130944