#include <bits/stdc++.h>
using namespace std;
#if __has_include(<boost/multiprecision/cpp_int.hpp>)
	#include <boost/multiprecision/cpp_int.hpp>
	#include <boost/multiprecision/cpp_dec_float.hpp>
	using bll = boost::multiprecision::cpp_int;
	using bdouble = boost::multiprecision::cpp_dec_float_100;
	using namespace boost::multiprecision;
#endif
#if __has_include(<boost/stacktrace.hpp>)
	#define BOOST_STACKTRACE_USE_ADDR2LINE
	#define BOOST_STACKTRACE_ADDR2LINE_LOCATION /usr/local/opt/binutils/bin/addr2line
	#define _GNU_SOURCE 1
	#include <boost/stacktrace.hpp>
#endif
#ifdef LOCAL_TEST
	namespace std {
		template<typename T> class dvector : public std::vector<T> {
		public:
			dvector() : std::vector<T>() {}
			explicit dvector(size_t n, const T& value = T()) : std::vector<T>(n, value) {}
			dvector(const std::vector<T>& v) : std::vector<T>(v) {}
			dvector(const std::initializer_list<T> il) : std::vector<T>(il) {}
			dvector(const std::string::iterator first, const std::string::iterator last) : std::vector<T>(first, last) {}
			dvector(const typename std::vector<T>::iterator first, const typename std::vector<T>::iterator last) : std::vector<T>(first, last) {}
			dvector(const typename std::vector<T>::reverse_iterator first, const typename std::vector<T>::reverse_iterator last) : std::vector<T>(first, last) {}
			dvector(const typename std::vector<T>::const_iterator first, const typename std::vector<T>::const_iterator last) : std::vector<T>(first, last) {}
			dvector(const typename std::vector<T>::const_reverse_iterator first, const typename std::vector<T>::const_reverse_iterator last) : std::vector<T>(first, last) {}
			T& operator[](size_t n) {
				try { return this->at(n); } catch (const std::exception& e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; return this->at(n); }
			}
			const T& operator[](size_t n) const {
				try { return this->at(n); } catch (const std::exception& e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; return this->at(n); }
			}
		};
	}
	class dbool {
	private:
		bool boolvalue;
	public:
		dbool() : boolvalue(false) {}
		dbool(bool b) : boolvalue(b) {}
		operator bool&() { return boolvalue; }
		operator const bool&() const { return boolvalue; }
	};
	#define vector dvector
	#define bool dbool
#endif
#ifdef LOCAL_DEV
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::vector<T>& v) {
		for (size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; }
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::vector<std::vector<T>>& vv) {
		s << "\\\n"; for (size_t i = 0; i < vv.size(); ++i){ s << vv[i] << "\n"; } return s; }
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::deque<T>& v) {
		for (size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; }
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::set<T>& se) {
		s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::multiset<T>& se) {
		s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
	template <typename T, size_t N> std::ostream& operator<<(std::ostream& s, const std::array<T, N>& a) {
		s << "{ "; for (size_t i = 0; i < N; ++i){ s << a[i] << "\t"; } s << "}"; return s; }
	template<typename T1, typename T2> std::ostream& operator<<(std::ostream& s, const std::map<T1, T2>& m) {
		s << "{\n"; for (auto itr = m.begin(); itr != m.end(); ++itr){ s << "\t" << (*itr).first << " : " << (*itr).second << "\n"; } s << "}"; return s; }
	template<typename T1, typename T2> std::ostream& operator<<(std::ostream& s, const std::pair<T1, T2>& p) {
		return s << "(" << p.first << ", " << p.second << ")"; }
	class SIGFPE_exception : std::exception {};
	class SIGSEGV_exception : std::exception {};
	void catch_SIGFPE([[maybe_unused]] int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGFPE_exception(); }
	void catch_SIGSEGV([[maybe_unused]] int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGSEGV_exception(); }
	signed convertedmain();
	signed main() { signal(SIGFPE, catch_SIGFPE); signal(SIGSEGV, catch_SIGSEGV); return convertedmain(); }
	#define main() convertedmain()
	void debug_impl() { std::cerr << '\n'; }
	template<typename Head, typename... Tail> void debug_impl(Head head, Tail... tail) { std::cerr << " " << head << (sizeof...(tail) ? "," : ""); debug_impl(tail...); }
	#define debug(...) do { std::cerr << "(" << #__VA_ARGS__ << ") ="; debug_impl(__VA_ARGS__); } while (false)
#else
	#define debug(...) do {} while (false)
#endif
//#define int long long
using ll = long long;
//constexpr int INF = 1e9;//INT_MAX=(1<<31)-1=2147483647
constexpr ll INF = (ll)1e18;//(1LL<<63)-1=9223372036854775807
constexpr ll MOD = (ll)1e9 + 7;
constexpr double EPS = 1e-9;
constexpr ll dx[4] = {1, 0, -1, 0};
constexpr ll dy[4] = {0, 1, 0, -1};
constexpr ll dx8[8] = {1, 0, -1, 0, 1, 1, -1, -1};
constexpr ll dy8[8] = {0, 1, 0, -1, 1, -1, 1, -1};
#define rep(i, n)   for(ll i=0, i##_length=(n); i< i##_length; ++i)
#define repeq(i, n) for(ll i=1, i##_length=(n); i<=i##_length; ++i)
#define rrep(i, n)   for(ll i=(n)-1; i>=0; --i)
#define rrepeq(i, n) for(ll i=(n)  ; i>=1; --i)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
void p() { std::cout << '\n'; }
template<typename Head, typename... Tail> void p(Head head, Tail... tail) { std::cout << head << (sizeof...(tail) ? " " : ""); p(tail...); }
template<typename T> inline void pv(std::vector<T>& v) { for(ll i=0, N=v.size(); i<N; i++) std::cout << v[i] << " \n"[i==N-1]; }
template<typename T> inline bool chmax(T& a, T b) { return a < b && (a = b, true); }
template<typename T> inline bool chmin(T& a, T b) { return a > b && (a = b, true); }
template<typename T> inline void uniq(std::vector<T>& v) { v.erase(std::unique(v.begin(), v.end()), v.end()); }

/*-----8<-----template-----8<-----*/

/*
PersistentSegmentTree(f, M1):= コンストラクタ。f は2つの区間の要素をマージする二項演算, M1 はモノイドの単位元である。
Node* build(vector< Monoid > &v) := 配列 v を各要素としたセグメント木を構築し, その根を返す。
Node* update(ll k, const Monoid &x, Node t) := t を根とするセグメント木に対し k 番目の要素を x に更新し, 更新後の根を返す。
Monoid query(ll a, ll b, Node *t) := t を根とするセグメント木に対し, 区間 [a,b) の要素を二項演算した結果を返す。
*/
template< typename Monoid, typename F >
class PersistentSegmentTree {
public: 
	struct Node {
		Monoid data;
		Node *l, *r;
		Node(const Monoid& data) : data(data), l(nullptr), r(nullptr) {}
	};
	ll sz;
	const F f;
	const Monoid M1;

	PersistentSegmentTree(const F& f, const Monoid& M1) : f(f), M1(M1) {}

private:
	Node* merge(Node* l, Node* r) {
		auto t = new Node(f(l->data, r->data));
		t->l = l;
		t->r = r;
		return t;
	}

	Node* build(ll l, ll r, vector< Monoid > &v) {
		if(l + 1 >= r) return new Node(v[l]);
		return merge(build(l, (l + r) >> 1, v), build((l + r) >> 1, r, v));
	}

	Node* update(ll a, const Monoid &x, Node* k, ll l, ll r) {
		if(r <= a || a + 1 <= l) {
			return k;
		} else if(a <= l && r <= a + 1) {
			return new Node(x);
		} else {
			return merge(update(a, x, k->l, l, (l + r) >> 1), update(a, x, k->r, (l + r) >> 1, r));
		}
	}

	Monoid query(ll a, ll b, Node* k, ll l, ll r) {
		if(r <= a || b <= l) {
			return M1;
		} else if(a <= l && r <= b) {
			return k->data;
		} else {
			return f(query(a, b, k->l, l, (l + r) >> 1),
							 query(a, b, k->r, (l + r) >> 1, r));
		}
	}

public:
	Node* build(vector< Monoid > &v) {
		sz = (ll) v.size();
		return build(0, (ll) v.size(), v);
	}

	Node* update(ll k, const Monoid &x, Node* t) {
		return update(k, x, t, 0, sz);
	}

	Monoid query(ll a, ll b, Node* t) {
		return query(a, b, t, 0, sz);
	}
};

/*-----8<-----library-----8<-----*/
 
void solve() {
	ll N;
	scanf("%lld", &N);
	vector<ll> a(N, 0);
	rep(i, N) { scanf("%lld", &a[i]); }
	vector<ll> u(N-1, 0), v(N-1, 0);
	rep(i, N-1) { scanf("%lld%lld", &u[i], &v[i]); u[i]--; v[i]--; }
	vector<vector<ll>> g(N);
	rep(i,N-1){
		g[v[i]].push_back(u[i]);
		g[u[i]].push_back(v[i]);
	}

	auto F = [](ll x, ll y){ return x + y; };
	using Node = PersistentSegmentTree<ll,decltype(F)>::Node;
	PersistentSegmentTree<ll,decltype(F)> pseg(F, 0);

	vector<ll> v0(N,0);
	Node* start=pseg.build(v0);
	vector<Node*> nodev(N);
	nodev[0]=pseg.update(0, a[0], start);
 
	vector<ll> length(N,-INF);
	length[0]=1;
	auto f=[&](auto&& f, vector<vector<ll>> &g, ll v,ll p)->void{
		if(p!=-1){
			ll len=length[p];
			ll last=pseg.query(len-1, len, nodev[p]);
			if(last<a[v]){
				nodev[v]=pseg.update(len, a[v], nodev[p]);
				len++;
			}else{
				//初期は left->OK / right->NG になっています
				using rangetype = ll;
				rangetype left = -1;
				rangetype right = len;
				auto isOK = [&](rangetype val) -> bool {
					return pseg.query(val, val+1, nodev[p]) < a[v];
				};
				while((rangetype)abs(right - left) > 1) {
					rangetype mid = left + (right - left) / 2;
					if(isOK(mid)) left = mid;
					else right = mid;
				}
				nodev[v]=pseg.update(right, a[v], nodev[p]);
			}
			length[v]=len;
		}
		
		for(ll nextv:g[v]){
			if(nextv==p)continue;
			f(f,g,nextv,v);
		}
	};
	f(f,g,0,-1);

	rep(i,N)printf("%lld\n", length[i]);
}

// https://atcoder.jp/contests/abc165/tasks/abc165_f
signed main() {
	solve();
	return 0;
}


Measured memory_bytes: 183868