#include<bits/stdc++.h>

using namespace std;
#define INFS (1LL<<28)
#define DEKAI 1000000007
#define INF 1000000007
//#define MOD 1000000007
#define lp(i,n) for(int i=0;i<n;i++)
#define lps(i,n) for(int i=1;i<=n;i++)
#define all(c) begin(c), end(c)

//#define int long long 

namespace {
	#define __DECLARE__(C)    \
	    template <typename T> \
	std::ostream &operator<<(std::ostream &, const C<T> &);

	#define __DECLAREM__(C)               \
	    template <typename T, typename U> \
	std::ostream &operator<<(std::ostream &, const C<T, U> &);

	__DECLARE__(std::vector)
	__DECLARE__(std::deque)
	__DECLARE__(std::set)
	__DECLARE__(std::stack)
	__DECLARE__(std::queue)
	__DECLARE__(std::priority_queue)
	__DECLARE__(std::unordered_set)
	__DECLAREM__(std::map)
	__DECLAREM__(std::unordered_map)

	template <typename T, typename U>
	std::ostream &operator<<(std::ostream &, const std::pair<T, U> &);
	template <typename... T>
	std::ostream &operator<<(std::ostream &, const std::tuple<T...> &);
	template <typename T, std::size_t N>
	std::ostream &operator<<(std::ostream &, const std::array<T, N> &);

	template <typename Tuple, std::size_t N>
	struct __TuplePrinter__ {
		static void print(std::ostream &os, const Tuple &t) {
			__TuplePrinter__<Tuple, N - 1>::print(os, t);
			os << ", " << std::get<N - 1>(t);
		}
	};

	template <typename Tuple>
	struct __TuplePrinter__<Tuple, 1> {
		static void print(std::ostream &os, const Tuple &t) { os << std::get<0>(t); }
	};

	template <typename... T>
	std::ostream &operator<<(std::ostream &os, const std::tuple<T...> &t) {
		os << '(';
		__TuplePrinter__<decltype(t), sizeof...(T)>::print(os, t);
		os << ')';
		return os;
	}

	template <typename T, typename U>
	std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &v) {
		return os << '(' << v.first << ", " << v.second << ')';
	}

	#define __INNER__                             \
	os << '[';                                \
	for (auto it = begin(c); it != end(c);) { \
		os << *it;                            \
		os << (++it != end(c) ? ", " : "");   \
	}                                         \
	return os << ']';

	template <typename T, std::size_t N>
	std::ostream &operator<<(std::ostream &os, const std::array<T, N> &c) {
		__INNER__
	}

	#define __DEFINE__(C)                                           \
	    template <typename T>                                       \
	std::ostream &operator<<(std::ostream &os, const C<T> &c) { \
		__INNER__                                               \
	}

	#define __DEFINEM__(C)                                             \
	    template <typename T, typename U>                              \
	std::ostream &operator<<(std::ostream &os, const C<T, U> &c) { \
		__INNER__                                                  \
	}

	#define __DEFINEW__(C, M1, M2)                                  \
	    template <typename T>                                       \
	std::ostream &operator<<(std::ostream &os, const C<T> &c) { \
		std::deque<T> v;                                        \
		for (auto d = c; !d.empty(); d.pop()) v.M1(d.M2());     \
			return os << v;                                         \
	}

	__DEFINE__(std::vector)
	__DEFINE__(std::deque)
	__DEFINE__(std::set)
	__DEFINEW__(std::stack, push_front, top)
	__DEFINEW__(std::queue, push_back, front)
	__DEFINEW__(std::priority_queue, push_front, top)
	__DEFINE__(std::unordered_set)
	__DEFINEM__(std::map)
	__DEFINEM__(std::unordered_map)
}

#define pii pair<int,int>
#define ll long long
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; }

// modint 
template <signed M, unsigned T>
struct mod_int {
	constexpr static signed MODULO = M;
	constexpr static unsigned TABLE_SIZE = T;

	signed x;

	mod_int() : x(0) {}

	mod_int(long long y) : x(static_cast<signed>(y >= 0 ? y % MODULO : MODULO - (-y) % MODULO)) {}

	mod_int(int y) : x(y >= 0 ? y % MODULO : MODULO - (-y) % MODULO) {}

	mod_int &operator+=(const mod_int &rhs) {
		if ((x += rhs.x) >= MODULO) x -= MODULO;
		return *this;
	}

	mod_int &operator-=(const mod_int &rhs) {
		if ((x += MODULO - rhs.x) >= MODULO) x -= MODULO;
		return *this;
	}

	mod_int &operator*=(const mod_int &rhs) {
		x = static_cast<signed>(1LL * x * rhs.x % MODULO);
		return *this;
	}

	mod_int &operator/=(const mod_int &rhs) {
		x = static_cast<signed>((1LL * x * rhs.inv().x) % MODULO);
		return *this;
	}

	mod_int operator-() const { return mod_int(-x); }

	mod_int operator+(const mod_int &rhs) const { return mod_int(*this) += rhs; }

	mod_int operator-(const mod_int &rhs) const { return mod_int(*this) -= rhs; }

	mod_int operator*(const mod_int &rhs) const { return mod_int(*this) *= rhs; }

	mod_int operator/(const mod_int &rhs) const { return mod_int(*this) /= rhs; }

	bool operator<(const mod_int &rhs) const { return x < rhs.x; }

	mod_int inv() const {
		assert(x != 0);
		if (x <= static_cast<signed>(TABLE_SIZE)) {
			if (_inv[1].x == 0) prepare();
			return _inv[x];
		} else {
			signed a = x, b = MODULO, u = 1, v = 0, t;
			while (b) {
				t = a / b;
				a -= t * b;
				std::swap(a, b);
				u -= t * v;
				std::swap(u, v);
			}
			return mod_int(u);
		}
	}

	mod_int pow(long long t) const {
		assert(!(x == 0 && t == 0));
		mod_int e = *this, res = mod_int(1);
		for (; t; e *= e, t >>= 1)
			if (t & 1) res *= e;
		return res;
	}

	mod_int fact() {
		if (_fact[0].x == 0) prepare();
		return _fact[x];
	}

	mod_int inv_fact() {
		if (_fact[0].x == 0) prepare();
		return _inv_fact[x];
	}

	mod_int choose(mod_int y) {
		assert(y.x <= x);
		return this->fact() * y.inv_fact() * mod_int(x - y.x).inv_fact();
	}

	static mod_int _inv[TABLE_SIZE + 1];

	static mod_int _fact[TABLE_SIZE + 1];

	static mod_int _inv_fact[TABLE_SIZE + 1];

	static void prepare() {
		_inv[1] = 1;
		for (int i = 2; i <= (int)TABLE_SIZE; ++i) {
			_inv[i] = 1LL * _inv[MODULO % i].x * (MODULO - MODULO / i) % MODULO;
		}
		_fact[0] = 1;
		for (unsigned i = 1; i <= TABLE_SIZE; ++i) {
			_fact[i] = _fact[i - 1] * int(i);
		}
		_inv_fact[TABLE_SIZE] = _fact[TABLE_SIZE].inv();
		for (int i = (int)TABLE_SIZE - 1; i >= 0; --i) {
			_inv_fact[i] = _inv_fact[i + 1] * (i + 1);
		}
	}
};

template <int M, unsigned F>
std::ostream &operator<<(std::ostream &os, const mod_int<M, F> &rhs) {
	return os << rhs.x;
}

template <int M, unsigned F>
std::istream &operator>>(std::istream &is, mod_int<M, F> &rhs) {
	long long s;
	is >> s;
	rhs = mod_int<M, F>(s);
	return is;
}

template <int M, unsigned F>
mod_int<M, F> mod_int<M, F>::_inv[TABLE_SIZE + 1];

template <int M, unsigned F>
mod_int<M, F> mod_int<M, F>::_fact[TABLE_SIZE + 1];

template <int M, unsigned F>
mod_int<M, F> mod_int<M, F>::_inv_fact[TABLE_SIZE + 1];

template <int M, unsigned F>
bool operator==(const mod_int<M, F> &lhs, const mod_int<M, F> &rhs) {
	return lhs.x == rhs.x;
}

template <int M, unsigned F>
bool operator!=(const mod_int<M, F> &lhs, const mod_int<M, F> &rhs) {
	return !(lhs == rhs);
}

const int MF = 1000010;
const int MOD = 1000000007;

using mint = mod_int<MOD, MF>;

mint binom(int n, int r) { return (r < 0 || r > n || n < 0) ? 0 : mint(n).choose(r); }

mint fact(int n) { return mint(n).fact(); }

mint inv_fact(int n) { return mint(n).inv_fact(); }
const ll mod = 1000000007;
const int MAX_N = 10000;  // 400MB
// const int MAX_N = 1024; // 4MB
// nCr % mod

#define int long long
#define double long double 
#define RK 20000000000
#define LK 30000000000

inline ll gcds(ll a, ll b) { return b ? gcds(b, a % b) : a; }
/*
void sol_A(){
	int k;
	cin>>k;
	int a,b;
	cin>>a>>b;
	for(int i=a;i<=b;i++){
		if(i%k==0){
			cout<<"OK"<<endl;
			return;
		}
	}
	cout<<"NG"<<endl;
}

void sol_B(){
	int x;
	cin>>x;
	int ans=0,now=100;
	while(1){
		ans++;
		now*=1.01;
		if(x<=now){
			break;
		}
	}
	cout<<ans<<endl;
}

void sol_C(){
	int n,m,q;
	cin>>n>>m>>q;

}
*/
int n;
vector<int> v;
vector<vector<int>> g;
vector<int> p;
vector<int> j;
vector<bool> ha;

void makep(){
	queue<int> q;
	p.resize(n);
	lp(i,n)p[i]=-1;
	p[0]=0;
	q.push(0);
	while(!q.empty()){
		int now=q.front();
		q.pop();
		lp(i,g[now].size()){
			int next=g[now][i];
			if(p[next]!=-1)continue;
			p[next]=now;
			q.push(next);
		}
	}
}

void makej(){
	stack<int> s;
	vector<int> done(n,0);
	s.push(0);
	done[0]=1;
	while(!s.empty()){
		int now=s.top();
		s.pop();
		j.push_back(now);
		lp(i,g[now].size()){
			int next=g[now][i];
			if(done[next]==1)continue;
			done[next]=1;
			s.push(next);
		}
	}
}

stack<pair<int,pair<int,int>>> st;
vector<int> lis;
vector<int> ans;

void modoru(int now,int targ){
	while(now!=targ){
		now=p[now];
		int tg=st.top().first;
		int bef=st.top().second.first;
		int af=st.top().second.second;
		st.pop();
		//assert(af==lis[tg]);
		//cout<<"AAA "<<tg<<" "<<bef<<" "<<af<<endl;
		lis[tg]=bef;
	}
}

void solve(){
	lis.resize(n);
	ans.resize(n);
	lp(i,n){
		lis[i]=INF;
	}
	lp(i,n){
		int now=j[i];
		int pl=lower_bound(all(lis),v[now])-lis.begin();
		st.push({pl,{lis[pl],v[now]}});
		lis[pl]=v[now];
		int dis=lower_bound(all(lis),INF)-lis.begin();
		ans[now]=dis;
		//cout<<now<<" "<<lis<<endl;
		if(ha[now]&&i!=n-1){
			modoru(now,p[j[i+1]]);
			//cout<<" "<<lis<<endl;
		}
	}
	lp(i,n){
		if(i!=0)cout<<" ";
		cout<<ans[i];
	}
	cout<<endl;
	return;
}

signed main(){
	cin>>n;
	v.resize(n);
	g.resize(n);
	p.resize(n);
	lp(i,n){
		cin>>v[i];
	}
	lp(i,n-1){
		int a,b;
		cin>>a>>b;
		a--;
		b--;
		g[a].push_back(b);
		g[b].push_back(a);
	}
	ha.resize(n);
	lp(i,n){
		if(g[i].size()==1)ha[i]=true;
		else ha[i]=false;
	}
	makep();
	makej();
	solve();
}

Measured memory_bytes: 39344