#include <bits/stdc++.h>

using namespace std;

//using ll = int64_t;
using ll = long long;
using ull = uint64_t;
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using ld = double;

#define X first
#define Y second

#ifndef ONLINE_JUDGE
#define FWRITE
#endif

namespace io
{

#ifndef FWRITE
#include <unistd.h>
#endif
	const int BUFSIZE = 1 << 20;

	int isize, osize;
	char ibuf[BUFSIZE + 10], obuf[BUFSIZE + 10];
	char* is, * it, * os = obuf, * ot = obuf + BUFSIZE;

	char getchar()
	{
		if (is == it)
		{
			is = ibuf;
#ifdef FWRITE
			it = ibuf + fread(ibuf, 1, BUFSIZE, stdin);
#else
			it = ibuf + read(STDIN_FILENO, ibuf, BUFSIZE);
#endif
			if (is == it) return EOF;
		}
		return *is++;
	}

	char getalpha()
	{
		char c = getchar();
		while (!isalpha(c)) c = getchar();
		return c;
	}

	void putchar(char c)
	{
		*os++ = c;
		if (os == ot)
		{
#ifdef FWRITE
			fwrite(obuf, 1, BUFSIZE, stdout);
#else
			write(STDOUT_FILENO, obuf, BUFSIZE);
#endif
			os = obuf;
		}
	}

	int inp() {
		int x = 0, f = 0; char ch;
		for (ch = getchar(); !isdigit(ch); ch = getchar())
		{
			if (ch == EOF) return -1;
			if (ch == '-') f = 1;
		}
		for (; isdigit(ch); x = x * 10 + ch - '0', ch = getchar());
		return f ? -x : x;
	}

	ll inp_ll() {
		ll x = 0; int f = 0; char ch;
		for (ch = getchar(); !isdigit(ch); ch = getchar())
			if (ch == '-') f = 1;
		for (; isdigit(ch); x = x * 10 + ch - '0', ch = getchar());
		return f ? -x : x;
	}

	template<class T>
	bool read(T& x)
	{
		x = 0;
		char ch = getchar();
		if (ch == EOF) return 0;
		for (; !isdigit(ch); )
		{
			ch = getchar();
			if (ch == EOF) return 0;
		}
		for (; isdigit(ch); x = x * 10 + ch - '0', ch = getchar());
		return 1;
	}

	template<class T>
	void write(T x)
	{
		static char s[22];
		static char* it = s + 20;
		static char* end = s + 20;

		if (x < 0)
		{
			putchar('-');
			x = -x;
		}

		do
		{
			*--it = x % 10 + '0';
			x /= 10;
		} while (x);
		/*
		if (!x)
			*-- it = '0';
		while (x)
		{
			*-- it = x%10+'0';
			x /= 10;
		}
		*/
		for (; it < end; ++it)
			putchar(*it);
	}

	template<>
	void write(const char* s)
	{
		for (; *s; ++s) putchar(*s);
	}

	template<>
	void write(char c)
	{
		putchar(c);
	}

	template<class T, class V>
	void write(T x, V y)
	{
		write(x);
		write(y);
	}

	template<class T>
	void writeln(T x)
	{
		write(x);
		putchar('\n');
	}

	struct ender
	{
		~ender()
		{
			if (os != obuf)
#ifdef FWRITE
				fwrite(obuf, 1, os - obuf, stdout);
#else
				write(STDOUT_FILENO, obuf, os - obuf);
#endif
		}
	}__ender;

}

template<class T>
void print(const T& a)
{
	for (auto x : a) printf("%d ", x); puts("");
}

int64_t power(int64_t a, int64_t b, int64_t p)
{
	if (!b) return 1;
	int64_t t = power(a, b >> 1, p);
	t = t * t % p;
	if (b & 1) t = t * a % p;
	return t;
}

//mt19937_64 rd(chrono::steady_clock::now().time_since_epoch().count());
mt19937 rd(chrono::steady_clock::now().time_since_epoch().count());

using namespace io;

template<class T>
inline void freshmin(T& a, const T& b)
{
	if (a > b) a = b;
}

template<class T>
inline void freshmax(T& a, const T& b)
{
	if (a < b) a = b;
}

const ll B = 31;
//const ll MOD = 998244353;
const int INF = 1000000010;
const ll INFll = 1000000000000000000LL;
const int MAXN = 200010;

int dx[] = { -1, 1, 0, 0, -1, -1, 1, 1 };
int dy[] = { 0, 0, -1, 1, -1, 1, -1, 1 };

ld det(ld x1, ld y1, ld x2, ld y2, ld x3, ld y3)
{
	return x1 * y2 - x2 * y1 + x2 * y3 - x3 * y2 + x3 * y1 - x1 * y3;
}

int n;
int a[MAXN], b[MAXN];
vector<int> v[MAXN];

int m;

struct node
{
	node* Lc, * Rc;
	int val;
	void update()
	{
		this->val = max(this->Lc->val, this->Rc->val);
	}
};

int tot;
//node tree[MAXN * 80];

node* new_node()
{
	node* it = new node;
	it->Lc = it->Rc = 0;
	it->val = 0;
	return it;
}

node* build(int L, int R)
{
	node* it = new_node();
	if (L == R)
	{
		it->Lc = it->Rc = 0;
		it->val = 0;
		return it;
	}
	int m = (L + R) / 2;
	it->Lc = build(L, m);
	it->Rc = build(m + 1, R);
	it->update();
	return it;
}

int get(node* it, int L, int R, int x, int y)
{
	if (L == x && R == y)
	{
		return it->val;
	}
	int m = (L + R) / 2;
	if (y <= m)
		return get(it->Lc, L, m, x, y);
	if (x > m)
		return get(it->Rc, m+1, R, x, y);
	return max(get(it->Lc, L, m, x, m), get(it->Rc, m + 1, R, m + 1, y));
}

node* add(node* it, int L, int R, int x, int d)
{
	node* p = new_node();
	*p = *it;
	if (L == R)
	{
		p->val = max(p->val, d);
		return p;
	}
	int m = (L + R) / 2;
	if (x <= m)
		p->Lc = add(it->Lc, L, m, x, d);
	else
		p->Rc = add(it->Rc, m + 1, R, x, d);
	p->update();
	return p;
}

node* root[MAXN];
int f[MAXN];

void dfs(int x, int pre)
{
	f[x] = get(root[pre], 0, m, 0, a[x] - 1) + 1;
	root[x] = add(root[pre], 0, m, a[x], f[x]);
	f[x] = max(f[x], f[pre]);
	for (auto y : v[x])
	{
		if (y == pre) continue;
		dfs(y, x);
	}
}

void solve()
{
	n = inp();
	vector<int> p;
	for (int i = 1; i <= n; ++i)
	{
		a[i] = inp();
		p.push_back(a[i]);
	}
	sort(p.begin(), p.end());
	p.erase(unique(p.begin(), p.end()), p.end());
	for (int i = 1; i <= n; ++i)
	{
		a[i] = lower_bound(p.begin(), p.end(), a[i]) - p.begin() + 1;
	}
	m = p.size();
	for (int i = 1; i < n; ++i)
	{
		int x = inp(), y = inp();
		v[x].push_back(y);
		v[y].push_back(x);
	}
	root[0] = build(0, m);
	dfs(1, 0);
	for (int i = 1; i <= n; ++i)
	{
		writeln(f[i]);
	}
}

int main()
{

	//for (int T = inp(); T --; )
	solve();

	return 0;
}

Measured memory_bytes: 156680