using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using static System.Console;
using static System.Math;
using static MyIO;
using static MyUtil;

public class F { public static void Main() => (new Solver()).Solve(); }

public class Solver
{
	private const long INF = long.MaxValue / 2;
	private long N;
	private long[] a;
	private List<long>[] adj;
	private long[] ans;
	private long[] dp;
	private Stack<(long, long)> stack;

	public void Solve()
	{
		N = GetLong();
		a = GetLongs(N);
		adj = Range(0, N).Select(_ => new List<long>()).ToArray();
		for(long i = 0; i < N - 1; i++)
		{
			long u = GetLong() - 1;
			long v = GetLong() - 1;
			adj[u].Add(v);
			adj[v].Add(u);
		}

		ans = new long[N];
		dp = Enumerable.Repeat(INF, (int)N + 1).ToArray();
		stack = new Stack<(long, long)>();

		dfs(0);

		WriteLine(string.Join("\n", ans));
	}

	private void dfs(long v)
	{
		long pos = bs(a[v]);
		stack.Push((pos, dp[pos]));
		dp[pos] = a[v];
		ans[v] = length();

		foreach(var u in adj[v])
		{
			if(ans[u] != 0)
				continue;

			dfs(u);
		}

		var pair = stack.Pop();
		dp[pair.Item1] = pair.Item2;
	}

	private long bs(long key)
	{
		long ng = -1;
		long ok = N;
		while(Abs(ok - ng) > 1)
		{
			long mid = (ok + ng) / 2;
			if(dp[mid] >= key)
				ok = mid;
			else
				ng = mid;
		}
		return ok;
	}

	private long length()
	{
		long ng = N;
		long ok = -1;
		while(Abs(ok - ng) > 1)
		{
			long mid = (ok + ng) / 2;
			if(dp[mid] < INF)
				ok = mid;
			else
				ng = mid;
		}
		return ok + 1;
	}
}

public static class MyIO
{
	private static string[] args = new string[0];
	private static int cnt = 0;
	private static IEnumerable<string> getArgs(long N) => Range(0, N).Select(_ => getArg());
	private static string getArg()
	{
		if(cnt == args.Length) { args = Console.ReadLine().Split(); cnt = 0; }
		return args[cnt++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static decimal GetDecimal() => decimal.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(long N) => getArgs(N).Select(int.Parse).ToArray();
	public static long[] GetLongs(long N) => getArgs(N).Select(long.Parse).ToArray();
	public static double[] GetDoubles(long N) => getArgs(N).Select(double.Parse).ToArray();
	public static decimal[] GetDecimals(long N) => getArgs(N).Select(decimal.Parse).ToArray();
	public static string[] GetStrings(long N) => getArgs(N).ToArray();
}

public static class MyUtil
{
	public static void chmax<T>(ref T x, T y) where T : IComparable<T> { if(x.CompareTo(y) < 0) x = y; }
	public static void chmin<T>(ref T x, T y) where T : IComparable<T> { if(x.CompareTo(y) > 0)	x = y; }
	public static void swap<T>(ref T x, ref T y) { T tmp = x; x = y; y = tmp; }
	public static long rightShift(long x, long y) => (x >> (int)y);
	public static long leftShift(long x, long y) => (x << (int)y);
	public static bool contains(long s, long x) => (rightShift(s, x) & 1L) == 1L;
	public static long gcd(long x, long y) => (y == 0) ? x : gcd(y, x % y);
	public static long lcm(long x, long y) => (x / gcd(x,y)) * y;	
	public static IEnumerable<int> Range(long start, long count) => Enumerable.Range((int)start, (int)count);
	public static void Sort(this List<string> source) => source.Sort(StringComparer.Ordinal);
}


Measured memory_bytes: 117592