package main

import (
	"bufio"
	"fmt"
	"io"
	"os"
	"strconv"
)

const mod = 998244353
const facNum = 300001
const INF = 1001001001

//var seen []int

//var graph [][]int
var LIS []int
var dp []int
var cost []int

func dfs(graph [][]int, v int, p int) {
	//seen[v] = 1
	//old := 0
	//index := 0
	i := lowerBound(dp, cost[v-1])
	old := dp[i]
	dp[i] = cost[v-1]
	LIS[v] = i
	if p != -1 {
		LIS[v] = max(i, LIS[p])
	}
	//for i := 0; i < len(dp); i++ {
	//	if cost[v-1] <= dp[i] {
	//		index = i
	//		old = dp[i]
	//		dp[i] = cost[v-1]
	//		LIS[v] = i
	//		if p != -1 {
	//			LIS[v] = max(i, LIS[p])
	//		}
	//		break
	//	}
	//}
	for _, nv := range graph[v] {
		if nv == p {
			continue
		}
		//if seen[nv] == 1 {
		//	continue
		//}
		dfs(graph, nv, v)
	}
	dp[i] = old
}

func main() {
	sc := newScanner(os.Stdin)
	N := sc.i()
	cost = sc.is(N)
	////cost
	//for i := range cost {
	//
	//}
	graph := make([][]int, N+1)
	for i := 0; i < N-1; i++ {
		v, u := sc.i(), sc.i()
		graph[v] = append(graph[v], u)
		graph[u] = append(graph[u], v)
	}
	//seen = make([]int, N+1)
	LIS = make([]int, N+1)
	dp = make([]int, N+1)
	for i := range dp {
		dp[i] = INF
	}
	dp[0] = -INF
	dfs(graph, 1, -1)

	for i := 1; i < N+1; i++ {
		fmt.Println(LIS[i])
	}
}

// fmt.Println("Yes")
// fmt.Println("No")

// I/O
type scanner struct {
	sc *bufio.Scanner
}

func newScanner(input io.Reader) *scanner {
	sc := bufio.NewScanner(input)
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, 1024), int(1e+9))
	return &scanner{sc}
}

func (s *scanner) s() string {
	s.sc.Scan()
	return s.sc.Text()
}

func (s *scanner) i() int {
	i, e := strconv.Atoi(s.s())
	if e != nil {
		panic(e)
	}
	return i
}

func (s *scanner) f() float64 {
	f, e := strconv.ParseFloat(s.s(), 64)
	if e != nil {
		panic(e)
	}
	return f
}

func (s *scanner) bs() []byte {
	return []byte(s.s())
}

func (s *scanner) is(n int) []int {
	res := make([]int, n)
	for i := 0; i < n; i++ {
		res[i] = s.i()
	}
	return res
}

func (s *scanner) fs(n int) []float64 {
	res := make([]float64, n)
	for i := 0; i < n; i++ {
		res[i] = s.f()
	}
	return res
}

//const factorial = new
func Pow(a, n int) int {
	ans := 1
	for n > 0 {
		if (n & 1) == 1 {
			ans = ans * a % mod
		}
		a = a * a % mod
		n = n >> 1
	}
	return ans
}

func Gcd(a, b int) int {
	if a < b {
		return Gcd(b, a)
	}
	for b != 0 {
		a, b = b, a%b
	}
	return a
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}
func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func combination(n, k int, fac, ifac []int) int {
	if n < k || n < 0 {
		return 0
	}
	if k == 0 {
		return 1
	}
	//while n != 0
	ans := ifac[k] * ifac[n-k] % mod
	return ans * fac[n] % mod
}

// 階乗: factorial
// コンビネーションを計算する際に前もって計算しておく
// fac[k] => k! (mod M)
// ifac[k] => k!^(M-2) (mod M)
// n: ex. 2 * 10^5 => 200001
// fac, ifac := factorial()
func factorial() (fac []int, ifac []int) {
	fac = make([]int, facNum)
	fac[0] = 1
	ifac = make([]int, facNum)
	ifac[0] = 1
	for i := 1; i < facNum; i++ {
		fac[i] = fac[i-1] * i % mod
		ifac[i] = ifac[i-1] * Pow(i, mod-2) % mod
	}
	return
}

// vs: sorted slice int value
func lowerBound(vs []int, v int) (index int) {
	n := len(vs) / 2
	m := len(vs)
	for m != n {
		if vs[n] < v {
			n = (m-n+1)/2 + n
			//m = m
		} else {
			m = n
			n = n / 2
		}
	}
	return n
}


Measured memory_bytes: 69984