### BUGGY CODE ###

import sys
import math
from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN
from collections import deque
def I(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def S(): return sys.stdin.readline().rstrip()
def LS(): return sys.stdin.readline().split()
def LS2(N): return [sys.stdin.readline().split() for i in range(N)]
def FILL(i,h): return [i for j in range(h)]
def FILL2(i,h,w): return [FILL(i,w) for j in range(h)]
def FILL3(i,h,w,d): return [FILL2(i,w,d) for j in range(h)]
def FILL4(i,h,w,d,d2): return [FILL3(i,w,d,d2) for j in range(h)]
def sisha(num,digit): return Decimal(str(num)).quantize(Decimal(digit),rounding=ROUND_HALF_UP)
#'0.01'や'1E1'などで指定、整数に戻すならintをかます
MOD = 1000000007
INF = float("inf")
sys.setrecursionlimit(10**5+10)
#input = sys.stdin.readline
from bisect import bisect_left

def dfs(i,before):
    global seq
    global ans
    added  = 0

    #現在地のAの値を、以前までのseqリストのどこに追加するか決める
    pos = bisect_left(seq,a[i-1])
    if len(seq)<= pos:
        seq.append(a[i-1])
        added  = 1
    else:
        old = seq[pos]
        seq[pos]=a[i-1]
    ans[i-1]=len(seq)

    #隣接する頂点に関して再帰
    for u in to[i]:
        if u==before:
            continue
        dfs(u,i)

    #seq配列をもとに戻す
    if added==1:
        seq=seq[:-1]
    else:
        seq[pos]=old


N = I()
a = LI()
to = [[] for i in range(N+1)]
to[0] += [1]
for i in range(N-1):
    u,v = MI()
    to[u].append(v)
    to[v].append(u)
seq = []
ans = [-1]*(N)

dfs(1,-1)
[print(i) for i in ans]


### FIXED CODE ###

import sys
import math
from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN
from collections import deque
def I(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def S(): return sys.stdin.readline().rstrip()
def LS(): return sys.stdin.readline().split()
def LS2(N): return [sys.stdin.readline().split() for i in range(N)]
def FILL(i,h): return [i for j in range(h)]
def FILL2(i,h,w): return [FILL(i,w) for j in range(h)]
def FILL3(i,h,w,d): return [FILL2(i,w,d) for j in range(h)]
def FILL4(i,h,w,d,d2): return [FILL3(i,w,d,d2) for j in range(h)]
def sisha(num,digit): return Decimal(str(num)).quantize(Decimal(digit),rounding=ROUND_HALF_UP)
#'0.01'や'1E1'などで指定、整数に戻すならintをかます
MOD = 1000000007
INF = float("inf")
sys.setrecursionlimit(10**5+10)
#input = sys.stdin.readline
from bisect import bisect_left

def dfs(i,before):
    global seq
    global ans
    added  = 0

    #現在地のAの値を、以前までのseqリストのどこに追加するか決める
    pos = bisect_left(seq,a[i-1])
    old = seq[pos]
    seq[pos]=a[i-1]
    ans[i-1]=bisect_left(seq,INF)

    #隣接する頂点に関して再帰
    for u in to[i]:
        if u==before:
            continue
        dfs(u,i)

    #seq配列をもとに戻す
    seq[pos]=old


N = I()
a = LI()
to = [[] for i in range(N+1)]
to[0] += [1]
for i in range(N-1):
    u,v = MI()
    to[u].append(v)
    to[v].append(u)
seq = [INF]*N
ans = [-1]*N

dfs(1,-1)
[print(i) for i in ans]