# Original solution
# -*- coding: utf-8 -*-
import bisect
# import heapq
# import math
# import random
import sys
# from collections import Counter, defaultdict, deque
# from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal
# from functools import lru_cache, reduce
# from itertools import combinations, combinations_with_replacement, product, permutations
# from operator import add, mul, sub

sys.setrecursionlimit(100000)
# input = sys.stdin.buffer.readline
INF = 2**62-1

def read_int():
    return int(input())


def read_int_n():
    return list(map(int, input().split()))


def read_float():
    return float(input())


def read_float_n():
    return list(map(float, input().split()))


def read_str():
    return input().strip()


def read_str_n():
    return list(map(str, input().split()))


def error_print(*args):
    print(*args, file=sys.stderr)


def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap


ans = [-1] * (2*10**5+1)

@mt
def slv(N, A, UV):
    A.insert(0, -1)
    g = [list() for _ in range(0, N+1)]
    for u, v in UV:
        g[u].append(v)
        g[v].append(u)


    def dfs(u, p, dp):
        global ans

        for v in g[u]:
            if v == p:
                continue

            i = bisect.bisect_left(dp, A[v])
            if len(dp) <= i:
                dp.append(A[v])
                ans[v] = len(dp)
                dfs(v, u, dp)
                dp.pop()
            else:
                b = dp[i]
                dp[i] = A[v]
                ans[v] = len(dp)
                dfs(v, u, dp)
                dp[i] = b
    dp = [A[1]]
    dfs(1, 0, dp)

    ans[1] = 1
    for i in range(1, N+1):
        print(ans[i])

    # return ans[:N]


def main():
    N = read_int()
    A = read_int_n()
    UV = [read_int_n() for _ in range(N-1)]
    (slv(N, A, UV))


if __name__ == '__main__':
    main()


# Optimized solution
# -*- coding: utf-8 -*-
import bisect
import sys

sys.setrecursionlimit(100000)
input = sys.stdin.buffer.readline
INF = 2**62-1


def read_int():
    return int(input())


def read_int_n():
    return list(map(int, input().split()))


def read_float():
    return float(input())


def read_float_n():
    return list(map(float, input().split()))


def read_str():
    return input().strip()


def read_str_n():
    return list(map(str, input().split()))


def error_print(*args):
    print(*args, file=sys.stderr)


def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap


ans = [-1] * (2*10**5+1)


@mt
def slv(N, A, UV):
    A.insert(0, -1)
    g = [list() for _ in range(0, N+1)]
    for u, v in UV:
        g[u].append(v)
        g[v].append(u)

    def dfs(u, p, dp):
        global ans

        for v in g[u]:
            if v == p:
                continue

            i = bisect.bisect_left(dp, A[v])
            if len(dp) <= i:
                dp.append(A[v])
                ans[v] = len(dp)
                dfs(v, u, dp)
                dp.pop()
            else:
                b = dp[i]
                dp[i] = A[v]
                ans[v] = len(dp)
                dfs(v, u, dp)
                dp[i] = b
    dp = [A[1]]
    dfs(1, 0, dp)

    ans[1] = 1
    for i in range(1, N+1):
        print(ans[i])

    # return ans[:N]


def main():
    N = read_int()
    A = read_int_n()
    UV = [read_int_n() for _ in range(N-1)]
    (slv(N, A, UV))


if __name__ == '__main__':
    main()