output_description: Print N lines. The k-th line, print the length of the longest increasing
  subsequence of the sequence obtained from the shortest path from Vertex 1 to
  Vertex k.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      a_1 a_2 ... a_N
      u_1 v_1
      u_2 v_2
      :
      u_{N-1} v_{N-1}
attempt: # from collections import deque,defaultdict
  printn = lambda x: print(x, end="")
  inn = lambda: int(input())
  inl = lambda: list(map(int, input().split()))
  inm = lambda: map(int, input().split())
  ins = lambda: input().strip()
  DBG = True  # and False
  BIG = 10**18
  R = 10**9 + 7
  # R = 998244353
  
  
  def ddprint(x):
      if DBG:
          print(x)
  
  
  import sys, resource, bisect
  
  
  def setrlim():
      sys.setrecursionlimit(250000)
      soft, hard = resource.getrlimit(resource.RLIMIT_STACK)
      # setrlimit works on ubuntu (and atcoder), but not on WSL
      resource.setrlimit(resource.RLIMIT_STACK, (128 * 1024 * 1024, hard))
  
  
  def dfs(u, j, dp):
      ans[u] = j
      for v in dst[u]:
          if ans[v] >= 0:
              continue
          x = bisect.bisect_left(dp, a[v])
          tmp = dp[x]
          dp[x] = a[v]
          dfs(v, j + (1 if tmp == BIG else 0), dp)
          dp[x] = tmp
  
  
  setrlim()
  n = inn()
  a = inl()
  a[0:0] = [0]
  dst = [{} for i in range(n + 1)]
  for i in range(n - 1):
      u, v = inm()
      dst[u][v] = dst[v][u] = 1
  ans = [-1] * (n + 1)
  dp = [BIG] * (n + 1)
  dp[1] = a[1]
  dfs(1, 1, dp)
  for i in range(1, n + 1):
      print(ans[i])
  
problem_description: Statement
  
  We have a tree with N vertices, whose i-th edge connects Vertex u_i and Vertex
  v_i. Vertex i has an integer a_i written on it. For every integer k from 1
  through N, solve the following problem:
  
    * We will make a sequence by lining up the integers written on the vertices along the shortest path from Vertex 1 to Vertex k, in the order they appear. Find the length of the longest increasing subsequence of this sequence.
  
  Here, the longest increasing subsequence of a sequence A of length L is the
  subsequence A_{i_1} , A_{i_2} , ... , A_{i_M} with the greatest possible value
  of M such that 1 \leq i_1 < i_2 < ... < i_M \leq L and A_{i_1} < A_{i_2} < ...
  < A_{i_M}.
samples: [{"input": "10\n    1 2 5 3 4 6 7 3 2 4\n    1 2\n    2 3\n    3 4\n    4 5\n    3 6\n    6 7\n    1 8\n    8 9\n    9 10", "output": "1\n    2\n    3\n    3\n    4\n    4\n    5\n    2\n    2\n    3\n    \n\nFor example, the sequence A obtained from the shortest path from Vertex 1 to\nVertex 5 is 1,2,5,3,4. Its longest increasing subsequence is A_1, A_2, A_4,\nA_5, with the length of 4."}]