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: def n0():
      return int(input())
  
  
  def n1():
      return [int(x) for x in input().split()]
  
  
  def n2(n):
      return [int(input()) for _ in range(n)]
  
  
  def n3(n):
      return [tuple([int(x) for x in input().split()]) for _ in range(n)]
  
  
  n = n0()
  a = [0]
  a.extend(n1())
  s = n3(n - 1)
  
  import networkx as nx
  
  G = nx.Graph()
  G.add_edges_from(s)
  
  last_node = [[0, 0, 0] for i in range(0, n + 1)]  # 頂点名、パスの前の頂点、パスの長さ
  for i in range(2, n + 1):
      path = nx.dijkstra_path(G, 1, i)
      last_node[i] = [i, path[-2], len(path)]
  
  last_node.sort(key=lambda x: x[2])
  
  info = {i: [0, 0] for i in range(1, n + 1)}  # 現在の最長列、今までの最長列
  info[1] = [1, 1]
  for line in last_node[2:]:
      now = line[0]
      last = line[1]
      if a[last] < a[now]:
          info[now] = [info[last][0] + 1, max(info[last][0] + 1, info[last][1] + 1)]
      else:
          info[now] = [1, info[last][1]]
  for line in info.values():
      print(line[1])
  
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."}]