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: n, a, b, c = [int(i) for i in input().split(" ")]
  s = []
  # AB,BC,AC=0
  for i in range(n):
      s.append(input())
      # if s[i]=="AB":
      #     AB+=1
      #
      # elif s[i]=="AC":
      #     AC+=1
      #
      # elif s[i] == "BC":
      #     BC+=1
  
  for str in s:
      if str == "AB":
          if a > b:
              a -= 1
              b += 1
              print("B")
          else:
              b -= 1
              a += 1
              print("A")
      if str == "AC":
          if a > c:
              a -= 1
              c += 1
              print("C")
          else:
              a += 1
              c -= 1
              print("A")
      if str == "BC":
          if b > c:
              b -= 1
              c += 1
              print("C")
          else:
              b += 1
              c -= 1
              print("B")
  
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."}]