output_description: Print the maximum possible number of i such that p_i = i after operations.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N M
      p_1 p_2 .. p_N
      x_1 y_1
      x_2 y_2
      :
      x_M y_M
attempt: import collections
  
  n, m = map(int, input().split())
  p = list(map(int, input().split()))
  base = 0
  basemap = []
  for i in range(n):
      if (i + 1) == p[i]:
          base += 1
          basemap.append(i + 1)
  
  branch = dict()
  for i in range(1, n + 1):
      branch[i] = []
  
  for i in range(m):
      x, y = map(int, input().split())
      branch[x].append(y)
      branch[y].append(x)
  compare = [0 for i in range(n + 1)]
  for i in range(1, n + 1):
      if branch[i] != []:
          compare[i] = 1
  
  arrival = [0 for i in range(n + 1)]
  ans = []
  q = []
  
  ind = 1
  while arrival != compare:
      counter = base
      while not (arrival[ind] == 0 and compare[ind] == 1):
          ind += 1
      q.append(ind)
      arrival[ind] = 1
      section = [q[0]]
      while len(q) > 0:
          next = branch[q[0]]
          for i in range(len(next)):
              if arrival[next[i]] == 0:
                  section.append(next[i])
                  arrival[next[i]] = 1
                  q.append(next[i])
          q.pop(0)
      psec = []
      for i in range(len(section)):
          psec.append(p[section[i] - 1])
      t = section + psec + basemap
      search = collections.Counter(t)
      for i in search:
          if search[i] == 2:
              counter += 1
      ans.append(counter)
  print(max(ans))
  
problem_description: Statement
  
  We have a permutation of the integers from 1 through N, p_1, p_2, .., p_N. We
  also have M pairs of two integers between 1 and N (inclusive), represented as
  (x_1,y_1), (x_2,y_2), .., (x_M,y_M). AtCoDeer the deer is going to perform the
  following operation on p as many times as desired so that the number of i (1 ≤
  i ≤ N) such that p_i = i is maximized:
  
    * Choose j such that 1 ≤ j ≤ M, and swap p_{x_j} and p_{y_j}.
  
  Find the maximum possible number of i such that p_i = i after operations.
samples: [{"input": "5 2\n    5 3 1 4 2\n    1 3\n    5 4", "output": "2\n    \n\nIf we perform the operation by choosing j=1, p becomes `1 3 5 4 2`, which is\noptimal, so the answer is 2.\n\n* * *"}, {"input": "3 2\n    3 2 1\n    1 2\n    2 3", "output": "3\n    \n\nIf we perform the operation by, for example, choosing j=1, j=2, j=1 in this\norder, p becomes `1 2 3`, which is obviously optimal. Note that we may choose\nthe same j any number of times.\n\n* * *"}, {"input": "10 8\n    5 3 6 8 7 10 9 1 2 4\n    3 1\n    4 1\n    5 9\n    2 5\n    6 5\n    3 5\n    8 9\n    7 9", "output": "8\n    \n\n* * *"}, {"input": "5 1\n    1 2 3 4 5\n    1 5", "output": "5\n    \n\nWe do not have to perform the operation."}]