text: # Time:  O(n!)
  # Space: O(n^2)
  
  import collections
  
  
  class Solution(object):
      def numSquarefulPerms(self, A):
          """
          :type A: List[int]
          :rtype: int
          """
          def dfs(candidate, x, left, count, result):
              count[x] -= 1
              if left == 0:
                  result[0] += 1
              for y in candidate[x]:
                  if count[y]:
                      dfs(candidate, y, left-1, count, result)
              count[x] += 1
  
          count = collections.Counter(A)
          candidate = {i: {j for j in count if int((i+j)**0.5) ** 2 == i+j} 
                             for i in count}
  
          result = [0]
          for x in count:
              dfs(candidate, x, len(A)-1, count, result)
          return result[0]
  