# 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]