output_description: Print the maximum possible number of pairs such that the sum of the integers
  written on each pair of balls is a power of 2.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      A_1 A_2 ... A_N
attempt: import copy
  
  N = int(input())
  A = [int(i) for i in input().split()]
  
  ans = 0
  even = []
  odd = []
  
  for i in range(N):
      if A[i] % 2 == 0:
          even.append(A[i])
      else:
          odd.append(A[i])
  
  even = sorted(even)
  odd = sorted(odd)
  
  even2 = copy.deepcopy(even)
  odd2 = copy.deepcopy(odd)
  
  for i in range(len(even)):
      for j in reversed(range((len(even2)))):
          if i >= j:
              break
          num = even[i] + even2[j]
              ans += 1
              del even2[j]
              break
  
  for i in range(len(odd)):
      for j in reversed(range((len(odd2)))):
          if i >= j:
              break
          num = odd[i] + odd2[j]
          if not (num & (num - 1)):
              ans += 1
              del odd2[j]
              break
  
  print(ans)
problem_description: Statement
  
  Takahashi has N balls with positive integers written on them. The integer
  written on the i-th ball is A_i. He would like to form some number of pairs
  such that the sum of the integers written on each pair of balls is a power of
  2. Note that a ball cannot belong to multiple pairs. Find the maximum possible
  number of pairs that can be formed.
  
  Here, a positive integer is said to be a power of 2 when it can be written as
  2^t using some non-negative integer t.
samples: [{"input": "3\n    1 2 3", "output": "1\n    \n\nWe can form one pair whose sum of the written numbers is 4 by pairing the\nfirst and third balls. Note that we cannot pair the second ball with itself.\n\n* * *"}, {"input": "5\n    3 11 14 5 13", "output": "2"}]