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: #AGC030 B - Powers of two
  import collections
  import math
  N=int(input())
  A=list(map(int,input().split()))
  A.sort(reverse=True)
  cnter=collections.Counter(A)
  ans=0
  for a in A:
      inv=2**(int(math.log2(a))+1)
      if cnter[a]==0:
          continue
      if cnter[a]>=2 and a==inv//2:a
          cnter[a]=cnter[a]-2
          ans=ans+1
          continue
      if inv-a in cnter:
          cnter[inv-a]=cnter[inv-a]-1
          ans=ans+1
  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"}]