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 math
  N=int(input())
  A=list(map(int,input().split()))
  Ae=[]
  Ao=[]
  for i in range(N):
      if A[i]%2==0:
          Ae.append(A[i])
      else:
          Ao.append(A[i])
  if Ao!=[]:
      s=0
      Ao.sort()
      i=1
      while i<=len(Ao):
          a=int(math.log2(Ao[-i]))
          if 2**(a+1)-Ao[-i] in Ao[:-i]:
              s+=1
              Ao.remove(2**(a+1)-Ao[-i])
              i+=1
          else:
              i+=1
  else:
      s=0
  if Ae!=[]
      t=0
      j=1
      Ae.sort()
      while j<=len(Ae):
          b=int(math.log2(Ae[-j]))
          if 2**(a+1)-Ae[-j] in Ae[:-j]:
              s+=1
              Ae.remove(2**(a+1)-Ae[-j])
              j+=1
          else:
              j+=1
  else:
      t=0
  print(s+t)
          
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"}]