Problem:
Score : 600 points

Problem 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.

Constraints

1 \leq N \leq 2\times 10^5

1 \leq A_i \leq 10^9

A_i is an integer.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

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.

Sample Input 1

3
1 2 3

Sample Output 1

1

We can form one pair whose sum of the written numbers is 4 by pairing the first and third balls.
Note that we cannot pair the second ball with itself.

Sample Input 2

5
3 11 14 5 13

Sample Output 2

2

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

from collections import Counter
import math

N=int(input())

A=list(map(int,input().split()))

answer=0
A.sort(reverse=True)

Amax=A[0]
limit=1
while(True):
  if limit>Amax:
    break;
  limit*=2

Acounter=Counter(A)
print(Acounter)

while(limit!=1):
  eraserlist=[]
  for number,count in Acounter.items():
    if limit-number in Acounter.keys():
      if number==limit-number:
        dec=math.floor(Acounter[number]/2)
        Acounter[number]-=dec*2
      else:
        dec=min(Acounter[number],Acounter[limit-number])
        Acounter[number]-=dec
        Acounter[limit-number]-=dec
        if Acounter[limit-number]==0:
          eraserlist.append(limit-number)
      if Acounter[number]==0:
        eraserlist.append(number)
      answer+=dec
    if number>=limit/2:
      eraserlist.append(number)
  for i in range(len(eraserlist)):
    if eraserlist[i] in Acounter.keys():
      Acounter.pop(eraserlist[i])
  limit=int(limit/2)
print(answer)
print(Acounter)