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 PyPy3 (2.4.0) (judge verdict: Accepted)

n=int(input())
arr=list(map(int,input().split()))
arr=sorted(arr,reverse=True)
dic={}
for val in arr:
  if val not in dic:
    dic[val]=1
  else:
    dic[val]+=1
ans=0
for val in arr:
  for i in range(40):
    if val<2**i:
      persuit=2**i
      break
  if persuit-val==val:
    if val in dic:
      if dic[val]>=2:
        ans+=1
        dic[val]-=2
        if dic[val]==0:
          del dic[val]
      else:
        continue
    else:
      continue
  else:
    if val in dic and persuit-val in dic:
      ans+=1
      dic[val]-=1
      if dic[val]==0:
        del dic[val]
      dic[persuit-val]-=1
      if dic[persuit-val]==0:
        del dic[persuit-val]
    else:
      continue
print(ans)