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: Wrong Answer)

n=int(input())
a=list(map(int,input().split()))
al=list(set(a))
a.sort(reverse=1)
al.sort(reverse=1)
calc=lambda a:(1<<a.bit_length())-a
d={i:calc(i) for i in a}
from collections import Counter
c=Counter(a)
ans=0
for i in al:
  if d[i]==i:ans+=c[i]*(c[i]-1)//2
  elif d[i] in c:
    m=min(c[i],c[d[i]])
    c[i]-=m
    c[d[i]]-=m
    ans+=m
print(ans)