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)

def main():
    N = int(input())
    A = [int(i) for i in input().split()]
    bi = [2**i for i in range(1, 31)]
    from collections import Counter
    ans = 0
    for tar in bi:
        B = [a % tar if a < tar else -1 for a in A]
        c = Counter(B)
        cur = 0
        for k, v in c.items():
            if k == -1:
                continue
            if tar - k in c.keys() and v + c[tar - k] >= 2:
                cur += (v + c[tar - k])//2
        ans = max(ans, cur//2)
    print(ans)


if __name__ == '__main__':
    main()