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)

from collections import Counter
import sys
def main():
    input = sys.stdin.readline
    N = int(input())
    A = list(map(int, input().split()))

    ans = 0
    A.sort(reverse=True)
    C = Counter(A)
    for a in A:
        if C[a] == 0: continue
        C[a] -= 1
        p = (1 << a.bit_length()) - a
        if p in C and C[p] > 0:
            ans += 1
            C[p] -= 1
    print(ans)

if __name__ == '__main__':
    main()