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.

Examples

Input

3
1 2 3


Output

1


Input

5
3 11 14 5 13


Output

2
import collections


def run(N, A):
    cnt = 0
    beki = [2**i for i in range(1, 32)]
    A = sorted(A, reverse=True)
    used = collections.Counter(A)
    for a in A:
        if used[a] == 0:
            continue
        used[a] -= 1
        while beki[-1] > 2*a:
            beki.pop(-1)
        if used[beki[-1] - a] >= 1:
            cnt += 1
            used[beki[-1] - a] -= 1
    return cnt


def main():
    N = int(input())
    A = list(map(int, input().split()))
    print(run(N, A))


if __name__ == '__main__':
    main()
