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
input()
nbs = map(int, input().split())

answer = 0
count = {}

for nb in nbs:
    count[nb] = count.get(nb, 0) + 1

for nb in sorted(count.keys(), reverse=True):
    searching = (1 << nb.bit_length()) - nb
    nb_count = count[nb]
    sr_count = count.get(searching, 0)
    if sr_count:
        if nb == searching:
            increment = nb_count // 2
        else:
            increment = nb_count if nb_count < sr_count else sr_count
            count[searching] -= increment
        answer += increment

print(answer)