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
from bisect import bisect_left
from bisect import bisect_right

n = int(input())
a = [int(x) for x in input().split()]
a = sorted(a)

ans = 0
visited = [False]*n

while a:
    s = a.pop()
    if visited.pop():
        continue
    m = 1
    while m <= s:
        m *= 2
    r = bisect_right(a, m-s)
    l = bisect_left(a, m-s)
    for x in range(l, r)[::-1]:
        if not visited[x]:
            visited[x] = True
            ans += 1
            break

print(ans)
