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
n = int(input())
a = list(map(int,input().split()))

used = collections.Counter(a)
a.sort()
a.reverse()

two = [2]
i = 0
while two[i]*2 <= 2*10**9:
    two.append(two[i]*2)
    i += 1

counter = 0
for i in range(n):
    if used[a[i]] > 0:
        used[a[i]] -= 1
        while two[-1] > 2*a[i]:
            two.pop(-1)

        if used[two[-1]-a[i]] >= 1:
            counter += 1
            used[two[-1]-a[i]] -= 1

print(counter)