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 bisect
 
n = int(input())
a = list(map(int, input().split()))
a.sort()
 
res = 0
for i in range(n - 1 , -1, -1):
    if a[i] == int(a[i]):#判定
        b = 1
        while b <= a[i]:
            b =b*2
 
        j = bisect.bisect_left(a, b - a[i])
        if i > j:
            if b - a[i] == a[j]:
                res += 1
                a[j] = a[j] - 0.5
                a[i] = a[i] + 0.5
print(res)