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 = sorted(list(map(int, input().split())))

ans = 0
for k in range(N-1,1,-1):
    if A[k]==int(A[k]):
        b = 1
        while b <= A[k]:
            b *= 2
        p = bisect.bisect_left(A,b-A[k])
        if p != k and A[p]+A[k] == b:
            ans += 1
            A[k] += 0.9
            A[p] -= 0.9
print(ans)
