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):
    t = A[k]
    for d in range(1,32):
        if A[0] <= 2**d - t <= A[k]:
            i = bisect.bisect_left(A,2**d-t)
            if A[i] == 2**d-t and k != i:
                ans += 1
                A[k] += 0.01
                A[i] -= 0.01

print(ans)
