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
N = int(input())
As = sorted(map(int, input().split()))

used = [False] * N

ans = 0
for i in range(31, 0, -1):
    power_of_two = 1 << i
    l = 0
    r = N - 1
    while True:
        while l < N and used[l]:
            l += 1
        while r >= 0 and used[r]:
            r -= 1
        if l >= r:
            break

        if As[l] + As[r] == power_of_two:
            used[l] = True
            used[r] = True
            l += 1
            r -= 1
            ans += 1
        elif As[l] + As[r] < power_of_two:
            l += 1
        else:
            r -= 1

print(ans)

