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
def main():
    N = int(input())
    A = list(map(int, input().split()))
    A.sort(reverse=True)
    retval = 0
    memo = {}
    for a in A:
        pair_created = False
        for i in range(30, 0, -1):
            s = pow(2, i)
            if a < s and (s-a) in memo and memo[s-a]:
                memo[s-a] -= 1
                pair_created = True
                break
        if pair_created:
            retval += 1
            continue
        if a not in memo:
            memo[a] = 0
        memo[a] += 1
    print(retval)


if __name__ == "__main__":
    main()
