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
from collections import Counter

def main():
    N, *A = map(int, open(0).read().split())
    A.sort(reverse=True)
    C = Counter(A)
    ans = 0
    for a in A:
        if C[a] != 0:
            k = (1 << a.bit_length()) - a
            if k in C and C[k] != 0 and not (k == a and C[a] == 1):
                ans += 1
                C[a] -= 1
                C[k] -= 1
    print(ans)

if __name__ == "__main__":
    main()