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 ans_solve(N, As):
    C = Counter(As)
    ans = 0
    for d in reversed(sorted(As)):
        n = (2 ** d.bit_length()) - d
        if d != n:
            if C[d] > 0 and C.get(n, 0) > 0:
                C[d] -= 1
                C[n] -= 1
                ans += 1
        else:
            ans += C[d]//2
            C[d] = 0
    return ans
 
 
if __name__ == "__main__":
    N = input()
    As = [int(c) for c in input().split()]
    print(ans_solve(N, As))