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():
    from bisect import bisect_right as br
    from collections import Counter as ct
    check=[]
    i=1
    while i<=10**10:
        check.append(i)
        i*=2
    n=int(input())
    c=ct(list(map(int,input().split())))
    c_l=sorted(list(c.keys()),reverse=True)
    ans=0
    for i in c_l:
        j=check[br(check,i)]-i
        if i==j:
            ans+=c[i]//2
        else:
            ans+=min(c[i],c[j])
            c[j]-=min(c[i],c[j])
    print(ans)
main()