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())
A=list(map(int, input().split()))

A.sort(reverse=True)
dic={}
for a in A:
    dic[a]=dic.get(a,0)+1

ans=0

for a in A:
    small=(1<<(len(format(a,"b")))) -a
    if small==a:
        if dic[a]>=2:
            dic[a]-=2
            ans+=1
        continue
    if dic.get(a,0)>0 and dic.get(small,0)>0:
        dic[a]-=1
        dic[small]-=1
        ans+=1
print(ans)