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 inv(x):
    z=1
    while z<=x:
        z<<=1
    return z-x

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

d={}
for x in A:
    if x in d:
        d[x]+=1
    else:
        d[x]=1

l=sorted(d,reverse=True)

ans=0

for x in l:
    if d[x]>0:
        y=inv(x)
        if x==y:            
            ans+=d[x]//2
            d[x]%=2
        elif y in d and d[y]>0:
            ans+=min(d[x],d[y])
            d[x],d[y]=d[x]-min(d[x],d[y]),d[y]-min(d[x],d[y])
            
print(ans)