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*
from bisect import*
p=[1]
for _ in range(30):p+=p[-1]*2,
n,*a=map(int,open(0).read().split())
d=Counter(a)
c=0
for i,b in enumerate(sorted(a)[::-1]):
  if d[b]<1:continue
  d[b]-=1
  x=p[bisect(p,b)]-b
  if d[x]:
    d[x]-=1
    c+=1
print(c)