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=sorted(A)
from collections import Counter as co
D=co(A)

cnt=0
for i in range(N):
  if D[A[-1-i]]>0:
    D[A[-1-i]]-=1
    d=A[-1-i]
    f=len(bin(d))-2
    e=2**f-d
    if D[e]>0:
      cnt+=1
      D[e]-=1
print(cnt)
