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
import bisect
import collections
def f(n):
  return n.bit_length()
n=int(input())
A=[int(i) for i in input().split()]
D=dict(collections.Counter(A))
C=sorted(list(D.keys()))
ans=0
for i in range(len(C)):
  pair=2**f(C[-(i+1)])-C[-(i+1)]
  k=bisect.bisect_left(C,pair)
  if C[k]==pair:
    if k==len(C)-(i+1):
      ans+=D[pair]//2
      D[pair]%=2
    else:
      aa=min(D[pair],D[C[-(i+1)]])
      ans+=aa
      D[pair]-=aa
      D[C[-(i+1)]]-=aa
print(ans)