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=[int(i) for i in input().split()]
T=[2**i for i in range(1,35)]
table=[True]*N
A.sort()
ans=0
for t in T[::-1]:
  l,r=0,N-1
  while l<r:
    if A[l]+A[r]>t:
      r-=1
    elif A[l]+A[r]==t:
      if table[l] and table[r]:
        ans+=1
        table[l],table[r]=False,False
      if not table[l]:
        l+=1
      if not table[r]:
        r-=1
    elif A[l]+A[r]<t:
      l+=1
print(ans)
        
