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 defaultdict
N, *A = map(int, open(0).read().split())
ans = 0
A.sort()
dic = defaultdict(list)
for i, a in enumerate(A):
  dic[a] += [i]
for i in range(N-1,-1,-1):
  a = A[i]
  if dic[a]==[]:
    continue
  dic[a].pop()
  k = 1
  while k<=a:
    k *= 2
  n = k-a
  if dic[n]!=[]:
    dic[n].pop()
    ans += 1
print(ans)
