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 Counter
N,*A = map(int, open(0).read().split())
Cnt = Counter(A)
m = 2**31
ans = 0
for i in range(31):
  for k in Cnt.keys():
    if Cnt[k]==0:
      continue
    if k==m-k:
      ans += Cnt[k]//2
      Cnt[k] %= 2
    else:
      if Cnt[m-k]==0:
        continue
      if Cnt[k]<Cnt[m-k]:
        ans += Cnt[k]
        Cnt[m-k] -= Cnt[k]
        Cnt[k] = 0
      else:
        ans += Cnt[m-k]
        Cnt[k] -= Cnt[m-k]
        Cnt[m-k] = 0
  m >>= 1
print(ans)