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, = map(int, raw_input().split())
A = map(int, raw_input().split())
c = Counter(A)
ks = c.keys()
ks.sort()
r = 0
for i in ks[::-1]:
  for j in xrange(60):
    p = 1<<j
    if i<=p:
      break
  if p==i:
    r += c[i]//2
  else:
    q = p-i
    x = min(c[i], c[q])
    r += x
    c[i] -= x
    c[q] -= x
print r