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 math import log,floor
from collections import Counter
N = int(input())
A = list(map(int, input().split()))

A.sort(reverse=True)
C = Counter(A)

cnt = 0
last_a = -1
for i in range(N):
  a = A[i]
  if last_a == a:
    continue
  last_a = a
  count_a = C[a]
  if count_a <= 0:
    continue
  b = pow(2,floor(log(a)/log(2))+1) - a
  count_b = C[b]
  if count_b <= 0:
    continue
  i += count_a - 1
  x = min(count_a, count_b) if a != b else count_a // 2
  cnt += x
  C[a] -= x
  C[b] -= x
  
print(cnt)