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 heapq import heappush, heappop, heapify
from bisect import bisect_right

pow2 = [2]
for i in range(29):
  pow2.append(pow2[-1]*2)

N = int(input())
A = list(map(int, input().split()))
d = {}
for a in A:
  if a in d:
    d[a] += 1
  else:
    d[a] = 1

A = [-a for a in A]
heapify(A)
ans = 0
while A:
  a = - heappop(A)
  if d[a] == 0:
    continue
  pair = pow2[bisect_right(pow2, a)] - a
  if a == pair:
    if d[a] >= 2:
      d[a] -= 2
      ans += 1
  elif pair in d and d[pair] > 0:
    ans += 1
    d[pair] -= 1
    d[a] -= 1

print(ans)