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 log2
import heapq as hq
from collections import Counter
n = int(input())
a = list(map(int,input().split()))
c = Counter(a)
a = [-a[i] for i in range(n)]
hq.heapify(a)
ans = 0
while a:
  x = hq.heappop(a)
  x = -x
  if c[x]>0:
    y = 2**(int(log2(x))+1)
    if x*2 == y:
      ans += c[x]//2
      c[x] = c[x]%2
    else:
      if c[y-x]>0:
        ans += 1
        c[x] -= 1
        c[y-x] -= 1
print(ans)