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
import math
import bisect
import collections

N = int(input())
A = list(map(int,input().split()))
C = collections.Counter(A)
A = sorted(list(C.keys()))
#print(C)
#print(A)

ans = 0
for i in range(len(A)-1,-1,-1):
  a = A[i]
  b = (1<<(int(math.log(a,2))+1))-a
  if a == b:
    ans += C[a]//2
    C[a] -= C[a]//2*2
  else:
    r = bisect.bisect_left(A, b)
    if r < i and A[r] == b:
      mn = min(C[a],C[A[r]])
      ans += mn
      C[a] -=  mn
      C[A[r]] -= mn
print(ans)
