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 collections

N = input()
A = map(int, raw_input().split())
C = collections.Counter(A)
K = C.keys()
K.sort(reverse=1)
res = 0
for i in K:
    for j in xrange(60):
        p = 2 ** j
        if i <= p:
            break
    if i == p:
      res += C[i] // 2
      C[i] = C[i] // 2 * 2
    else:
      num = min(C[i], C[p - i])
      res += num
      C[i] -= num
      C[p - i] -= num
print res
