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 collections import defaultdict
import math
N = int(input())
A = [int(x) for x in input().split()]
D = defaultdict(int)
for a in A:
  D[a] += 1
cnt = 0
for a in sorted(D.keys(), reverse=True):
  p = 2 ** math.ceil(math.log(a + 1, 2))
  d = p - a
  if a == d:
    cnt += D[a] // 2
    D[a] %= 2
  else:
    m = min(D[a], D[d])
    cnt += m
    D[a] -= m
    D[d] -= m
print(cnt)