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 bisect import bisect_right as br
from collections import Counter
n = int(input())
cnt = Counter(list(map(int, input().split())))
keys = sorted(cnt.keys(), reverse=True)
bs = [2 ** i for i in range(32)]
ans = 0
for k in keys:
  if k in bs:
    while cnt[k] >= 2:
      cnt[k] -= 2
      ans += 1
    continue
  to = bs[br(bs, k)] - k
  while cnt[k] > 0:
    if to in cnt and cnt[to]:
      ans += 1
      cnt[to] -= 1
      cnt[k] -= 1
    else:
      break
print(ans)

