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

def twosum(n):
  now = 1
  while n >= now:
    now *= 2
  return now - n
n=int(input())
a=sorted(list(map(int,input().split())))
d = defaultdict(int)
for i in a:
    d[i] += 1
ans = 0
for i in a[::-1]:
    find = twosum(i)
    if d[i] <= 0:
        continue
    d[i] -= 1
    if d[find] <= 0:
        d[i] += 1
    else:
        ans += 1
        d[find] -= 1
print(ans)