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_list = list(map(int, input().split()))
d = defaultdict(int)

for a in a_list:
  d[a] += 1

a_list = reversed(sorted(list(set(a_list))))
c = 0
for a in a_list:
  m = int(math.log(a, 2))
  x = 2 ** (m+1) - a
  if x == a:
    c += d[a] // 2
    d[a] -= d[a] // 2
  else:
    c += min(d[x], d[a])
    d[x] -= min(d[x], d[a])

print(c)
    