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
def i1():
 return int(input())
def i2():
 return [int(i) for i in input().split()]

n=i1()
a=i2()
from collections import defaultdict
d = defaultdict(int)
for i in a:
 d[i]+=1
a.sort()
import math
f=0
for i in range(n)[::-1]:
 if d[a[i]]>0:
  x=2**(int(math.log2(a[i]))+1)-a[i]
  d[a[i]]-=1
  if d[x]>0:
    d[x]-=1
    f+=1
  else:
    d[a[i]]+=1
print(f)